Free Essays on Elliptic Functions

The terminology for elliptic integrals and functions has changed during their investigation. What were originally called elliptic functions are now called elliptic integrals and the term elliptic functions reserved for a different idea. We will therefore use modern terminology throughout this article to avoid confusion. It is important to understand how mathematicians thought differently at different periods. Early algebraists had to prove their formulas by geometry. Similarly early workers with integration considered their problems solved if they could relate an integral to a geometric object. Many integrals arose from attempts to solve mechanical problems. For example the period of a simple pendulum was found to be related to an integral which expressed arc length but no form could be found in terms of 'simple' functions. The same was true for the deflection of a thin elastic bar. The study of elliptical integrals can be said to start in 1655 when Wallis began to study the arc length of an ellipse. In fact he considered the arc lengths of various cycloids and related these arc lengths to that of the ellipse. Both Wallis and Newton published an infinite series expansion for the arc length of the ellipse. At this point we should give a definition of an elliptic integral. It is one of the form r(x, p(x) )dx where r(x,y) is a rational function in two variables and p(x) is a polynomial of degree 3 or 4 with no repeated roots. In 1679 Jacob Bernoulli attempted to find the arc length of a spiral and encountered an example of an elliptic integral. Jacob Bernoulli, in 1694, made an important step in the theory of elliptic integrals. He examined the shape the an elastic rod will take if compressed at the ends. He showed that the curve satisfied ds/dt = 1/(1 - t4) then introduced the lemniscate curve (x2+y2)2 = (x2-y2) whose arc length is given by the integral from 0 to x of dt/(1 - t4) This integral, whi... Free Essays on Elliptic Functions Free Essays on Elliptic Functions The terminology for elliptic integrals and functions has changed during their investigation. What were originally called elliptic functions are now called elliptic integrals and the term elliptic functions reserved for a different idea. We will therefore use modern terminology throughout this article to avoid confusion. It is important to understand how mathematicians thought differently at different periods. Early algebraists had to prove their formulas by geometry. Similarly early workers with integration considered their problems solved if they could relate an integral to a geometric object. Many integrals arose from attempts to solve mechanical problems. For example the period of a simple pendulum was found to be related to an integral which expressed arc length but no form could be found in terms of 'simple' functions. The same was true for the deflection of a thin elastic bar. The study of elliptical integrals can be said to start in 1655 when Wallis began to study the arc length of an ellipse. In fact he considered the arc lengths of various cycloids and related these arc lengths to that of the ellipse. Both Wallis and Newton published an infinite series expansion for the arc length of the ellipse. At this point we should give a definition of an elliptic integral. It is one of the form r(x, p(x) )dx where r(x,y) is a rational function in two variables and p(x) is a polynomial of degree 3 or 4 with no repeated roots. In 1679 Jacob Bernoulli attempted to find the arc length of a spiral and encountered an example of an elliptic integral. Jacob Bernoulli, in 1694, made an important step in the theory of elliptic integrals. He examined the shape the an elastic rod will take if compressed at the ends. He showed that the curve satisfied ds/dt = 1/(1 - t4) then introduced the lemniscate curve (x2+y2)2 = (x2-y2) whose arc length is given by the integral from 0 to x of dt/(1 - t4) This integral, whi...

