Edhec Family Business

Family business How to apply your MBA learning in your family business? There are a few EDHEC Global MBA participants who decided to study in this program to search for better understanding of business disciplines in order to improve their quality as managers with the main goal of returning to their countries and continue their family business. Family business can be very large, a big example is Walmart that even after 43 years and being the third largest company in the world, the Walton family still owns 48% of the stake. However, most cases of family business still relate to medium or smaller sizes.The good thing about a family business is that it has a strong sense of commitment and honor from the members. Family businesses are more likely to last because there will always be an effort on the part of the family members not to let it die or fade related to their inner values. Brazilian candidate, Andressa Lass Santos provides us with her testimony on her family business case: †Å"The EDHEC MBA program has been helping me gain a broader perspective in relation to several business facets such as leadership, accounting, management, studying the local economy and the industry and how to combine them all in a strategic manner.Every class has been helping me come up with ideas and is making me notice flaws that I had never perceived before, as well as areas where there are room for improvements in my family business. My father started a construction company and asphalt plant 25 years ago in Curitiba, Brazil. He is an engineer and agrees with me that if I gain more management skills it would be very useful for the company, since he has little time to invest in that, and in fact he is beginning to think to step out of the picture and work more as a counselor.As each single class goes by, I learn something new and try to think how to implement in our family business. My ideas arise from the hiring process, motivations of the employees until thinking globally of mac roeconomics and strategically trying to apply how we could possibly expand our business or even find new ideas related to it, such as maybe starting another business or company that could support the construction company. For that reason I will choose the Entrepreneurship track in the MBA program, I believe it is the track that I will most benefit from when thinking about my family business and how we want to expand it. †

Assignment 302

Assignment 302 Candidates name†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. Principles of personal development in adult social care settings Assignment composition Assignment overview In this assignment, you will look at the importance of reflective practice in adult social care. You will explore how reflective practice can improve your development and practice and contribute to the quality of service provision You will also look at the process of planning development, and the importance of feedback and reflect on how your values, belief systems may affect your practice.Tasks There are three tasks to this assignment. A Guidance B Personal development plan (PDP) C Reflecting on learning experiences Task Evidence Learning outcomes covered Task A Guidance 1. 1, 1. 2, 1. 3, 2. 1, 2. 2, 2. 3 Task B Personal development plan (PDP) 3. 1, 3. 2, 3. 3, 3. 4 Task C Reflecting on learning experiences 1. 4 Assignment mark sheet Candidate name†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. Candidate number†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Centre name†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Holistic Community Support Training†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Centre number†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 09368†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ Task Evidence Results A Guidance Passed Y/N B Personal development plan (PDP) Passed Y/N C Reflecting on learning experiences Passed Y/N I can confirm that the evidence listed for this unit is my own work and was carried out under the conditions and context specified in the assessment specification. Candidate signature DateI confirm that the candidate has achieved all the requirements of this unit with the evidence listed and the assessment was conducted under the specified conditions and context, and is valid, authentic, reliable, current and sufficient. Tutor / assessor signature†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Date†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. External verifier signature (where applicable) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ Date†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Tasks Task A Guidance (A)Explain 8 core aspects of your job descriptionIdentify 4 different legislations which underpins the way you are expected to carry out your job and describe how you have performed in accordance to t hose standards 1. 1, 1. 2, 3. 1 You are going to be a mentor for a new social care worker as part of their induction process. Part of your role is to help them prepare for the review after their probation period. Ai Create a guide for the new social care worker about how to reflect on their practice. The guide must include the headings listed with an explanation of each. a) What is reflective practice? b) Why is reflective practice important? ) Give example of how reflective practice has contributed to improving the quality of your service provision. d) How standards can be used to help a social care worker reflect on their practice. 5. 1, 5. 2, 2. 1, 2. 2 Aii You arrange a mentor meeting to feed back to the social care worker. You have comments to make which include both praise and constructive criticism. Write notes to prepare for your meeting. In your notes, explain: a) Why it is important for a social care worker to seek feedback on performance. b) The different ways that people may react to receiving constructive feedback. ) Why it is important for a social care worker to use the feedback to improve their practice. 3. 2, 4. 1, (d) Give example of feedbacks you have received and how you have used it to improve your practice Aiiiidentify one national inquiry into serious failures to protect individuals from abuse. Describe the incident and explain how the recommendations from the inquiry report have changed or improved the way your organisation work Task B Personal development plan (PDP) Bi Design a template for a personal development plan (PDP) that you could use to improve your learning, development and professional practice.For each heading in the template, provide a brief summary describing what should be included. 4. 1 Bii (a) Explain how a PDP can help a social care worker identify improvements in their knowledge, understanding and practice. 5. 1, 5. 3, (b) Give example of how a plan has helped you develop or improve __________________________________ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ BiiiIdentify sources of support for planning and reviewing your development. Explain how this has been beneficial to you 4. 1, 4. 2, 4. 3 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Biv Identify people who can help you develop your knowledge, understanding and practice. Give example of how and when this occured ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Bv Explain how the people identified above can help you appreciate your strengths and areas for development. 4. 1, 4. 2, 4. 3 _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Increasing Number of Overweight Children

Nowadays, the number of children in the obese range is increasing in developed countries. This has led to a rise in the medical fees paid by the government to treat these children. Such medical expenses have reached an alarming rate that a solution is necessary to mitigate this problem. Who should we blame for the children’s health? What some people are maintaining is that the number of fast food outlets has risen dramatically. They argue that food rich in fat is usually prepared in these restaurants such as McDonald’s, KFC, and Burger King.Customers could save their time by eating in these outlets. Instant cooked meals are served within a short time. Furthermore, the food which is high in salt and calories tastes good to most of the children. Finally, they will be addicted to this food. The fast food advertisements shown on the television seem to enhance the appetite of the children. They would eventually persuade to their parents to bring them to the outlets. While th e above example may be true to some extent, some people claim that the role of the parents is the main factor.The quality of people’s lives is improving. To achieve a higher standard of living, the parents have to work from day to night. Therefore, less time is accounted for the health of the children. They may even bring the children to fast food outlets for their staple meals. Some parents may not prepare a balanced meal just because their children reject vegetables. Ultimately, it is a pity that the children have to carry their extra body mass around. In my opinion, if all the fast food outlets could be closed, our younger generation would not suffer from being overweight.

A Critical Asessment of the Boston Matrix and its practical Essay

A Critical Asessment of the Boston Matrix and its practical application in BMW - Essay Example For the critical evaluation of the strategic competitive strengths, weaknesses, opportunities and threats that face the company, the most recent and reliable management and marketing literature will be used in order to provide an overview of the operations of BMW. BMW is a global leader in the luxury car market segment and has attained high brand recognition and customer loyalty due to its superior manufacturing technology that aims at satisfying the premium market with stylish, quality and comfortable cars. The report has identified that the concept of marketing has shifted from the time the BCG model was developed to the current marketing concept that is characterized by customer relationships management and societal marketing. The advancement in car manufacturing technologies, the shifts in consumer preferences and decline in natural resources has provided companies with opportunities for product differentiation, formation of strategic relationships and re-organization of the prod uct portfolio. The strategic audit has revealed that BMW is endowed with high technology, high financial resources and customer loyalty and thus it is possible to overcome the market challenges. The automobile industry is faced with scarcity of raw materials, increased global warming awareness, shifts in consumer preferences towards eco-friendly cars, ... increase in global warming†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.5 4.2. Intense competition in the industry†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..5 4.3. Possible product recalls and lawsuits†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.6 4.4. Scarcity of raw materials †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.6 5.0. Critical evaluation of the Boston Matrix†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦6 5.1. Cash cows†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦7 5.2. Stars †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢ € ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦...7 5.3. Question marks/problem child†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦8 5.4. Dogs†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦8 5.5. Traditional views of marketing †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦...†¦9 5.5. Positive perspective of BCG in modern marketing concept†¦Ã¢â‚¬ ¦..†¦9 5.6. Negative perception of BCG in modern marketing concept†¦.†¦Ã¢â‚¬ ¦11 6.0.Recommendations for the next three years†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. †¦11 6.1. Formation of strategic partnerships†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.11 6.2. Product differentiation †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦12 6.3. Maintain customer relationships†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦...12 7.0. Conclusion†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦12 8.0.Bibliography†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..14

Managerial leadership Assignment Example | Topics and Well Written Essays - 1000 words

Managerial leadership - Assignment Example The movie establishes different characters, playing different social roles and it is upon their intrinsic roles, that the movie presents the theory of social leadership. Trevor McKinney Trevor McKinney, being the main character denotes a social person, who was ready to mingle with anybody in the society as long as he perceived the need to solve a given problem in the person. Trevor lives a disturbed life as his mother is a drunkard while the father is always away, but insinuates psychological torture whenever he goes back to his family. Despite all the mayhem surrounding Trevor’s life, he engaged in a plan to give the society the best of his help following Mr. Simonet’s intervention to help him remit help to the society. In his quest to people in the society, Trevor embarks on shared leadership strategies, whereby he ensures that his subjects derive an environment to portray their initiatives (Graen, & Graen, 2006:45). Trevor portrays the concept of shared purpose by ta rgeting to help the affected individuals who he happens to meet during his life. For instance, he perceives the plight of the homeless man, Jerry as overwhelming and requiring immediate redress. Trevor’s obsession to help the affected individuals emanates from the desire of accountability in rendering long-lasting solutions after having been a victim of antisocial circumstances. Trevor establishes a concept of internal definition of the antisocial effects that the subjects undergo before redemption. He is a victim of similar circumstances and seeks to alleviate them from their current situations. However, Trevor’s devotion aims at ensuring a continuous rate of repossession of the ideas upon his subjects, who will further deliver the attributes other needy people in the society (Crosby, 2005:87). Such an aspect shall ensure continuity in delivering fruitful leadership policies to alleviate the problems of the entire society. Eugene Simonet In the movie, Eugene Simonetâ €™s role inspires his social studies student, Trevor to perceive the need to overcome his social fears, and seek to provide the society with the best alternative solutions to their problems. At such a point, the teacher represented the characteristics of fear and the need to ensure that the society derives earlier resolutions into alleviating prevailing problems before prolonged and imminent scars control their livelihoods (Miller, 2009:69). Arguably, the movie portrays the teacher with possessing facial and neck scars that the people are unable to withstand. However, Simonet reacts positively to the stigma and ensures that he devices knowledgeable approaches that would serve to rescue other individual from being victimized into the same situation (Chrispeels, 2004:58). Simonet expresses the concepts of accountability, partnership, and ownership by expressing his views to Trevor and the need for him to devise an appropriate approach that would serve as remedies to the affected i ndividuals. He solely derives the importance of acquainting individuals with present advantages that would service the prevailing social problems. Therefore, he intrigues into the people’s future lives and understands their mishaps. Therefore, he ascertains that the best correctional approach to alleviate the social discontent would be through

Law 5 Formation of Business Entities; Assignment

Law 5 Formation of Business Entities; - Assignment Example Sole proprietorship is a business formed and controlled by the same person whereby the owner shares all profits and risks in the business (Balotti, 2011). A sole proprietor bears all the liabilities of the business including all debts, violations and losses associated with the business. From my professional experience, some of the advantages of a sole proprietorship include the ease of formation since only a business name and business license is needed to start the business (Emerson, 2009). The sole proprietor enjoys all the profits, decision making and control of the business. A small amount of capital is needed to form the business and tax benefits arise since tax returns are not filled as a separate business but as personal income of the business owner (Emerson, 2009). However, some disadvantages of a sole proprietorship business include the difficulties in securing expansion capital in the capital markets, the lack of continuity after the death or incapacitation of the sole proprietor and the direct responsibility for all debts, losses and business violations of the sole proprietorship business (Balotti, 2011). The second common form of business entity is the partnership. Some types of the partnership include the general partnership and limited partnership. General partnership business is created under common law where two or more people form a business with the sole objective of making a profit. It is created by partnership agreement that outlines the duties and method of sharing profits and losses amongst the partners (Emerson, 2009). Without such agreement, the profits and losses are shared equally amongst the partners. In my own experience, partnership has certain disadvantages since each partner is jointly liable for the wrong actions of the other partners and the business can terminate after the death, bankruptcy or on agreement of the partners (Emerson, 2009). The

