Chaos theory Applications to PDEs (geometry design) Essay

Chaos theory Applications to PDEs (geometry design) - Essay Example 55). Therefore, there has been a growing demand for the development for a much stronger theory than for the finite dimensional systems. In mathematics, there are significant challenges in the studies on the infinite dimensional systems (Taylor, 1996; p. 88). For instance, as phase spaces, the Banach spaces have many structures than in Euclidean spaces. In application, the most vital natural phenomena are explained by the partial differential equations, most of important natural phenomena are described by the Yang-Mills equations, partial differential equations, nonlinear wave equations, and Navier-Stokes equations among others. Problem Statement Chaos theory has led to profound mathematical equations and theorems that have numerous applications in different fields including chemistry, biology, physics, and engineering among other fields or professions. Problem Definition The nonlinear wave equations are usually significant class of equations especially natural sciences (Cyganowski, K loeden, and Ombach, 2002; p. 33). They usually describe a wide spectrum of phenomena including water waves, motion of plasma, vortex motion, and nonlinear optics (laser) among others (Wasow, 2002). Notably, these types of equations often describe differences and varied phenomena; particularly, similar soliton equation that describes several different situations. These types of equations can be described by the nonlinear Schrodinger equation 1 The equation 1 above has a soliton solution 2 Where the variable This leads to 3 The equation leads to the development of the soliton equations whose Cauchy problems that are solved completely through the scattering transformations. The soliton equations are similar to the integrable Hamiltonian equations that are naturally counterparts of the finite dimensionalintegrable differential systems. Setting up the systematic study of the chaos theory in the partial differential equations, there is a need to start with the perturbed soliton equations (Wasow, 2002). The perturbed soliton equations can be classified into three main categories including: 1. Perturbed (1=1) dimensional soliton equations 2. Perturbed soliton lattices 3. Perturbed (1 + n) dimensional soliton equations (n? 2). For each of the above categories, to analyze the chaos theory in the partial differential equations, there is needed to choose a candidate for study. The integrable theories are often parallel for every member within the same category (Taylor, 1996; p. 102). Moreover, members of different categories are often different substantial. Therefore, the theorem that describes the existence of chaos on each candidate can be generalized parallely to other members under the same category (Wasow, 2002). For instance; The candidate in the first category is often described by a perturbed cubic that often focuses on the nonlinear Schrodinger equation 4 Under even and periodic boundary conditions q (x+1) = q (x) and q (x) =q (x), and is a real constant. The can didates in category 2 are often considered as the perturbed discrete cubic that often focus on the nonlinear Schrodinger equation + Perturbations, 5 The above equation is only valid under even and periodic boundary conditions described by +N = The candidates falling under category 3 are perturbed Davey-Stewartson II equations 6 The equation is only satisfied under the even and periodic

Classical Theory Essay Example for Free

Classical Theory Essay The Difference Between a Classical Management Theory a Human Relations Theory by Stacy Zeiger, Demand Media Human relations theory seeks to develop satisfied employees. Classical management theory and human relations theory represent two views of management on the opposite ends of the spectrum. One view focuses on looking at workers solely as a means to get work done, while the other focuses on developing an organization and the behaviors and motivations of employees. Most managers find that a combination of the two theories serves them best in their businesses. Ads by Google Ssangyong Korando Special New Offer On SsangYong Korando From Only R2499p/m. Enquire Online Now! www.ssangyongdeals.co.za What is Classical Management Theory? Classical management theory involves creating multiple levels of workers to improve productivity. Employees at the lowest levels find their tasks overseen by supervisors who, in turn, are overseen by managers. At every level, employees are expected to perform tasks according to specific procedures designed to maximize productivity. In addition, this theory focuses on an impersonal side of business. Employees and managers should not allow friendliness and personal interactions to become involved with the organization. Rules must be followed exactly, and the hiring and firing of employees must relate only to the skills they possess. Pros and Cons of Classical Management Theory Classical management theory is not used in many organizations because of its shortcomings. While some components of the theory, such as designing procedures for completing a task and keeping personal issues out of business, help an organization focus on the job at hand, the theory fails to recognize the differences among employees. When employee feelings and opinions are not taken into account, the business may not grow or may experience high levels of employee turnover as employees fail to develop a relationship with the business and leave in search of a more satisfying job. What is Human Relations Theory? Human relations theory, also known as behavioral management theory, focuses more on the individuals in a workplace than the rules, procedures and processes. Instead of directives coming directly from management, a human relations theory provides communication between employees and managers, allowing them to interact with one another to help make decisions. Instead of giving workers quotas and requiring certain procedures, workers are exposed to motivational and emotional tactics to get them to increase productivity. The focus of this style is creating fulfilled, productive workers and helping workers invest in a company. Pros and Cons of Human Relations Theory While many companies operate based on the human relations theory, this type of management has dangers. Companies risk workers becoming too social or easily swayed by personal emotions and opinions when making decisions, rather than relying on hard data. It may be more difficult to reprimand employees for poor performance or dismiss them once they have become invested in the company. Despite these risks, human relations theory has the potential to increase employee retention rates and productivity. As employees feel more valued by a company, they invest in that company and its greater good.