Definition and Examples of Word Triplets in English

Definition and Examples of Word Triplets in English In  English grammar  and  morphology, triplets  or word triplets are three distinct words derived from the same source but at different times and by different paths, such as place, plaza, and piazza (all from the Latin platea, a broad street). In most cases, such words have the same ultimate origin in Latin. Captain, Chief,andChef The triplets wont necessarily be obvious just by looking at the words but will take a little investigation for their relationship to come clear. English words encode interesting and useful historical information. For example, compare the words captainchiefchef All three derive historically from cap, a Latin word element meaning head, which is also found in the words capital, decapitate, capitulate, and others. It is easy to see the connection in meaning between them if you think of them as the head of a vessel or military unit, the leader or head of a group, and the head of a kitchen respectively. Furthermore, English borrowed all three words from French, which in turn borrowed or inherited them from Latin. Why then is the word element spelled and pronounced differently in the three words?The first word, captain, has a simple story: the word was borrowed from Latin with minimal change. French adapted it from Latin in the 13th century, and English borrowed it from French in the 14th. The sounds /k/ and /p/ have not changed in English since that time, and so the Latin element cap-  /kap/ remains substantially intact in that word.French did not borrow the next two words from Latin...French developed from Latin, with the grammar and vocabula ry being passed down from speaker to speaker with small, cumulative changes. Words passed down in this way are said to be inherited, not borrowed. English borrowed the word chief from French in the 13th century, even earlier than it borrowed captain. But because chief was an inherited word in French, it had undergone many centuries of sound changes by that time...It was this form that English borrowed from French.After English borrowed the word chief, further changes took place in French...Subsequently English also borrowed the word in this form [chef]. Thanks to the linguistic evolution of French and the English propensity to borrow words from that language, a single Latin word element, cap-, which was always pronounced /kap/ in Roman times, now appears in English in three very different guises. (Keith M. Denning, Brett Kessler, and William R. Leben, English Vocabulary Elements, 2nd ed. Oxford University Press, 2007) Hostel, Hospital, and Hotel Another example [of triplets] is hostel (from Old French), hospital (from Latin), and hotel (from modern French), all derived from the Latin hospitale. (Katherine Barber, Six Words You Never Knew Had Something to Do With Pigs. Penguin, 2007) Similar but From Different Sources The resulting English triplets might not even look similar, depending on the route they took to get to English. The simultaneous borrowing of French and Latin words led to a highly distinctive feature of modern English vocabulary: sets of three items (triplets), all expressing the same fundamental notion but differing slightly in meaning or style, e.g., kingly, royal, regal; rise, mount, ascend; ask, question, interrogate; fast, firm, secure; holy, sacred, consecrated. The Old English word (the first in each triplet) is the most colloquial, the French (the second) is more literary, and the Latin word (the last) more learned. (Howard Jackson and Etienne Zà © Amvela, Words, Meaning and Vocabulary: An Introduction to Modern English Lexicology. Continuum, 2000)Still more remarkable is the fact that there are in our language words that have made three appearances- one through Latin, one through Norman-French, and one through ordinary French. These seem to live quietly side by side in the language, and no one asks by what claim they are here. They are useful; that is enough. These triplets are- reg al, royal, and real; legal, loyal, and leal; fidelity, faithfulness, and fealty. The adjective real we no longer possess in the sense of royal, but Chaucer uses it...Leal is most used in Scotland, where it has a settled abode in the well-known phrase the land o the leal. (J.M.D. Meiklejohn, The English Language, Its Grammar, History, and Literature.  12th ed. W.J. Gage, 1895)

Decision Making Assignment Essay Example | Topics and Well Written Essays - 1500 words

Decision Making Assignment - Essay Example Value refers to what one visualizes significance in life that is, what is right or valuable in life. Values provides priorities setting base for deciding worthwhile actions and goals and less important ones and thus gives meaning to the life’s of people. By knowing the values of a family for example, the members of the family can decide on the goals, make the required and critical decisions and subsequently take the needed action which can meet the predetermined goals. Some differences and individual conflicts have to be resolved by establishing the best way while forming a basis for the family values using the individual values. A decision maker must be acquitted on the environment on which the decisions are being made. The environment comprises of opportunities, limitations and change possibility. Where there is presence of only one course of alternative, there can be no decision to be made. One possible alternative can not constitute a decision making process. In existence of limited choice, where one has a choice of selecting to undertake an action or to decline taking action, there is involvement of decision making in such a situation. Primarily, the decisions can concern personal or individuals while others can involve the community wholly or the society at large. The other decisions may engage group members. A group of members carry easily, acceptable decisions more efficiently if involved in the process of decision making. If there is suggestion of more available alternatives and options that are not productive as identified earlier, group decisions are always better. Decisions may be reached through dominance that is, submission where the situation is dominated by one person and others consent with the decision as it is made. This is however, given the name to as win-lose situation. A win-win situation can also be adopted through what is called conversions. Additional points of facts are brainstormed, presented, and the person persuades the othe rs members of the group. Through integration, decisions can be reached through synthesis of the developed ideas which can be agreed upon and supported by everyone. They are many types of decisions which can be differentiated by their content. These types includes social and in other terms human decisions which involves goal setting and the various priorities that determine and influence the individuals general roles and the relationships of the group individuals. Decisions involving allocation of resources and distribution of these available resources among the various set goals are economic and in other term can be called allocation decisions. Another type of a decision is technical decisions which describes what, how, who, when, and why to accomplish a specific task and also regarding the efficient allocation of resources to attain a single goal. The other type of a decision relates to social economic and technical matters. They can be called coordination and interaction decisions because they deal with family communications and also the larger community and the kind of the needed information, while making other decisions, and way of motivating people to carry out their roles. Decisions are not dependent and also interrelated among each other. This makes the decision making process to be termed as dynamic. Decisions are often affected by and affects other decisions at appoint in time. There are models used

Ethical Leadership Martin Luther King Jr Essay Example | Topics and Well Written Essays - 1750 words