The usage of derivative instruments Essay Example | Topics and Well Written Essays - 3000 words

The usage of derivative instruments - Essay Example The paper tells that in the present day context, the degree of competition was observed to be witnessing a significant rise along with the environment of business undergoing a constant alteration. The constant alterations have been giving rise to unforeseen situations that calls for effectual management with respect to the companies as well as banks. Therefore, it can be inferred that in relation to the mentioned context, it becomes important for the business enterprises to effectually manage the unforeseen risks from beforehand. It was identified in this regard that the most widely used financing strategies to overcome the challenges raised by business risks are the use of financial derivatives. Examples of financial derivatives used in the current risk management strategies are options and futures, and forward contracts. Options are defined as â€Å"the right and not the obligation to buy or sell something on a specified date at a specified price†. On the similar context, fu tures and forward contracts are also considered as significant risk management tools that are based on the value of fundamental assets. However, these techniques are subject to various factors such as credit rates, interest rates, currency fluctuations and other financial aspects which should be taken into consideration prior to the execution of this strategy. A derivative has been defined as an agreement that is found to take place among a buyer as well as a seller and gets initiated on the current date with regard to a particular transaction that is expected to be realised on a future date or time. For example, the tr

Physical Inactivity Research Paper Example | Topics and Well Written Essays - 750 words

Physical Inactivity - Research Paper Example This paper reviews the literature available to know more about various consequences of childhood physical inactivity. Millar and Dean (2012), pointed out that â€Å"Obesity is the most significant risk factor for the development of type 2 diabetes in childhood. The main causes of obesity and diabetes in the developed and the developing world include a lack of adequate physical activity (Millar and Dean, 2012). The intrusion of internet, computers and mobile phones, forced children to shift their attention from painful physical activities to less painful mental activities. From the above data, it is evident that girls are undergoing severe harassments both in the family and in other social circles because of overweight. Such harassments can affect the development of self-esteem among children. â€Å"According to the WHO, the regional differences in overweight and obesity could be explained by a number of factors including differences in socioeconomic status and the availability and preferences of food and leisure-time physical activities† (Malkogeorgos, 2010, p.137). Different countries have different overweight statistics among teenage community. This is because of the differences in life styles and eating habits in different countries. It should be noted that underweight is the problem among children in some of the poor African countries whereas in American and European countries children are suffered because of overweight. It is evident from the figure that only 7% of the available 39% of other than classroom hours is used for physical workouts. TV watching and reading take 26% of the available 39% of leisure time. All these facts clearly show that modern children are using negligible time for physical workouts and the percentage of physical inactivity time is more than the desired level. Adegoke and Oyeyemi (2011) mentioned the consequences associated with physical inactivity. In their opinion, â€Å"Physical inactivity is

Group Minds Essay Example | Topics and Well Written Essays - 250 words

Group Minds - Essay Example However, the fact of life is that all individuals live their life in a group. There are very few people who appreciate to live a solitary life as numerous cannot stand solitude for long. Majority of the people are group animals, even if they fail to recognize it and this is what creates problem i.e. the failure to understand the social law that governs the group and thus that governs us. It is undeniable that the ideas and opinion of an individual belonging to a certain group is influenced by the opinion of that group. It is a tough task to maintain individuality against group opinion. Psychologist and sociologists have carried out various experiments to exhibit that usually the individuals are influenced by the opinion of the group and give up their opinion because the opinion of the majority in-group does not agree with them. People who have experienced this scenario agree that it is a shameful memory of theirs that they gave up their opinion under the influence of the group. It is important to realize this and various other mechanisms of human behavior so that in future we just do not limit our self to collection of information about ourselves but use it to improve our life and situation and free people from blind loyalties and obedience (Lessing,

Writing prompts for middle school Essay Example for Free

Writing prompts for middle school Essay Imagine that you could give advice to someone—it could be someone you know personally, a historical figure, or a famous pers on living today. Write an essay that identifies the person and the advice you would give. Choose a fam iliar subject so that you can provide details and elaboration that explain why this person needs your advice. 2. In an essay, explain how disappointments can have a good side. 3. Write an essay explaining why someone you care about is important to you. 4. Dress for success is a phrase all of us have heard before, but it means something different to each person. Write an essay explaining  what dress for success means to you. 5. Write an essay to explain why honesty is important in a friendship. 6. Through the years new inventions have changed th e way we live. Think about one invention that has had an impact on the way you live. Now write to explain to your teacher how this invention has changed your life. 7. Write an essay explaining how you changed when you entered middle school. 8. The amount of graffiti has greatly increased at your school. The members of the school board must find ways to stop the graffiti. Write a com position in which you fully explain the solution  the school board could use to solve this problem. 9. There are both good things and bad things about playing on a team, such as the school soccer team or the school volleyball team. Write a composition for your teacher in which you explain both what is good and what is ba d about playing on a school team. Be sure to explain each point fully. 10. A role model is a person you look up to. Befo re you begin writing, think about someone you look up to. Why do you admire this person? Write a composition in which you explain to your classmates whom you admire and why you admire this person. Middle School Persuasive Prompts  1. NEW A wealthy donor plans to build a new facility that will benefit young people in your area. It could be a swimming pool, a theater, a skateboard park, an art school, or any other facility that would provide young people with constructive ways to spend their time. The donor is not sure what kind of facility would be most useful. Write a letter to the donor in which you identify the type of facility you would like to have built, and pe rsuade her that it is the best choice. Be sure to support your opinion with convincing reasons and evidence. 2. Your principal wants to invite a celebrity speaker to your school. Think about the celebrity you would choose to have speak; then, write a letter to persuade your principal to invite this person. Be sure to include convincing reasons and details to support your choice. 3. Girls and boys often enjoy playing the same sport. Some people believe that girls and boys should be able to play on the same team. What is your opinion on this issue? Write an essay stating your opinion and supporting it with convincing reasons. Be sure to explain your reasons in detail. 4. It has been said that television has little real educational value. What is your opinion on this issue? Write an essay stating your opinion and su  pporting it with convincin g reasons. Be sure to explain your reasons in detail. 5. The principal of your school is considering co nducting random locker searches several times a year without letting students know in advance. What is your position concerning this issue? Write a letter to the principal stating your position and supporting it with convincin g reasons. Be sure to explain your reasons in detail. 6. Suppose Congress wants to make a new national ho liday honoring an important person or event. Choose a person or event you would like to honor. Write an essay to convince members of Congress to accept your choice. 7. Your principal has asked students to suggest a school rule that should be changed. Think of one rule that you would like to have changed. Write a letter convincing your principal that this rule should be changed. Be sure to support your opinion with convi ncing reasons and evidence. 8. Your school principal is considering a new policy that will require all students to wear uniforms. What is your position concerning this issue? Write a letter to your principal stating your position and supporting it with convincing reasons. Be sure to explain your reasons in detail. Middle School How-To Prompts 1. Write a composition in which you explain how to make something. You might write about a food item, a handcrafted item, or anything else that you know how to make. Be sure to clearly explain each step in the process so that a read er could make the item the way you do. 2. Think about one favorite activity that you enjoy. For example, it could be playing a favorite sport or participating in a hobby. Write a compos ition in which you tell a friend how to do your favorite activity. Be sure to include all the details your friend will need to do the activity. Middle School Descriptive Prompts 1. Think about the last time you attended a special even  t such as a concert, a fair, or a sports event. Describe what it was like to be there and include sights, sounds, and smells that will make the reader feel he or she is there with you. 2. Think of a favorite object that you own. In a descriptive essay, use sensory details—words that tell how something looks, feels, tastes, smells , and sounds—to clearly describe this favorite object so that a classmate could picture it. 3. Think of what your school is like at lunchtime. Pick one particular place, and picture it in your mind. This place could be large or small. In a co mposition, describe clearly to a friend what the  place is like at lunchtime so your friend can imagine what it is like to be there. Middle School Narrative Prompts 1. Eleanor Roosevelt once said, You must do the th ing you think you cannot do. Write a narrative about a time when you did something you thought you could not do. Be sure to include specific details so that a reader can follow your story. 2. Think about a time when something unexpected happened. Write a narrative in which you tell about an unexpected event that happened to you or someone you know. Be sure to include specific details so that a reader can follow your story. 3. You have made a very important discovery–one th  at will make you famous throughout the world. Write a story in which you tell about your discove ry and how you made it. Be sure to include details about the setting and any characters in th e story, and be sure that your story has a beginning, a middle, and an end. 4. Think of your best day in school. What happened that makes this day stand out in your memory? Write a story for a friend that tells about what happened on this day in school. Middle School Writing About Literature Prompts 1. Under the Rice Moon tells a story about a caged bird and a sickly young girl who understand one another. Read the story. Then write an essay discussing the storys theme, or message, and how the author uses the bird and the storys characters to express the message. Be sure to include examples and details from the story to support your ideas. Do not merely summarize the story. Remember that your response will be evaluated in two ways—on your understanding of the story and on the quality of our writing. 2. The Dinner Party tells a story about a social gathering in India. Read the story. Then write an essay in which you discuss how the author uses the characters in the story to express a message. Support your ideas with examples and details from the story. Do not merely summarize the story. Remember that your response will be evaluated in two ways–on your understanding of the story and on the quality of your writing. Middle School Writing About Nonfiction Prompts 1. Read Heeding the Call. Then, write an essay explaining how Martin Luther King, Jr. s experiences as a young person shaped his beliefs and actions as an adult. Be sure to include specific information from the article to support your explanation. Do not merely summarize the article. Remember that your response will be ev aluated in two ways—on  your understanding of the article and on the quality of your writing. 2. Read But Im Not Tired! Think about the ideas th e author presents in this article. What changes should schools make to adjust to students sl eep patterns? Write a letter to the principal recommending changes that could be made at your sch ool to adjust to students sleep patterns. Be sure to include specific information from the ar ticle to support your recommendations. Do not merely summarize the article. Re member that your response will be evaluated in two ways–on your understanding of the article and on the quality of your writing.