Men, Football, and TV Essay -- Sports Televison

Men, Football, and TV By a series of surveys, interviews, and looking at people’s personal history I will prove that even though some women enjoy watching football, a higher majority of men enjoy watching football more than women because most men grow up watching football. Because most men grow up watching football it is a logical conclusion that they would continue to watch it when they grow up. On the other hand most women do not grow up watching football so it is logical to conclude that since they do not watch it when they are young they have no reason to watch it when they grow up. It is my opinion that men enjoy watching football more than women do. I know that some women do watch football; however, I believe they watch it for different reasons than men do. I decided that this would be an interesting topic for a research paper because I believe that football is a more masculine sport that most males grow up watching with other males in their households. They continue to primarily watch football with males, as they grow older. I used many different methods in determining if my thesis was correct. I took surveys, conducted interviews, and looked at each individual’s personal history to try to support my thesis. By using these different methods I tried to eliminate possible error. I interviewed a male and female student about the game of football to see if gender plays a role in determining whether football attracts more males or females. I then surveyed five women and five men. One male student told me that he only began watching football this season because of his roommate. He stated that even though he watched football with his father when he was younger, he... ...they told me it was not to support a team but rather they like how it feels and they like how certain jerseys match their clothes. I asked the men if they buy football memorabilia. They responded that they have bought some football jerseys but they would only buy jerseys of their favorite teams or favorite players. My final conclusion is that personal history plays a role in whether or not men and women watch football. All the men who told me their personal history told me that they watched football when they were young and most of the men still watch it to this day. All of the women told me that they did not watch football when they were young. When asked if they watch it now many said no and some said that they watch it every once in a while. Because of this I concluded that personal history plays a role in whether or not men and women watch football.

What is racism?