Hopf Algebra Project

Hopf Algebra Project Petros Karayiannis Chapter 0 Introduction Hopf algebras have lot of applications. At first, they used it in topology in 1940s, but then they realized it has applications through combinatorics, category theory, Hopf-Galois theory, quantum theory, Lie algebras, Homological algebra and functional analysis. The purpose of this project is to see the definitions and properties of Hopf algebras.(Becca 2014) Preliminaries This chapter provides all the essential tools to understand the structure of Hopf algebras. Basic notations of Hopf algebra are: Groups Fields Vector spaces Homomorphism Commutative diagrams 1.Groups Group G is a finite or infinite set of elements with a binary operation. Groups have to obey some rules, so we can define it as a group. Those are: closure, associative, there exist an identity element and an inverse element. Let us define two elements U, V in G, closure is when then the product of UV is also in G. Associative when the multiplication (UV) W=U (VW) à ªÃ¢â‚¬Å" ¯ U, V, W in G. There exist an identity element such that IU=UI=U for every element U in G. The inverse is when for each element U of G, the set contains an element V=U-1 such that UU-1=U-1U=I. 2.Fields A field Ã’Å“ is a commutative ring and every element b à Ã‚ µ Ã’Å“ has an inverse. 3.Vector Space A vector space V is a set that is closed under finite vector addition and scalar multiplication. In order for V to be a vector space, the following conditions must hold à ªÃ¢â‚¬Å" ¯ X, Y à Ã‚ µ V and any scalar a, b à Ã‚ µ Ã’Å“: a(b X) = (a b) X (a + b) X=aX + bX a(X+Y)=aX + aY 1X=X A left ideal of K-algebra is a linear subspace that has the property that any element of the subspace multiplied on the left by any element of the algebra produces an element of the subspace. We say that a subset L of a K-algebra A is a left ideal if for every x and y in L, z in A and c in K, we have the following: X +y is in L cx is in L zà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ x is in L If we replace c) with xà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ z is in L, then this would define a right ideal. A two-sided ideal is a subset that is both a left and a right ideal. When the algebra is commutative, then all of those notions of ideal are equivalent. We denote the left ideal as à ¢Ã…  Ã‚ ³. 4.Homomorphism Given two groups, (G,*) and (H, °) is a function f: Gà ¢Ã¢â‚¬  Ã¢â‚¬â„¢H such that à ªÃ¢â‚¬Å" ¯ u, v à Ã‚ µ G it holds that f(u*v)=f(u) °f(v) 5.Commutative diagrams A commutative diagram is showing the composition of maps represented by arrows. The fundament operation of Hopf algebras is the tensor product. A tensor product is a multiplication of vector spaces V and W with a result a single vector space, denoted as V    W. Definition 0.1 Let V and W be Ã’Å“-vector spaces with bases {ei } and {fj } respectively. The tensor product V and W is a new Ã’Å“-vector space,  Ãƒâ€šÃ‚   V      W with basis { ei fj }, is the set of all elements v    w= à ¢Ã‹â€ Ã¢â‚¬Ëœ (ci,j ei    fj ). ci,j à Ã‚ µÃƒâ€™Ã…“ are scalars. Also tensor products obey to distributive and scalar multiplication laws. The dimension of the tensor product of two vector spaces is: Dim(V   W)=dim(V)dim(W) Theorem of Universal Property of Tensor products 0.2 Let V, W, U be vector spaces with map f: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ U is defined as f: (v, w) à ¢Ã¢â‚¬  Ã¢â‚¬â„¢vw. There exists a bilinear mapping b: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ V   W , (v,w) à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ v   Ãƒâ€šÃ‚   w If f: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ U is bilinear, then there exist a unique function, f: V   Wà ¢Ã¢â‚¬  Ã¢â‚¬â„¢U with f=f °b   Extension of Tensor Products0.3 The definition of Tensor products can be extended for more than two vectors such as; V1 à ¢Ã…  -   V2à ¢Ã…  -  Ãƒâ€šÃ‚   V3 à ¢Ã…  -   à ¢Ã¢â€š ¬Ã‚ ¦..à ¢Ã…  -   VN = à ¢Ã‹â€ Ã¢â‚¬Ëœ( biv1à ¢Ã…  -   v2à ¢Ã…  -   à ¢Ã¢â€š ¬Ã‚ ¦.à ¢Ã…  -   vn )   (Becca 2014) Definition0.4 Let U,V be vector spacers over a field k and ÃŽÂ ½ à Ã‚ µ Uà ¢Ã‚ ¨Ã¢â‚¬Å¡V. If ÃŽÂ ½=0 then Rank (ÃŽÂ ½) =0. If ÃŽÂ ½Ãƒ ¢Ã¢â‚¬ °Ã‚  0 then rank (ÃŽÂ ½) is equal to the smallest positive integer r arising from the representations of ÃŽÂ ½= à ¢Ã‹â€ Ã¢â‚¬Ëœui à ¢Ã‚ ¨Ã¢â‚¬Å¡ vi à Ã‚ µUà ¢Ã‚ ¨Ã¢â‚¬Å¡V for i=1,2,à ¢Ã¢â€š ¬Ã‚ ¦,r. Definition0.5 Let U be a finite dimensional vector space over the field k with basis {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un}   be a basis for U. the dual basis for U*is {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un} where ui(uj)= ÃŽÂ ´ij for 1à ¢Ã¢â‚¬ °Ã‚ ¤I,jà ¢Ã¢â‚¬ °Ã‚ ¤n. Dual Pair0.6 A dual pair is a 3 -tuple (X,Y,) consisting two vector spaces X,Y over the same field K and a bilinear map, : X x Yà ¢Ã¢â‚¬  Ã¢â‚¬â„¢K with à ªÃ¢â‚¬Å" ¯x à Ã‚ µ X{0} yà Ã‚ µY: 0 and à ªÃ¢â‚¬Å" ¯y à Ã‚ µ Y{0} xà Ã‚ µX: 0 Definition0.7 The wedge product is the product in an exterior algebra. If ÃŽÂ ±, ÃŽÂ ² are differential k-forms of degree p, g respectively, then   ÃƒÅ½Ã‚ ±Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ²=(-1)pq ÃŽÂ ²Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ±, is not in general commutative, but is associative, (ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ²)à ¢Ã‹â€ Ã‚ §u= ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §(ÃŽÂ ²Ãƒ ¢Ã‹â€ Ã‚ §u) and bilinear (c1 ÃŽÂ ±1+c2 ÃŽÂ ±2)à ¢Ã‹â€ Ã‚ § ÃŽÂ ²= c1( ÃŽÂ ±1à ¢Ã‹â€ Ã‚ § ÃŽÂ ²) + c2( ÃŽÂ ±2à ¢Ã‹â€ Ã‚ § ÃŽÂ ²) ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §( c1 ÃŽÂ ²1+c2 ÃŽÂ ²2)= c1( ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ § ÃŽÂ ²1) + c2( ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ § ÃŽÂ ²2).  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Becca 2014) Chapter 1 Definition1.1 Let (A, m, ÃŽÂ ·) be an algebra over k and write mop (ab) = ab à ªÃ¢â‚¬Å" ¯ a, bà Ã‚ µ A where mop=mà Ã¢â‚¬Å¾ÃƒÅ½Ã¢â‚¬Ëœ,Α. Thus ab=ba à ªÃ¢â‚¬Å" ¯a, b à Ã‚ µA. The (A, mop, ÃŽÂ ·) is the opposite algebra. Definition1.2 A co-algebra C is A vector space over K A map Ά: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢C à ¢Ã…  -   C which is coassociative in the sense of à ¢Ã‹â€ Ã¢â‚¬Ëœ (c(1)(1) à ¢Ã…  -  Ãƒâ€šÃ‚   c(1)(2) à ¢Ã…  -   c(2))= à ¢Ã‹â€ Ã¢â‚¬Ëœ (c(1) à ¢Ã…  -  Ãƒâ€šÃ‚   c(2)(1) à ¢Ã…  -   c(2)c(2) )  Ãƒâ€šÃ‚   à ªÃ¢â‚¬Å" ¯ cà Ã‚ µC (Ά called the co-product) A map ÃŽÂ µ: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k obeying à ¢Ã‹â€ Ã¢â‚¬Ëœ[ÃŽÂ µ((c(1))c(2))]=c= à ¢Ã‹â€ Ã¢â‚¬Ëœ[(c(1)) ÃŽÂ µc(2))] à ªÃ¢â‚¬Å" ¯ cà Ã‚ µC ( ÃŽÂ µ called the counit) Co-associativity and co-unit element can be expressed as commutative diagrams as follow: Figure 1: Co-associativity map Ά Figure 2: co-unit element map ÃŽÂ µ Definition1.3 A bi-algebra H is An algebra (H, m ,ÃŽÂ ·) A co-algebra (H, Ά, ÃŽÂ µ) Ά,ÃŽÂ µ are algebra maps, where Hà ¢Ã…  -   H has the tensor product algebra structure (hà ¢Ã…  - g)(hà ¢Ã…  -   g)= hhà ¢Ã…  -  Ãƒâ€šÃ‚   gg à ªÃ¢â‚¬Å" ¯h, h, g, g à Ã‚ µH. A representation of Hopf algebras as diagrams is the following: Definition1.4 A Hopf Algebra H is A bi-algebra H, Ά, ÃŽÂ µ, m, ÃŽÂ · A map S : Hà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ H such that à ¢Ã‹â€ Ã¢â‚¬Ëœ [(Sh(1))h(2) ]= ÃŽÂ µ(h)= à ¢Ã‹â€ Ã¢â‚¬Ëœ [h(1)Sh(2) ]à ªÃ¢â‚¬Å" ¯ hà Ã‚ µH The axioms that make a simultaneous algebra and co-algebra into Hopf algebra is à Ã¢â‚¬Å¾:   Hà ¢Ã…  - Hà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Hà ¢Ã…  -H Is the map à Ã¢â‚¬Å¾(hà ¢Ã…  -g)=gà ¢Ã…  -h called the flip map à ªÃ¢â‚¬Å" ¯ h, g à Ã‚ µ H. Definition1.5 Hopf Algebra is commutative if its commutative as algebra. It is co-commutative if its co-commutative as a co-algebra, à Ã¢â‚¬Å¾ÃƒÅ½Ã¢â‚¬ =Ά. It can be defined as S2=id. A commutative algebra over K is an algebra (A, m, ÃŽÂ ·) over k such that m=mop. Definition1.6 Two Hopf algebras H,H are dually paired by a map : H H à ¢Ã¢â‚¬  Ã¢â‚¬â„¢k if, =à Ã‹â€ ,Άh>, =ÃŽÂ µ(h) g   >=, ÃŽÂ µ(à Ã¢â‚¬  )= = à ªÃ¢â‚¬Å" ¯ à Ã¢â‚¬  , à Ã‹â€ Ãƒ Ã‚ µ H and h, g à Ã‚ µH. Let (C, Ά,ÃŽÂ µ) be a co-algebra over k. The co-algebra (C, Άcop, ÃŽÂ µ) is the opposite co-algebra. A co-commutative co-algebra over k is a co-algebra (C, Ά, ÃŽÂ µ) over k such that Ά= Άcop. Definition1.7 A bi-algebra or Hopf algebra H acts on algebra A (called H-module algebra) if: H acts on A as a vector space. The product map m: AAà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A commutes with the action of H The unit map ÃŽÂ ·: kà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ A commutes with the action of H. From b,c we come to the next action hà ¢Ã…  Ã‚ ³(ab)=à ¢Ã‹â€ Ã¢â‚¬Ëœ(h(1)à ¢Ã…  Ã‚ ³a)(h(2)à ¢Ã…  Ã‚ ³b), hà ¢Ã…  Ã‚ ³1= ÃŽÂ µ(h)1, à ªÃ¢â‚¬Å" ¯a, b à Ã‚ µ A, h à Ã‚ µ H This is the left action. Definition1.8 Let (A, m, ÃŽÂ ·) be algebra over k and is a left H- module along with a linear map m: Aà ¢Ã…  -Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A and a scalar multiplication ÃŽÂ ·: k à ¢Ã…  - Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A if the following diagrams commute. Figure 3: Left Module map Definition1.9 Co-algebra (C, Ά, ÃŽÂ µ) is H-module co-algebra if: C is an H-module Ά: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢CC and ÃŽÂ µ: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k commutes with the action of H. (Is a right C- co-module). Explicitly, Ά(hà ¢Ã…  Ã‚ ³c)=à ¢Ã‹â€ Ã¢â‚¬Ëœh(1)à ¢Ã…  Ã‚ ³c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡h(2)à ¢Ã…  Ã‚ ³c(2), ÃŽÂ µ(hà ¢Ã…  Ã‚ ³c)= ÃŽÂ µ(h)ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯h à Ã‚ µ H, c à Ã‚ µ C.   Definition1.10 A co-action of a co-algebra C on a vector space V is a map ÃŽÂ ²: Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V such that, (idà ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ²) à ¢Ã‹â€ Ã‹Å"ÃŽÂ ²=(ΆÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ id )ÃŽÂ ²;   id =(ÃŽÂ µÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡id )à ¢Ã‹â€ Ã‹Å"ÃŽÂ ². Definition1.11 A bi-algebra or Hopf algebra H co-acts on an algebra A (an H- co-module algebra) if: A is an H- co-module The co-action ÃŽÂ ²: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is an algebra homomorphism, where Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A has the tensor product algebra structure. Definition1.12 Let C be co- algebra (C, Ά, ÃŽÂ µ), map ÃŽÂ ²: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is a right C- co- module if the following diagrams commute. Figure 6:Co-algebra of a right co-module Sub-algebras, left ideals and right ideals of algebra have dual counter-parts in co-algebras. Let (A, m, ÃŽÂ ·) be algebra over k and suppose that V is a left ideal of A. Then m(Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V)à ¢Ã…  Ã¢â‚¬  V. Thus the restriction of m to Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V determines a map Aà ¢Ã‚ ¨Ã¢â‚¬Å¡Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢V. Left co-ideal of a co-algebra C is a subspace V of C such that the co-product Ά restricts to a map Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V. Definition1.13 Let V be a subspace of a co-algebra C over k. Then V is a sub-co-algebra of C if Ά(V)à ¢Ã…  Ã¢â‚¬  Và ¢Ã‚ ¨Ã¢â‚¬Å¡V, for left co-ideal Ά(V)à ¢Ã…  Ã¢â‚¬  Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V and for right co-ideal Ά(V)à ¢Ã…  Ã¢â‚¬  Và ¢Ã‚ ¨Ã¢â‚¬Å¡C. Definition1.14 Let V be a subspace of a co-algebra C over k. The unique minimal sub-co-algebra of C which contains V is the sub-co-algebra of C generated by V. Definition1.15 A simple co-algebra is a co-algebra which has two sub-co-algebras. Definition1.16 Let C be co-algebra over k. A group-like element of C is c à Ã‚ µC with satisfies, Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s   and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à Ã‚ µS. The set of group-like elements of C is denoted G(C). Definition1.17 Let S be a set. The co-algebra k[S] has a co-algebra structure determined by Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s   and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à Ã‚ µS. If S=à ¢Ã‹â€ Ã¢â‚¬ ¦ we set C=k[à ¢Ã‹â€ Ã¢â‚¬ ¦]=0. Is the group-like co-algebra of S over k. Definition1.18 The co-algebra C over k with basis {co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦..} whose co-product and co-unit is satisfy by Ά(cn)= à ¢Ã‹â€ Ã¢â‚¬Ëœcn-là ¢Ã‚ ¨Ã¢â‚¬Å¡cl and ÃŽÂ µ(cn)=ÃŽÂ ´n,0 for l=1,à ¢Ã¢â€š ¬Ã‚ ¦.,n and for all nà ¢Ã¢â‚¬ °Ã‚ ¥0. Is denoted by Pà ¢Ã‹â€ Ã… ¾(k). The sub-co-algebra which is the span of co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦,cn is denoted Pn(k). Definition1.19 A co-matrix co-algebra over k is a co-algebra over k isomorphic to Cs(k) for some finite set S. The co-matrix identities are: Ά(ei, j)= à ¢Ã‹â€ Ã¢â‚¬Ëœei, là ¢Ã‚ ¨Ã¢â‚¬Å¡el, j ÃŽÂ µ(ei, j)=ÃŽÂ ´i, j à ¢Ã‹â€ Ã¢â€š ¬ i, j à Ã‚ µS. Set Cà ¢Ã‹â€ Ã¢â‚¬ ¦(k)=(0). Definition1.20 Let S be a non-empty finite set. A standard basis for Cs(k) is a basis {c i ,j}I, j à Ã‚ µS for Cs(k) which satisfies the co-matrix identities. Definition1.21 Let (C, Άc, ÃŽÂ µc) and (D, ΆD, ÃŽÂ µD) be co-algebras over the field k. A co-algebra map f: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢D is a linear map of underlying vector spaces such that ΆDà ¢Ã‹â€ Ã‹Å"f=(fà ¢Ã‚ ¨Ã¢â‚¬Å¡f)à ¢Ã‹â€ Ã‹Å" Άc and ÃŽÂ µDà ¢Ã‹â€ Ã‹Å"f= ÃŽÂ µc. An isomorphism of co-algebras is a co-algebra map which is a linear isomorphism. Definition1.22 Let C be co-algebra over the field k. A co-ideal of C is a subspace I of C such that ÃŽÂ µ (I) = (0) and Ά (ÃŽâ„ ¢) à ¢Ã…  Ã¢â‚¬   Ià ¢Ã‚ ¨Ã¢â‚¬Å¡C+Cà ¢Ã‚ ¨Ã¢â‚¬Å¡I. Definition1.23 The co-ideal Ker (ÃŽÂ µ) of a co-algebra C over k is denoted by C+. Definition1.24 Let I be a co-ideal of co-algebra C over k. The unique co-algebra structure on C /I such that the projection à Ã¢â€š ¬: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ C/I is a co-algebra map, is the quotient co-algebra structure on C/I. Definition1.25 The tensor product of co-algebra has a natural co-algebra structure as the tensor product of vector space Cà ¢Ã…  -D is a co-algebra over k where Ά(c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(1))à ¢Ã‚ ¨Ã¢â‚¬Å¡( c(2)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(2)) and ÃŽÂ µ(cà ¢Ã‚ ¨Ã¢â‚¬Å¡d)=ÃŽÂ µ(c)ÃŽÂ µ(d) à ¢Ã‹â€ Ã¢â€š ¬ c in C and d in D. Definition1.26 Let C be co-algebra over k. A skew-primitive element of C is a cà Ã‚ µC which satisfies Ά(c)= gà ¢Ã‚ ¨Ã¢â‚¬Å¡c +cà ¢Ã‚ ¨Ã¢â‚¬Å¡h, where c, h à Ã‚ µG(c). The set of g:h-skew primitive elements of C is denoted   by Pg,h (C). Definition1.27 Let C be co-algebra over a field k. A co-commutative element of C is cà Ã‚ µC such that Ά(c) = Άcop(c). The set of co-commutative elements of C is denoted by Cc(C). Cc(C) à ¢Ã…  Ã¢â‚¬  C. Definition1.28 The category whose objects are co-algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Coalg. Definition1.29 The category whose objects are algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Alg. Definition1.30 Let (C, Ά, ÃŽÂ µ) be co-algebra over k. The algebra (Cà ¢Ã‹â€ -, m, ÃŽÂ ·) where m= ΆÃƒ ¢Ã‹â€ -| Cà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Cà ¢Ã‹â€ -, ÃŽÂ · (1) =ÃŽÂ µ, is the dual algebra of (C, Ά, ÃŽÂ µ). Definition1.31 Let A be algebra over the field k. A locally finite A-module is an A-module M whose finitely generated sub-modules are finite-dimensional. The left and right Cà ¢Ã‹â€ --module actions on C are locally finite. Definition1.32 Let A be algebra over the field k. A derivation of A is a linear endomorphism F of A such that F (ab) =F (a) b-aF(b) for all a, b à Ã‚ µA. For fixed b à Ã‚ µA note that F: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A defined by F(a)=[a, b]= ab- ba   for all a à Ã‚ µA is a derivation of A. Definition1.33 Let C be co-algebra over the field k. A co-derivation of C is a linear endomorphism f of C such that ΆÃƒ ¢Ã‹â€ Ã‹Å"f= (fà ¢Ã‚ ¨Ã¢â‚¬Å¡IC + IC à ¢Ã‚ ¨Ã¢â‚¬Å¡f) à ¢Ã‹â€ Ã‹Å"Ά. Definition1.34 Let A and B ne algebra over the field k. The tensor product algebra structure on Aà ¢Ã‚ ¨Ã¢â‚¬Å¡B is determined by (aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)(aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)= aaà ¢Ã‚ ¨Ã¢â‚¬Å¡bb à ªÃ¢â‚¬Å" ¯ a, aà Ã‚ µA and b, bà Ã‚ µB. Definition1.35 Let X, Y be non-empty subsets of an algebra A over the field k. The centralizer of Y in X is ZX(Y) = {xà Ã‚ µX|yx=xy à ªÃ¢â‚¬Å" ¯yà Ã‚ µY} For y à Ã‚ µA the centralizer of y in X is ZX(y) = ZX({y}). Definition1.36 The centre of an algebra A over the field Z (A) = ZA(A). Definition1.37 Let (S, à ¢Ã¢â‚¬ °Ã‚ ¤) be a partially ordered set which is locally finite, meaning that à ªÃ¢â‚¬Å" ¯, I, jà Ã‚ µS which satisfy ià ¢Ã¢â‚¬ °Ã‚ ¤j the interval [i, j] = {là Ã‚ µS|ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j} is a finite set. Let S= {[i, j] |I, jà Ã‚ µS, ià ¢Ã¢â‚¬ °Ã‚ ¤j} and let A be the algebra which is the vector space of functions f: Sà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k under point wise operations whose product is given by (fà ¢Ã¢â‚¬ ¹Ã¢â‚¬  g)([i, j])=f([i, l])g([l, j])   ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j For all f, g à Ã‚ µA and [i, j]à Ã‚ µS and whose unit is given by 1([I,j])= ÃŽÂ ´i,j à ªÃ¢â‚¬Å" ¯[I,j]à Ã‚ µS. Definition1.38 The algebra of A over the k described above is the incidence algebra of the locally finite partially ordered set (S, à ¢Ã¢â‚¬ °Ã‚ ¤). Definition1.39 Lie co-algebra over k is a pair (C, ÃŽÂ ´), where C is a vector space over k and ÃŽÂ ´: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡C is a linear map, which satisfies: à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"ÃŽÂ ´=0 and (ÃŽâ„ ¢+(à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢)à ¢Ã‹â€ Ã‹Å"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ Ã¢â‚¬Å¾)+(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ Ã¢â‚¬Å¾)à ¢Ã‹â€ Ã‹Å" (à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢))à ¢Ã‹â€ Ã‹Å"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ´)à ¢Ã‹â€ Ã‹Å"ÃŽÂ ´=0 à Ã¢â‚¬Å¾=à Ã¢â‚¬Å¾C,C and I is the appropriate identity map. Definition1.40 Suppose that C is co-algebra over the field k. The wedge product of subspaces U and V is Uà ¢Ã‹â€ Ã‚ §V = Ά-1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡C+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V). Definition1.41 Let C be co-algebra over the field k. A saturated sub-co-algebra of C is a sub-co-algebra D of C such that Uà ¢Ã‹â€ Ã‚ §Và ¢Ã…  Ã¢â‚¬  D, à ªÃ¢â‚¬Å" ¯ U, V of D. Definition1.42 Let C be co-algebra over k and (N, à Ã‚ ) be a left co-module. Then Uà ¢Ã‹â€ Ã‚ §X= à Ã‚ -1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡N+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡X) is the wedge product of subspaces U of C and X of N. Definition1.43 Let C be co-algebra over k and U be a subspace of C. The unique minimal saturated sub-co-algebra of C containing U is the saturated closure of U in C. Definition1.44 Let (A, m, ÃŽÂ ·) be algebra over k. Then, Aà ¢Ã‹â€ Ã‹Å"=mà ¢Ã‹â€ 1(Aà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Aà ¢Ã‹â€ - ) (Aà ¢Ã‹â€ Ã‹Å", Ά, ÃŽÂ µ) is a co-algebra over k, where Ά= mà ¢Ã‹â€ -| Aà ¢Ã‹â€ Ã‹Å" and ÃŽÂ µ=ÃŽÂ ·Ãƒ ¢Ã‹â€ -. ÃŽÂ ¤he co-algebra (Aà ¢Ã‹â€ Ã‹Å", Ά, ÃŽÂ µ) is the dual co-algebra of (A, m, ÃŽÂ ·). Also we denote Aà ¢Ã‹â€ Ã‹Å" by aà ¢Ã‹â€ Ã‹Å" and ΆÃƒ ¢Ã‹â€ Ã‹Å"= aà ¢Ã‹â€ Ã‹Å"(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡ aà ¢Ã‹â€ Ã‹Å"(2), à ªÃ¢â‚¬Å" ¯ aà ¢Ã‹â€ Ã‹Å" à Ã‚ µ Aà ¢Ã‹â€ Ã‹Å". Definition1.45 Let A be algebra over k. An ÃŽÂ ·:ÃŽÂ ¾- derivation of A is a linear map f: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k which satisfies f(ab)= ÃŽÂ ·(a)f(b)+f(a) ÃŽÂ ¾(b), à ªÃ¢â‚¬Å" ¯ a, bà Ã‚ µ A and ÃŽÂ ·, ÃŽÂ ¾ à Ã‚ µ Alg(A, k). Definition1.46 The full subcategory of k-Alg (respectively of k-Co-alg) whose objects are finite dimensional algebras (respectively co-algebras) over k is denoted k-Alg fd (respectively  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   k-Co-alg fd). Definition1.47 A proper algebra over k is an algebra over k such that the intersection of the co-finite ideals of A is (0), or equivalently the algebra map jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")*, be linear map defined by jA(a)(aà ¢Ã‹â€ Ã‹Å")=aà ¢Ã‹â€ Ã‹Å"(a), a à Ã‚ µA and aà ¢Ã‹â€ Ã‹Å"à Ã‚ µAà ¢Ã‹â€ Ã‹Å". Then: jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")* is an algebra map Ker(jA) is the intersection of the co-finite ideals of A Im(jA) is a dense subspace of (Aà ¢Ã‹â€ Ã‹Å")*. Is one-to-one. Definition1.48 Let A (respectively C) be an algebra (respectively co-algebra ) over k. Then A (respectively C) is reflexive if jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")*, as defined before and jC:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(C*)à ¢Ã‹â€ Ã‹Å", defined as: jC(c)(c*)=c*(c), à ªÃ¢â‚¬Å" ¯ c*à Ã‚ µC* and cà Ã‚ µC. Then: Im(jC)à ¢Ã…  Ã¢â‚¬  (C*)à ¢Ã‹â€ Ã‹Å" and jC:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(C*)à ¢Ã‹â€ Ã‹Å" is a co-algebra map. jC is one-to-one. Im(jC) is the set of all aà Ã‚ µ(C*)* which vanish on a closed co-finite ideal of C*. Is an isomorphism. Definition1.49 Almost left noetherian algebra over k is an algebra over k whose co-finite left ideal are finitely generated. (M is called almost noetherian if every co-finite submodule of M is finitely generated). Definition1.50 Let f:Uà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V be a map of vector spaces over k. Then f is an almost one-to-one linear map if ker(f) is finite-dimensional, f is an almost onto linear map if Im(f) is co-finite subspace of V and f is an almost isomorphism if f is an almost one-to-one and an almost linear map. Definition1.51 Let A be algebra over k and C be co-algebra over k. A pairing of A and C is a bilinear map   ÃƒÅ½Ã‚ ²: AÃÆ'-Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k which satisfies, ÃŽÂ ²(ab,c)= ÃŽÂ ² (a, c(1))ÃŽÂ ² (b, c(2)) and ÃŽÂ ²(1, c) = ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯ a, b à Ã‚ µ A and  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   c à Ã‚ µC. Definition1.52 Let V be a vector space over k. A co-free co-algebra on V is a pair (à Ã¢â€š ¬, Tco(V)) such that: Tco(V) is a co-algebra over k and à Ã¢â€š ¬: Tco(V)à ¢Ã¢â‚¬  Ã¢â‚¬â„¢T is a linear map. If C is a co-algebra over k and f:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is a linear map,à ¢Ã‹â€ Ã†â€™ a co-algebra map F: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Tco(V) determined by à Ã¢â€š ¬Ãƒ ¢Ã‹â€ Ã‹Å"F=f. Definition1.53 Let V be a vector space over k. A co-free co-commutative co-algebra on V is any pair (à Ã¢â€š ¬, C(V)) which satisfies: C(V) is a co-commutative co-algebra over k and à Ã¢â€š ¬:C(V)à ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is a linear map. If C is a co-commutative co-algebra over k and f: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is linear map, à ¢Ã‹â€ Ã†â€™ co-algebra map F:C à ¢Ã¢â‚¬  Ã¢â‚¬â„¢C(V) determined by à Ã¢â€š ¬Ãƒ ¢Ã‹â€ Ã‹Å"F=f.   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Majid 2002, Radford David E) Chapter 2 Proposition (Anti-homomorphism property of antipodes) 2.1 The antipode of a Hopf algebra is unique and obey S(hg)=S(g)S(h), S(1)=1 and (Sà ¢Ã‚ ¨Ã¢â‚¬Å¡S)à ¢Ã‹â€ Ã‹Å"Άh=à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"ΆÃƒ ¢Ã‹â€ Ã‹Å"Sh, ÃŽÂ µSh=ÃŽÂ µh, à ¢Ã‹â€ Ã¢â€š ¬h,g à ¢Ã‹â€ Ã‹â€  H.   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Majid 2002, Radford David E) Proof Let S and S1 be two antipodes for H. Then using properties of antipode, associativity of à Ã¢â‚¬Å¾ and co-associativity of Ά we get S= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Sà ¢Ã…  -[ à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"Ά])à ¢Ã‹â€ Ã‹Å"Ά= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Idà ¢Ã…  - à Ã¢â‚¬Å¾)à ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"(Id à ¢Ã…  -Ά)à ¢Ã‹â€ Ã‹Å"Ά= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"(Ά à ¢Ã…  -Id)à ¢Ã‹â€ Ã‹Å"Ά = à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"( [à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ Ã‹Å"Ά]à ¢Ã‚ ¨Ã¢â‚¬Å¡S1)à ¢Ã‹â€ Ã‹Å" Ά=S1. So the antipode is unique. Let Sà ¢Ã‹â€ -id=ÃŽÂ µs idà ¢Ã‹â€ -S=ÃŽÂ µt To check that S is an algebra anti-homomorphism, we compute S(1)= S(1(1))1(2)S(1(3))= S(1(1)) ÃŽÂ µt (1(2))= ÃŽÂ µs(1)=1, S(hg)=S(h(1)g(1)) ÃŽÂ µt(h(2)g(2))= S(h(1)g(1))h(2) ÃŽÂ µt(g(2))S(h(3))=ÃŽÂ µs (h(1)g(1))S(g(2))S(h(2))= S(g(1)) ÃŽÂ µs(h(1)) ÃŽÂ µt (g(2))S(h(2))=S(g)S(h), à ¢Ã‹â€ Ã¢â€š ¬h,g à ¢Ã‹â€ Ã‹â€ H and we used ÃŽÂ µt(hg)= ÃŽÂ µt(h ÃŽÂ µt(g)) and ÃŽÂ µs(hg)= ÃŽÂ µt(ÃŽÂ µs(h)g). Dualizing the above we can show that S is also a co-algebra anti-homomorphism: ÃŽÂ µ(S(h))= ÃŽÂ µ(S(h(1) ÃŽÂ µt(h(2)))= ÃŽÂ µ(S(h(1)h(2))= ÃŽÂ µ(ÃŽÂ µt(h))= ÃŽÂ µ(h), Ά(S(h))= Ά(S(h(1) ÃŽÂ µt(h(2)))= Ά(S(h(1) ÃŽÂ µt(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡1)= Ά(S(h(1) ))(h(2)S(h(4))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µt (h(3))= Ά(ÃŽÂ µs(h(1))(S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡S(h(2)))=S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µs(h(1))S(h(2))=S(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡ S(h(1)). (New directions) Example2.2 The Hopf Algebra H=Uq(b+) is generated by 1 and the elements X,g,g-1 with relations gg-1=1=g-1g and g X=q X g, where q   is a fixed invertible element of the field k. Here ΆX= Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +g à ¢Ã‚ ¨Ã¢â‚¬Å¡ X, Άg=g à ¢Ã‚ ¨Ã¢â‚¬Å¡ g, Άg-1=g-1à ¢Ã‚ ¨Ã¢â‚¬Å¡g-1, ÃŽÂ µX=0, ÃŽÂ µg=1=ÃŽÂ µ g-1, SX=- g-1X, Sg= g-1, S g-1=g. S2X=q-1X. Proof We have Ά, ÃŽÂ µ on the generators and extended them multiplicatively to products of the generators. ΆgX=(Άg)( ΆX)=( gà ¢Ã‚ ¨Ã¢â‚¬Å¡g)( Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +gà ¢