What is racism? Is there still racism going on in the United States and even outside the United States? These are two questions that are often asked and discussed across the world in classroom settings. The definition of racism is the belief that members of a certain race are accounted for differences in human characteristics. Also, discrimination or prejudice is based on race. People all over the world still are facing racism until this day especially the people of the African diaspora. Whether you are half black or full black if you are part of that â€Å"One Drop† rule you are going to face some type of racism. Racism is a problem throughout Africa, Brazil, and Canada, and the United States. Many people like Marcus Garvey and Malcolm X has been leaders of powerful organizations that have fought against racism. Africa, of course is the motherland of Africans in the diaspora. You wouldn’t imagine Africa facing racism, but yes they do just as African Americans in the US. There are some white South Africans who treat the black South Africans as if they are in the United States. One example is the movie Skin. In this movie a little girl was born to two white South African parents, but had the complexion of a black South African. When she was enrolled in private white school the teachers, students, and administration looked down on her as if she wasn’t white and born to white parents. Even though her skin tone was of black, she was still white. Although she attended court, the court appealed that she was black and not white, but of course her parents fought until they appealed that she was white. Also, in this movie her father would give black South Africans hard times especially when one wanted to date her daughter. Even though, she was declared white and her birth certificate said the same that didn’t change a thing when she went out into the real world she was still looked upon as black. Brazilians are part of the African Diaspora as well so they also go through a time of racism. In Brazil it’s more on a different level as far as who you would marry or have sex with. Brazilian men would go for the white women to marry, the mulatto women for sex, and the leave black women to work. Why is that? Why can’t the black women give the men the same as the white and mulatto women? Canadian blacks go through the racism stage also. Canadian black women undergo through a laboring problem. Even though these African immigrants have some the best skills and high educational backgrounds they are forced to engage in low-paying jobs. Now, in the United States some of these things happen in the U. S. also, and if not worst. Dating back in history racism has occurred with not only African-Americans, but also with Native Americans and even Latinos and Hispanics. The most common form of racism happened with African-Americans starting with slavery era. Once slavery ended, white Americans still treated blacks like blacks were still inferior. Also, they didn’t treat them equally and the fact that they weren’t slaves anymore. The way black South Africans, African Immigrants in Canada, and Afro-Brazilians were treated is a bit less tense than the way African-Americans were treated. The racism here in the U. S. was a lot tenser. Racism in the U. S. has been going on for eras and still is a problem. Certain areas more in particular the south, are still lynching, killing, and beating blacks just because the color of their skin. Another issue is gang violence. Blacks are fighting black on black just because the color they are wearing. Rodney King is one huge example of racism that has occurred in Black American history where he was nearly beaten to death by four white police officers. Rosa Parks the black woman who refused to sit in the back of the bus along with the other blacks was another example of racism. Many African-Americans came together and made organizations that could possibly contribute to America’s Society. Without these leaders or organizations black America would not be where it is today. Many African-Americans have been major leaders of organizations that have fought against racism. A few of these leaders were Malcolm X, Marcus Garvey, and his wife Amy Garvey. Marcus Garvey led the largest mass organization of black people ever until this day. The name of this is called Universal of Negro Improvement Association also known as UNIA. Malcolm X mother worked for Marcus Garvey. Malcolm X preached self-determination, â€Å"Black Nationalism† which he is saying â€Å"do for yourself. † Malcolm X was the founder of the OAAU, which is the Organization of Afro-American Unity. This organization is a Pan-Africanist organization whose purpose was to fight for human rights of African Americans. Malcolm was basically trying to â€Å"un-brainwash† blacks from the lies the white people have said about blacks and their culture. Amy Garvey which was Marcus Garvey’s wife followed him in his footsteps as he preached Pan-Africanism. She taught Pan-Africanism on a more womanly level to help with the women. Also, she encouraged women to educate themselves and perform as leaders in their community. She also believed that Pan-Africanism would empower women to confront racism, colonialism, and imperialism and to have a masculine dominance as well. Marcus Garvey, Amy Garvey, and Malcolm X have really given a lot of attributions and contributions to the African-American history. These leaders has really help shape the United States against racism and helped express their feelings on why black Americans should be respected the same. As far as racism, it will forever continue go on throughout the United States and also outside the United States. As a young person, I have yet to experience racism other than little white kids joking around. I hope that I won’t have to experience racism because this world is changing and I hope it changes to the better and not worst.

Is It Better to Be a Member of a Group Than to Be the Leader?

ESSAY Do you agree with the following statement? It is better to be a member of a group than to be the leader of a group. Use specific reasons and examples to support your answer. I personally disagree with the statement that it is better to be a member of a group than a leader. It is true that being a member is certainly much more comfortable, as you have less responsibility, and you are not the one who makes the final decisions.Also, some people may be too shy, too reserved or not charismatic enough to become a leader. However, in my opinion, a leader is a member too, but a leader does more. First of all, a leader takes responsibility for making decisions and guiding the others in a certain direction. The second reason is that if you take the responsibility of being the leader, you are more active. Thus, your participation in the group is much more interesting and exciting.You are more concerned about what is happening around you, and you do not just wait for other people to do eve rything. In other words, you are not passive, and you get involved. Finally, if you are a good leader, then the others will respect you, and gaining people’s respect is important if you want to have a good place in society. As a conclusion, I would say that, to me, it is more interesting to be a leader than to be only a member, as it can be so much more stimulating and enriching for your personal and professional life.