Effect of Tissue Culture Plastic Surfaces

Effect of Tissue Culture Plastic Surfaces Summary: The design of this experiment was conducted in order to analyse the effect of tissue culture plastic surface and establish the optimal tissue culture plastic surface for growing the Human Fibrosarcoma HT 1080 cell line, which is still lacking even this human cell line is commonly used in vitro studies and it is strongly recommended as a gold standard for the Lentivirus titration. In this context it appears especially interesting to which extent the HT1080 cell line proliferation depends on which type of tissue culture plastic plates were used in any experiment. In this study we optimized the growth and the proliferation of the HT1080 cell line by growing them in three different 96 wells tissue culture plates including Falcon, Corning and Greiner, and study the cells proliferation using XTT assay Roche based. Thus we considered the HT 1080 cell line proliferation curve obtained on 2 weeks time and we investigated the proliferation influence of this cell line seeded in 3 diffe rent plastic plates. We found that falcon tissue culture plastic were could be more widely considered as a potential plastic ware tool for growing HT 1080 cell line from proliferation curves obtained under 3 different experimental plastic plates, Falcon 96 well tissue culture plate was more likely suitable plastic plate to be used in seeding the HT 1080 cell line. Introduction Cell culture known to be a complex process by removal of tissue or cells from plants, animals, microbes (such as bacteria and viruses), and fungi process them by growing them in specific conditions and atmospheres. In the 19th century scientist discovered the way of maintaining live cell lines taken from the animals tissue [1]. Principle of tissue culture was established by Wilhelm Roux In 1885, he removed a part of the medulla oblongataHYPERLINK http://en.wikipedia.org/wiki/Medullary_plate dish of an embryonic chicken and preserved it in a warm saline for some days2[2]. The methodology of tissue culture was established by Ross Granville Harrison, while he was published results of his research work from 1907-19103[3]. In 1950s Cell culture techniques were progressed significantly in virology research, which helped in manufacture of vaccines. Development of antibiotics helped tissue culturing to be success, as it made it easy to avoid tissue culture contaminations[4]. Types of tissue culture There are two types of tissue culture used for growing cells, adherent and suspension cultures. Adherent cells are known to be anchorage-dependent and attachment to a solid surface is a requirement for proliferation. Generally, the cells grow as an adherent monolayer and discontinue dividing when they reach a density that they touch each other. The majority of cells are adherent as they derived from solid tissues[5]. Cells cultured from bone marrow, spleen or blood adhere poorly if at all to the culture dishes. These cells in the body naturally live in suspension or they are loosely adherent. Adherent cells need a solid phase like tissue culture plastic, which might be layered with extracellular matrix components to raise adhesion properties and supply other signal required for differentiation and growth. Suspension cultures are easier to spread, since subculture requires only dilution with medium. Moreover, cultures with cells growing attached to each other or to a solid phase have to be treated by a protease to break the bond between the cells and solid surface. Trypsin is the most commonly enzyme used. Obviously, freely suspended cultures do not require trypsinization. Thus, they are easier to harvest. Maintain cells in culture Different cell types need different environments to survive in the culture. Environment means is to allow the cells to increase in number by mitosis (cell division). To achieve that, suitable temperature ( 37oC) is required as cells need it to grow happily and that can be achieved by proper calibration, frequent checking, and good maintained incubators. Second, good quality substrate (Glass and Plastic) for better attachment by using attachment factors (collagen, lamnin, and fibronectin) and excellent cell growth. Finally, proper culture media and maintained incubator for accurate pH and osmolality[10]. Cell culture medium The culture medium should got the proper nutrition of the cells requirement, growth factors, control the osmolality and pH, and present vital O2 and CO2 gases [11]. The culture medium provides necessary nutrients that are included into dividing cells, such as fatty acids, amino acids, sugars, vitamins and carbohydrates and all of these help to provide the necessary energy to build a new proteins and metabolism. The pH of the medium can be control by buffer which is usually a CO2 based or an organic buffer (e.g HEPES) to maintain the pH level in suitable range 7.0 7.4. Sodium Bicarbonate usually used in most cultures media as a standard buffer. Furthermore, Phenol Red is usually added as pH indicator in media, which change when if pH 7.4 decreased. The osmotic pressure adjust the regulation of the substances flow inside and outside of the cell, which is managed by adding salt to the medium. Supplement such as fetal serum enhance the cells growth when it is added to media as it consis t of high growth factor concentration and low antibiotics concentration. In addition, serum protein when added to media it acts as nutrition and it undertakes transporter function via cell membrane and combines toxic metabolic products. Antibiotics and antimycotics must be added to the culture media as it suppress the bacterial and fungus growth. Contamination and cell culture contamination consider to be a serious problem as it can end an experiment to misidentified or lead to wrong outcome. Recent, studies propose 15-20% of the time researchers been a victim of contamination[9]. There are two types of cell culture contamination, biological and chemicals. Biological contamination caused by fast growing yeast, bacteria and fungi. This type of contamination changes the turbidity of the medium and have observable effects on the cell culture. On the other hand, there are other types of biological contamination which are very difficult to detect such as; mycoplasmas and viruses. Chemical contamination caused by many different agents involve metal irons, plasticizers and Endotoxins[1]. Different plastic wares used in cell culture The use of disposable plastic materials for tissue culture has become popular, and in many laboratories plastic cell culture vessels have completely replaced glassware. For example, multiwell plastic plates are used for comparing different growth conditions, plastic wares, media, growth factor, sera and cytotoxines. Untreated plastic surfaces (usually made of polystyrene) are generally unsuitable for the culture of vertebrate cells, because they do not permit ready attachment and spreading of cells(19). Thus the polystyrene must be subjected to a surface treatment to make the plastic surface suitable for cell attachment(21).Chemical methods, such as sulfuric acid-sodium carbonate rinses (4) and alcohol rinses (5), have been proposed to modify plastic surfaces so that cell attachment occurs. Cell viability and proliferation The quantification of cellular growth, including viability and proliferation and, is essential to optimize the cell culture conditions. Measurements of cell viability assess the number of healthy living cells and dead cells, whereas measurement of cells proliferation is used to assess the response of cells to a specific stimulus or toxin quantitantion of culture growth. Cells proliferation is significant in steering maintenance as it is an essential element for controlling the stability of the culture and identifying the superlative time for the optimum dilution, sub culturing, and the estimated platting competence at various cell densities. Proliferation rate is a key quantitative parameter to be estimated when studying the dynamic behaviour of a cell population, measure of cells growth and obtain the cells growth curve. Fibrosarcoma cell line (HT1080) HT-1080 cell line is mainly human fibrosarcoma adherent cell line (15). It was instigated from a biopsy of a fibrosarcoma obtained from the acetablum of a 35 year old male in July 1972 the patient had never received radiation or chemotherapy therapy. A fine piece of the tumor tissue was cultured into plastic flasks and dishes were sheltered with Eagles minimum essential medium with 10% fetal bovine serum and antibiotics . Quick trypsinization and picking procedures were used to reduce fibroblasts from the cultures(16). The human fibrosarcoma cell line HT1080 is strongly recommend as the gold standard for reproducibly titrating Lentivirus. Lentiviruses belong to Retooviridae Family, which are the most multitalented of retroviruses since they are capable to infect, transduce and maintain expression in approximately any mammalian cell. Lentiviral vectors obtained from the human immunodeficiency virus (HIV-1) have become main apparatus in mammalian cells for gene delivery. The beneficial characteristic of Lentiviral vectors is the capability to mediate competent transduction, mixing and long-term expression into non-dividing and dividing cells both in vivo and in vitro. The most commonly used cell lines for titrating are adherent cells which show a replication time in the range of 18-25 hours. The human fibrosarcoma HT1080 cell line is able to give more accurate viral titres because these cells are easily transduced and very efficiently by recombinant Lentiviruses . To produce reliable transduction res ults using a known multiplicity of infection (MOI), it is essential to titrate Lentivirus stocks, and that can be determined by infecting HT1080 cells with serially diluted supernatants produced using control vector containing an easily detectable receptor gene (e.g. Lac Z and fluorescent protein). Furthermore, titration values will depend heavily on the cell type and method used for titration, so there may be significant differences between titres determined in cells typically used for titration and the number of target cells that are ultimately transduced. However titrations are important for determining the relative virus content of stocks prepared from different vectors , Confirming the viability of virus stocks, Determining the optimal transduction conditions, Adjusting the MOI to control the viral copy number of transduced cells, Determining the maximum number of cells that can be infected by a virus stock. Additionally, the human fibrosarcoma cell line HT-1080 has been used widely to study the consequence of anti-inflammatory agents such as glycocortiodis on the gene expression of inflammatory mediator(17) and in the study of the extracellular matrix proteins involved in attachment, invasion and metastasis. It is also has been involved in assessment the function of the Ras-oncogenes in the altered phenotype and the function of the expression of the rentiblastoma gene product in the cellular response to therapy(18). In most studies that used the Human Fibrosarcoma HT1080 cell line in their studies there is inconsistencies regarding the growth of this cell line with different media, different serum and different tissue culture plastic surface. Thus, it remains mainly descriptive and not quantify the relative influence of the underlying type of media, serum or plastic surface on cell growth and proliferation. Aim of this study In order to find the optimal plastic tissue culture plates for this cell line, I aimed to optimize the growth and the proliferation of the Human Fibrosarcoma HT1080 cell line by growing them in different tissue culture plastic plates including Falcon, Greiner and Corning plates and study their proliferation using colorimetric assay(XTT based, Roche). Materials and methods Tissue culture (pre-experiment to obtain growth curve of HT1080 cell) Tissue culture of HT1080 cell line Experiment was performed using Human fibrosarcoma cell line HT1080 (ATCCCCL121) epithelial cells. This cell line was obtained from ECACC European collection of animal cell cultures. Cells were grown in HPA culture collections facilities (catalogue number :85111505). Routinely, cells were grown in complete medium composed of Dulbeccos Modified Eagle Medium (DMEM supplemented with high glucose liquid without phenol red, without L-Glutamine + 1% Non Essential Amino Acids (NEAA) + 10% Foetal Bovine Serum (FBS) (all were purchased from PAA). The bench surface were cleaned before starting tissue culture, to avoid any contamination The cells were Cultured and grown in 75 cm2 falcon flask which was kept in a humidified atmosphere with 5% CO2 at 37oC for 24 hours to obtain the optimum growth condition. The cells were subculture every 3 days which helped to achieve 0.45-1.0X 106 cells/ml. all the culturing and sub-culturing procedure were done in class II safety cabinet. Cell count The cells were twice a week checked for any contamination before cell count done, the media should be in a good condition, and healthy clear yellow color should be observed. HT1080 cells were counted by using counting chamber (haemocytometer) as it shown below. (A, B, D, and C) as shown above contain 16 small squares of volume 0.1mm3 or 10-4 cm3 which means (length x width x height). 10ul of HT1080 cells were placed between the counting chamber and cover slips. After cells settle the haemocytometer were fixed under light microscope with X40 magnification. The cells were counted and equation was used to find out the total cells number and then it was divided by 4 to obtain an average X104 cells/ml. Cells can be sub-cultured in fresh supplemented media. Actual concentration = Dilution factor required Desired concentration Sub- Culture of HT1080 All cells were detached by using tryptirization by trypsine/EDTA (0.1% /0.02%) solution, average of 60X104 cells/ml of HT 1080 cells were reseed into new labeled flask (75 cm2). Then 20 ml of media was added to the same flask. Finally it were kept in the incubator for 24 hour at 37oC in 5% CO2 atmosphere. obtain growth curve of HT1080 cell Briefly, 1ml from the cell suspension were mixed with 480ul of MEM media (PAA). Then 100ul of the tissue culture medium equally distributed to all wells of 96 tissue culture plastic multiwells plate except the first row as 200ul of the cell suspension mixture was added to whole first row. Then Serial dilution was performed by taking 100ul from the first row of 96 wells and transferred to the second row wells (shown in the figure below). The last 100ul were discarded after doing serial dilution in the sixth well (each dilution included four wells) Finally the 96 wells tissue culture micro plate were kept for incubation (at 37Co, 5% CO2) for 24 hours. Proliferation assay The cells proliferation was studied by using XTT proliferation assay (Cat. No. 11465015001) by Roche. First, the XXT solution was prepared by thawing the XTT labeling reagent and the electron-coupling reagent, respectively in a water bath at 37oC. Mix each vial thoroughly to obtain a clear solution. Then XTT labeling mixture was prepared by mixing 4ml of XTT labeling reagent with 80ul of electron-coupling reagent, to prepare the XTT labeling mixture. Finally, 50ul of the XTT prepared mixture was added to all wells of 96 wells tissue culture plates wells after the incubation period of 24 hours and the plate was incubated in the incubator in humidified atmosphere with 5% CO2 at 37oC for 6 hours . Reading the tissue culture multiwell plate After 6 hours of the incubation period, the plate was kept in the ELISA spectrophotometer reader (Tecan sunrise colorimeter) to measure the absorbance of HT1080 cells at 450nm and obtain the cells growth curve. Tissue culture of HT1080 cell line (Actual experiment) Growing the HT1080 cell line in 3 different tissue culture plastic 96 wells plate including Greiner, Falcon and Corning.this experiment conducted within two weeks. From the previous obtained graph of growth curve of HT1080 cell line the seeding density of all our future subculture fixed to 60X104 cells/ml. First of all, the tissue cultured flask checked under the microscope to check the cell growth confluence. Then cell counting was performed to seed all the 3 different 96 wells tissue culture plastic plates at cell density of 60X104 cells/ml and that was possible after finding out the dilution factor by applying an equation (see below). Usually we used dilution factor 1:19. Actual concentration = Dilution factor required Desired concentration After preparing the correct dilution of HT1080 cell line, plates were seeded with 60X104 cells/ml ,100ul/well. Each plates was divided to four parts for four days to run the experiment, for example the first part was labeled as day 1, second part day 2, third part day 3 and the last part day 4 with 6 wells for each day along with 2 blank, total of 8 wells daily. Then the tissue culture plates were incubated in humidified atmosphere with 5% CO2 at 37Â °C for 24 hours. ( see figure 2). Day4 Day3b Day2 Day 1 Figure 2: Cells suspension +proliferation reagent Blank: media only Cells proliferation assay After the incubation period of 24 hours, the XTT solutions were prepared as explained previously and added to the first part of each different tissue culture plates each part was included 6 wells. Then the tissue culture plates were incubated again in the incubator at 37Â °C in 5% CO2 for 24 hours. After 6 hours of the incubation period, the platse were kept in the ELISA spectrophotometer reader (Tecan sunrise colorimeter) to measure the absorbance of HT1080 cells at 450nm. Then the plates were returned to the same incubator and used for the rest of days. The same procedure of preparing proliferation reagent and reading the plates was performed to obtain the results and check the cells proliferation for the rest of days . Results This investigation was done to rule out the growth density of the Human Fibrosarcoma HT1080 cell line to be seeded in three different 96 wells plastic tissue culture plates to study the growth and the proliferation of this cell line. HT1080 cells were seeded as described in 96 wells plastic plates and incubated for 24 hours in media. For cell proliferation, XTT mixture reagent was added after the incubation period . Briefly, 96 well plates of from each different plastics plates used were seeded with HT1080 cells(6X103 cells/ml, 100 ul/well) and incubated for 24 hours in media. After 6 hours of incubation, the HT1080 cell line proliferation rate were measured by using Tecan sunrise colorimeter at 450nm and the following growth curve was being obtained. Figure 1: shows a growth curve of the human fibrosarcoma HT 1080 cell line by using XTT assay. Measurement of the HT 1080 cell line proliferation incubated in the 96 well plate on culture medium alone for 24 hours and allowed to adhere. After adding XTT reagent cells were incubated for 6 hours. Then the cells proliferation was analyzed by Tecan sunrise colorimeter at 450 nm, the log phase were determined as 6X103. From the obtaining HT 1080 cell line growth curve (figure 1) the initial Lag phase where the cells were growing very slow started from 1562 cells /ml to approximately 6000 cells/ml. then the HT1080 cell growth starts to accelerate into the exponential phase which represents the period when the cells are growing most rapidly. This phase continued till the number of cells reached 25000 cells/ml which may due one or more nutrients became limited, oxygen became depleted and or metabolic by products accumulate to toxic level. After that the cells were Decelerated (Declined). This was followed by a Stationary phase, during which there was no discernible change in cell concretion. Finally if the cells were kept more time we may observe of cell death and lysis which results in a decrease of cells number. The cell growth density was determined by observing the ht1080 cell line growth proliferation curve and it was decided to be 6000 cells/ml as our standard density for this experiment. This investigation was designed to study the proliferation of Human Fibrosarcoma HT1080 cell line in 3 different 96 well plastic tissue culture plates including Falcon, Corning and Greiner. Briefly, 96 well plates from each different plastics plates used were seeded with HT1080 cells(6X103 cells/ml, 100 ul/well) and incubated for 24 hours in media. For each investigation sample were set up in 6 wells. After incubation, the HT1080 cell line proliferation rate were measured by using Tecan sunrise colorimeter at 450nm and the following result were being obtained. n = 2 Figure 2: Determine comparison of the HT1080 cells proliferation by growing them in three different 96 wells plastic microplates (Falcon, Greiner and Corning) by using XTT assay for 5 days in MEM media . Each experiment includes 6 duplicate reading . The graph represent the average of three independent experiments data mean, while the errors bars represent the standard deviation of the data. The results that obtained from this experiment revealed that, the Human fibrosarcoma HT1080 cell line showed different growth proliferation rate depends on the plastic wares including Falcon, Greiner and Corning that have been used in this study (figure 2). The same cells seeding density that was obtained previously from the HT1080 cells growing curve(6X103) were applied to all the 96 wells plastic tissue culture plates. Falcon, Greiner and corning plastic plates showed varies proliferation in the mean (ÂÂ ±SD) number of HT1080 cells. From our graph the cells that were grown in Greiner plate proliferate at slower rate in comparison to the other two types of plastic plates were used. On the other hand, the cells showed good proliferation in Corning plate with double increased in the mean (ÂÂ ±SD) number of HT1080 cells compared to the proliferation which was obtained in Greiner plate. In contrast the cells, which were seeded in Falcon plate showed the best proliferation of H T1080 cells from the first day of the experiment till the last day and reached a peak at day 4. Moreover, from the obtained data it was clear that we can see HT 1080 cell that were seeded in Falcon plate were proliferating two times more than the mean (ÂÂ ±SD) number of HT1080 cells in Corning plate and three times more than the mean (ÂÂ ±SD) number of HT1080 cells in Greiner this continued with same significant proliferation rate till the last day of our experiment . Discussion Our results confirm that the plastic wares have a major influence on the Human Fibrosarcoma HT1080 cell line adherence, growth and proliferation. It was very clear from our obtained data that Falcon tissue culture plastic plates shown to be the best plastic ware to optimize the growth and the proliferation of the Human Fibrosarcoma HT 1080 cell line between the other two plastic Corning and Greiner that were used in this experiment. Although the three types of plastic surface treatment almost the same but these cells were growing with different proliferation rate on these plastic wares surface. The human fibrosarcoma HT1080 cell line are extensively accepted as the standard target cell for titrating Lentivirus because these cells are transduced very efficiently by recombinant Lentiviruses. The health of HT1080 cells at the time of transfection has a significant effect on the success of Lentivirus production. Use of unhealthy cells will negatively affect the transfection efficiency, resulting in production of a low titre Lentiviral stock. For optimal Lentivirus production (i.e. producing Lentiviral stocks with the expected titers) the cells should be healthy and greater than 90% viable. Furthermore, the growth characteristics of this cell line HT1080 changes depending on media formulations, plastic ware used and sources of serum used. Generally, cell attachment, growth, and cell-to-cell contacts on a surface or extracellular matrix substrate are extremely complex proceedings involving cell adhesion molecules. An additional factor leading the growth of cells is the composition of the culture medium, especially serum which supplies the essential nutrients for cells and influences the cell attachment. As it contains numerous extracellular matrix proteins . However, there are known limitations to serum in culture medium. Apart from being expensive, it can interfere with specific assays and introduce variability due to inconsistencies and the presence of indeterminate components. When growing any cells, one of the first thing is to optimize all culture conditions. Generally people know about Media, FCS/FBS, CO2 concentration, split ratios etc, but very few ever think about TC Plastic.corning, costar, nunc, greiner, falcon, tpp etc will all support cell growth, but optimizing your conditions can save time and money in the long run. Culture environmental conditions influence the proliferative characteristics of cells, while this environment is not fully controlled. Plastic is one of the most important things to know about and understand. It can have a major influence on cell adherence and growth and can therefore ultimately influence the experimental results. Most of studies devoted to the analysis of HT1080 cell line growth relies on using different types of tissue culture plastic surface leading to inconsistencies regarding the growth of HT1080 in different plastic . Thus, optimal plastic surface for HT1080 cell line long term growth is usually unknown. For example, a study has been conducted by shalinsky et al for the modulation of dipyridamole (DPM) to act synerglstically with vinblastine (VBL) in the HT 1080 cell line, they have used corning plastic micro-plates to seed the cells and ran their experiment. The Human Fibrosarcoma HT1080 cell line used in the studies of the extracellular matrix proteins involved in attachment, invasion and metastasis as the HT1080 cells must attach to and spread underlying matrix in order to carry out normal metabolism, proliferation and differentiation. One of these studies is done by Miyake and colleges same corning 96 well micro-plates were used but it was coated with ECM and they found that HT1080 h ad better proliferation while cultured with coated microplate rather than uncoated and that can be explained due to capability of extracellular matrix (ECM) to hold the HT1080 cells and provide a highly organized lattice within cells can migrate and interact with each other. In addition, they found that HT 1080 cell line secret a large amount of extracellular matrix on the microplate surface, then HT1080 cell attach rapidly and they leave the underlying ECM intact and firmly attached to the plastic. Additionally, Ohizumai et al, have another choice of the plastic ware in their experiment as they have used falcon 96 well microplate to grow HT1080 cells and processed their study. In other study was done by Markus and Richard they have seeded the HT 1080 cell line in standard treated uncoated Falcon 24 well microplate and they have found that the HT1080 cell migration increased compared to other cell line such as HT29 and MCF7 cell lines, which confirms that different cell needs different types of plastic microplates to get the optimum growth and proliferation. Another study where HT1080 cells have been grown on different plastic ware type done by Simpson et al, in their study (combination of afusogenic Glycoprotein, producing Activation and oncolytic Herpes Simplex virus for Enhanced local tumor control). They have used coated Greiner plastic ware with lamim and they are of thousands of researchers who prefer to use coated plastic ware as its more effective and more significant while using plastic ware that are coated with ECM. In this context, the study of HT1080 cell line proliferation by growing the cells in different tissue culture plastics plates appears necessary for cell proliferation performance within different tissue culture plastic surfaces as well as cell response to such environmental changes In this study we have optimized the growth and the proliferation of the Human Fibrosarcoma HT1080 cells by growing them in different plastic ware including Falcon, Greiner and Corning plastic wares and study their proliferation using colorimetric assay(XTT based, Roche). The XTT assay method is based on the reduction of the tetrazolium salt XTT by viable cells in the presence of an electron coupling reagent. The reaction produces a soluble formazan salt. The XTT assay is sensitive, quantitative, reliable and automated methods led to the development of standard assays. Cell proliferation and viability assays are of particular importance for routine applications. Tetrazolium salts MTT and XTT are especially useful for assaying the quantification of viable cells. In this case variability of proliferation rates would more likely reflect plastic surface variability than real variations of inherent cell proliferation capabilities. Moreover, Measurement of HT1080 cell proliferation rates is used to determine the response of the cells growth as it is a significant element for monitoring the consistency of the culture and knowing the best time to subculture the optimum dilution, and the estimated platting efficiency at different HT1080 cell densities. Testing medium, serum, new culture vessels or substrate, and so forth, all require quantitative assessment. One of the difficulties in growing cells in vitro using conservative tissue culture techniques is that the cells rest on plastic rather than on their natural biological support and can only be nourished with media from their apical side. To explain my results it is important to know the plastic surface treatment of each type of plastic used in this study. Normal TC plastic has a net negative charge. TC treatment cross links carboxyl and amine groups and gives the plastic its net negative charge. TC surface modification is usually done by ionizing radiation or other physio-chemical methods ( F. Grinnell 1978 Int. Rev.Cytol 43. p.65 ). Falcon plastic ware showed better growth and proliferation of this cell line more than greiner and corning. The HT1080 cells were proliferating with Falcon plastic tissue culture plate two times more than with Greiner plastic plate and double its proliferation with Corning plastic plate. Falcon surface treatment is more advanced than Greiner plastic ware as Falcon Standard Tissue Culture (TC) surfaces exposed to vacuum-gas plasma or corona discharge treatment that create a number of negatively charged functional groups on the polystyrene surface and make it hydrophilic. Falcon company is believed to facilitate direct cell attachment and indirectly support attachment, spreading, and growth by binding serum proteins to the plastic surface. Each lot of Falcon plastic products is gamma irradiated to produce a sterile product and from the obtained results it was proved that Falcon is the best plastic substrate for the Human Fibrosarcoma HT1080 cell line growth and proliferation as the cel ls were proliferating increasingly till the last day. In contrast the HT1080 cells with Corning were growing and proliferating with gradual increase from the first day till the last day of experiment but their proliferation lower than the cells proliferation with Falcon. Although the Standard Corning polystyrene cell culture plastic wares have the same treatment of Falcon surface treatment. In addition from the results that we have obtained it seems to be that HT1080 cells were growing and proliferating more than when comparing their growth and proliferation with Greiner microplate. On the other hand, Greiner plastic ware are using different method to treat their tissue culture plastic wares, they are using a physical modification to make their TC-treated plates rather than chem

Nutrition Vs. Sport Performance :: Health Nutrition Pyramid Diet

The world is an orb of life. In its limited space all life forms compete to hold their own position. As Darwin concluded in his theory of evolution, “only the strong and most advanced survive, while the weak perish and are pushed aside.'; Evolution, the theory we use today to fuel our need to win and succeed in any organized competition. It is this drive that results in the vigorous preparation athletes’ go through to become superior among their race. To thrive, we must understand that proper nutrition is the basis any athlete must build from in order to achieve peak physical performance.   Ã‚  Ã‚  Ã‚  Ã‚  Prior to strenuous activity it is imperative that the body has the required amounts of nutrients to carry out an activity. At the latest reference it is recommended that a person consume an average of 2200 mg of calories, 60 g of fat, less than 5000 IU of vitamin A, more than 60 mg of vitamin C, 400 IU of vitamin D, more than 2000 mg of potassium, 2000 mg of sodium, 65 g of protein, 1.5 mg of thiamin, 1.7 mg of riboflavin, 20 mg of niacin, and 18 mg of iron. Nutritionists of today simplify this into an equation of 40% carbohydrates, 30% fats, and 30% protein that the entire day’s meals should be divided into. The total calorie intake must increase for active persons from 2200 to 2200 plus the total number used while exercising. This will ensure replenishment of the body’s system. Edgeworth 2   Ã‚  Ã‚  Ã‚  Ã‚  With the wide variety of athletic competitions, the specific meal a competitor may need to eat to benefit themselves differs widely, as do the events. The last meal or two are extremely important in both their time of consumption and content. It is these two factors that can cause a person to make or break their day just by their choices. Experience plays a large role since one must attempt many different pre-competition meals before they will find one that suits the individual. For most, the high carbohydrate diet is the choice; packing in as many as possible since it is such a huge energy source. Also, judging by time, one must decide the size of the meal. To digest a large meal takes 3-4 hours, a small meal 2-3 hours, liquid meal 1-2 hours, and a small snack takes less than an hour. A person may even find a burst of caffeine to be helpful or may just want a feeling of ease by not eating anything at all.

September 11: An American Victory :: September 11 Terrorism Essays

September 11: An American Victory The terrorist attack on the World Trade Center and Washington DC has been described as an act of war and a tremendous defeat for the United States, a defeat that must not be allowed to be repeated and a loss that must be avenged. Personally, I don't like the use of the phrase "Act of War". Wars are something that happen between states. Wars end when one side surrenders. If we treat this as a literal war, what will be the victory conditions? Who will surrender? How will we know that the war is over? Whose suit for peace will be listened to? But, for the sake of discussion, let us ignore these concerns, let us concede for the nonce that the language of war is appropriate. Let us put aside the questions of who exactly the enemy is. We know, at least, who 19 of the other side's foot soldiers were. We know, more or less what happened. I'm willing to set these questions aside because I have become angry, angry about how we ourselves are viewing the outcome of this attack, and how we are letting the world view it. I am angry about how we are viewing the acts of heroes, and how we are view ourselves as a nation. Let me state this quite clearly...   The United States did not lose the Battle of September 11, 2001. Claiming that we did diminishes the heroism that Americans showed. It underestimates American strength and it misses some very important points about the American character. There were four phases of the battle, four attacks. The first two took us completely by surprise, and can easily be viewed as a two pronged attack. Two transcontinental planes flying from Boston were turned into bombs and used to destroy the twin towers of the World Trade Center. Because they had the element of surprise the enemy's first thrust was extremely effective. The battle started very badly for us. The third phase occurred in Washington DC. The enemy hijacked a third commercial airliner. This time, however, US intelligence and technology began to come into play. At least one passenger was able to contact the Justice Department, inform them of what was happening and ask what instructions should be passed to the pilot. I'm speaking here, of course, of Barbara Olson's phone call to the Solicitor General, her husband Ted.

Ikea SWOT analysis Essay

1. Customer knowledge: one of the key competitive advantages IKEA has the deep knowledge about the customer. The company understands the purchasing factors that influence customers to buy and implements the best practices to induce that decision. IKEA offers low prices and a huge range of products. Designers constantly introduce new design products that look stylish in the eyes of customers. All the products are designed so it would be easy to transport and assemble. Moreover, the company offers the widest product range and positive shopping experience. All of these factors are aligned with what customers want and need and which results in higher sales. 2. Constantly using innovations to drive costs down. Low prices are the core business of IKEA business idea and company always tries to do things as efficient and cost-effective as possible. To drive costs down all the time, the company must find new and innovative ways to do that and to incorporate them in its businesses model. The business’ innovations include new materials that help IKEA using the recycle material to become a friendly environment company or using the newest ways of packaging. 3. Supply chain integration. IKEA is committed to long lasting relationships with its suppliers. In this way, the company can order large volumes and benefit from lower prices and greater quality while suppliers are assured of guaranteed orders. IKEA sources its materials close to suppliers to reduce transporting costs. All the efforts of closely integrating supply chain results in lower costs and a competitive advantage. 4. Brand reputation and market presence. According to Inter brand, IKEA is the most valuable furniture retailer brand in the world, valued at nearly $US 12. 8 billion in 2012. The business operates 332 stores in 38 countries and is present in the major world markets. More than 600 million customers visit IKEA stores every year. Worldwide market presence and strong brand reputation ensures that customers will often choose IKEA over its competitors. 5. Diversified product portfolio. Unlike IKEA’s largest competitors, the company has fairly diversified businesses. In addition to its furniture products, the company operates restaurants, houses and flats. Although, firm’s main business is designing, manufacturing and selling furniture it is not so affected by the changing forces in this market as other furniture retailers. 6. IKEA uses cheap labor which keeps its costs down and gives them a competitive advantage. Starting from the days when it discovered that furniture manufactured in Poland was as much as50% cheaper than furniture made in Sweeden, IKEA has started looking for cheap labor. It top five supplying countries are China (21% of supplies), Poland (17%), Italy (8%), Sweden (6%)and Germany (6%). China, as everyone knows, provides really cheap labor so IKEA gets its largest chunk of furniture manufactured from there. Cheap labor keeps the costs down and allow them to charge customers low price and helps IKEA sustain its competitive advantage. (IKEA SWOT 2013 ) Weaknesses 1. Negative publicity. The company has been criticized many times for issues like poor treatment of employees, questionable advertising practices or lobbying government authorities. Negative publicity decreases brand reputation and customer loyalty. 2. Low quality of products and services. IKEA is unable to find compromise between continuous cost reductions while maintaining the same quality of products. According to UK Customer Insights report on IKEA by Verdict, IKEA’s customers are less satisfied with its product and services quality than the average customer in UK buying at other stores. Firm’s cost reductions lead to decreasing product quality, which was followed by higher number of products returned and damaged brand. Furthermore, the Ikea product lack of innovation like KEA designs the price tag first, then the product. IKEA’s product strategy council is so much Obsessed with low price that they spend almost no time on product innovation. IKEA has been enjoying sustainable competitive advantage due to their low cost strategy 3. Standard products. IKEA’s main competitive advantage derives from low costs, which in part are achieved due to standardized products. Standardized products attract fewer customer segments. Therefore, the business inability to offer better quality more customized products allows its competitors to fill that niche and fortify their position in it. 4. It lacks thorough market research on customers’ preference before entering into a new market. To provide a good quality product and also value the customers need and wants should be the organizational motto; this is because it’s a furniture company. IKEA did not do any sort of market research regarding customer’s needs and wants. So they should come up with a market research results that will give them more profit. > Furniture > Ikea Online > Strategic > Ikea Design Opportunities 1. Further expansion into developing economies. Retail markets grew by at least 5% on average in emerging markets in the last year, opening huge opportunities for IKEA’s revenue growth. The company currently operates in most of the developed economies but hasn’t firmly stepped into developing economies, except China. There are great opportunities for IKEA to expand into Brazil, Mexico, Indonesia and Malaysia to increase its presence in these markets to sustain future growth. 2. Growing online sales. Online retail sales account for 17% and 4% of total retail sales in UK and US respectively. Online sales grow constantly and with 870 million visitors to its website IKEA could exploit this opportunity and benefit from increased sales and lower costs. 3. Expansion to growing grocery market. The current trend of eating healthier food has resulted in higher demand for grocery products in many developed economies. IKEA has an opportunity to expand its grocery business by introducing more grocery stores in its current retail places. The company is already successfully managing its food outlets, so this expansion opportunity would be well aligned with the current operations. Threats 1. Intensifying competition. Many low cost retailers such as Walmart, ASDA or Tesco are entering homeware specialists market where IKEA operates. These large retailers have similar specifics as IKEA, including low costs, well managed supply chain and huge market presence and can easily gain some market share from IKEA. 2. Growth of average consumer income. Growth of average consumer income means that people buy less low price and low quality products, which is exactly what IKEA offers in its stores. With the rising income people will be less attracted to IKEA and will turn to retailers that offer higher quality home ware products. ( IKEA SWOT 2013 ) Porter†s Five forces Analysis 1. Rivalry within the industry In Sweden there is handful of companies involved in the furniture industry. Moreover there are a lot of retailers in the market. The condition is pretty much same in USA. There are Home Depot,Wal-Mart, Costco and many other small retailers. On top of this many retailers import from china and sell it in the market at low price. This indicates that the competition within the industry is very high. 2. Bargaining power of suppliers It can be say that the bargaining power of suppliers is low. IKEA has a well-established relation with suppliers all over the world. Till 2008 IKEA has 1380 suppliers in 54 countries 21% of which are in China. Moreover IKEA also own manufacturing company like Swedwood Manufacturer. So it is evident that IKEA can threats the suppliers to enter into their business. 3. Bargaining power of buyers There are a lot of retailers who are directly involved in price war against each other. There are importers who are importing from china also in direct competition in the market. So the consumers have many alternatives. They can chose which manufacturers they will buy from. So the bargaining power of buyers is high. 4. Threats of new entrants There are no entry barriers in the industry. But the intensity of competition may scare off potential entrants. The required initial investment is not too much. Anyone can open a retail shop with small investments. But if someone wants to become a major player in the industry; than the firm needs to invest a lot of money, need to establish relation with suppliers, select suitable locations for outlets. These will require a lot patience and capital. So it is safe to say that the threats of new entrants are high if competitors want to do business for a long term. 5. Threats of substitutes Since the born of civilization men are using furniture. The styles are changing so as the trends. The industry is moving wood to plywood, rot iron even plastics. As the market is becoming more environment concerned many firms are giving slogan to go green. But the basic functional demand has remained the same. So it is safe to say that there are no threats of substitutes Opportunities IKEA can expand its product line by producing high end products From the very beginning IKEA’s target market has been the middle class to lower middle class people. This strategy has been worked for a long time but IKEA never wondered about how farther they can reach. In USA the trend was changing; people were getting thirstier for elegant design. IKEA can develop products that are designed for the high class people who are sensible about the design and quality and do not care about the price. For example Toyota: Lexus. IKEA can expand its business into interior designing and crockery products IKEA can expand its core business of furniture to a next level. IKEA can place crockery item swith the kitchenware furniture. This way when a customer walks through the kitchenware department he/she will be attracted to these products and may end up buying some. IKEA can go for environment friendly technology Customers now a days are now more concerned about the environment than ever. So IKEA can make products that are environment friendly; products that consume less water so the carbon footprint will be at minimum. Product customization can boost up IKEA’s sales IKEA can call for idea from its customers. This will definitely bring in some unique idea to the tent. IKEA can initiate a service that will allow customers to order customized products for some extra charges. This will help IKEA to capture the particular segment of the market who loves customization Threats Changing social trend can hinder the growth of sales of IKEA IKEA’s objective is to provide products to its customers at cheaper rate than the competitors. This objective does not recognize the necessity of a constant development of design and quality. In the pursuit of becoming a cost leader in the market IKEA can lose a major portion of the market that want quality and well designed products. Accelerated market competition in USA The furniture market of USA is very fragmented. But there are some well-established retailers who are selling functional furniture at a very low cost for example: Wal-Mart, Office Depot. These retailers will be in direct competition with IKEA. On top of this there are also some high end retailers who sell high-quality, well designed furniture. These high-end retailers often provide additional services like interior designing, home delivery and free set-up. The risk of global financial crisis The global is under a constant threat of depression since 2007. The whole economy of the world is suffering from a recession since fiscal year 2006-07. This economic condition may affect IKEA. Since the purchasing power of buyers has gone down they would be reluctant to purchase products that are not vital to them. This can cause a free-fall of sale revenue of IKEA worldwide; especially in USA ( Dahman J 2011). Reference Dahman, J 2011, IKEA’s Strategic Management, Scribd, viewed 12 October 2013,< http://www. scribd. com/doc/59951004/Case-Analysis-IKEA>. SWOT analysis of IKEA, IKEA’s Strategic management, viewed 11 October 2013, < http://www. strategicmanagementinsight. com/swot-analyses/ikea-swot-analysis. html>