Ethical Leadership Martin Luther King Jr - Essay Example Ethical leadership is about the quality of a leader to fight for the ethics which is applicable for everybody. This is really shown in the life of Martin Luther King Jr., whose says that "In struggling for human dignity the oppressed people of the world must not allow themselves to become bitter or indulge in hate campaigns. To retaliate with hate and bitterness would do nothing but intensify the hate in the world. Along the way of life, someone must have sense enough and morality enough to cut off the chain of hate. This can be done only by projecting the ethics of love to the center of our lives" "There are two types of laws: there are just laws and there are unjust laws...What is the difference between the two...An unjust law is a man-made code that is out of harmony with the moral law. The ultimate test of a man is not where he stands in moments of comfort and moments of convenience, but where he stands in moments of challenge and moments of controversy." (quietspaces.com n.pag) His purpose in life was to give the true meaning of freedom and he had taken the path of non-violence to achieve it. He had studied the life great leader Mahatma Gandhi, who also achieved freedom for his nation through the means of nonviolence. With this ethical means he fought against discrimination and racialism particularly, towards the black or the Negro community in United States. He fought for their rights by telling the suppressing community the true meaning of freedom that is equality in all human being without the discrimination in color of skin. Martin Luther King even while he was a student he was known for his leadership qualities and was rewarded several times. He was elected president of the senior class and delivered the valedictory address; he won the Pearl Plafker Award for the most outstanding student; and he received the J. Lewis Crozer fellowship for graduate study at a university of his choice. Dr. King was awarded honorary degrees from a number of colleges and universities in the United States and several other foreign countries (Brown et al. n.pag 2006). Martin Luther King also followed his father's and grandfather's steps and entered the Christian ministry. He was ordained in February 1948 at the age of nineteen at Ebenezer Baptist Church, Atlanta, Georgia and became Assistant Pastor of Ebenezer. Soon after the completion of his studies at Boston University, he accepted the call of Dexter Avenue Baptist Church, Montgomery, Alabama (Brown et al. n.pag 2006). Psychological research has discovered the following positive personality variables associated with strong leadership includes warmth, friendliness, self-confidence, ability to stand up to pressure. These researches have also found that the absence of the negative qualities of arrogance, hostility, boastfulness, egotism, and passivity are correlated with positive leadership (Romney, 1996). If we look into the life of King, it can be said that he is among the top leaders of the world. He was always a strong worker for civil rights for members of his race as a member of the executive committee of the National Association for the Advancement of Colored People. The Montgomery Bus Boycott, in 1955 led by King lasted for 382 days and was among ones in which he was arrested, his home was bombed, he was subjected to personal abuse. King was arrested during this campaign, which ended with a United States Supreme Court decision

Terrorism :: Terrorist

Terrorism The Good, the Bad, the Terrorist? Terrorism by nature is difficult to define. Acts of terrorism conjure emotional responses in the victims as well as in the practitioners. No two writers agree on what is terrorism. Even the U.S. government cannot agree on one single definition. The old adage, "One man's terrorist is another man's freedom fighter" is still alive and well today ("Terrorism Research Center: Definitions" 1). Although many people believe that terrorism is evil, it is merely misunderstood because there is no set definition. Terrorists are responsible to most of the freedom movements in every country. Terrorists have used violence to get their point across to the public. These acts are often necessary for the success of the movement or cause. The use of this violence can be justified in several ways. You can't make an omelet without breaking some eggs has been used by terrorist to describe their actions.

Employment Laws Chart Essay

Prevents discrimination of the hiring, compensation, conditions, and privileges of employment by basing them on on race, religion, color, sex, or nationality Heart of Atlanta Motel INC., v. United States  ensures every person is equal chance of getting hired based on their qualifications regardless of, sex race, color, religion, or national origin employers are required to post signs with the Title VII contents in company break-rooms Equal Employment Opportunity Act Prevents employers from discriminating against employees on the basis of age, race, sex, creed, religion, color, or national origin McDonnell Douglas Corp. v. Green Ensures that the Civil Rights Act is being followed and gives power to the Equal Opportunity Employment Commission Companies adopted practices that prevented discrimination in compliance with Equal Opportunity Employment Act. Equal Pay Act  mandates that men and women working in the same role within a company be given equal pay for equal work Schultz v. Wheaton Glass Co. 1970 Mandates that everyone is paid the equal wages for identical jobs regardless of their sex Merit based, knowledge based, and experience are criteria for pay rate rather than gender Age Discrimination in Employment Act of 1967 Protects employees ages 40 to 65 from discrimination Gomez v. Potter The importance of the ADEA is that it protects the older employees from discrimination. Wal-Mart for example hires older people specifically for the use as door greeters Americans with Disabilities Act of 1990 Prohibits discrimination against an essentially qualified individual, and requires companies to accommodate individuals reasonably Tennessee v. Lane in 2004 The importance of this act is that it requires companies to make reasonable accommodations for disabled employees so they will be able to perform their job Companies accommodate employees with disabilities by using TTD, speaking technology, and elevators Civil Rights Act of 1991 The updated version of this act nullified select supreme Court decisions and reinstates burden of proof by employer and allows for punitive and compensatory damages through jury trials Wards Cove Packing Co. v. Atonio Family and Medical Leave Act (FMLA) of 1993 Permits employees in organizations of 50 or more workers to take up to 12 weeks of unpaid leave for circumstances outlined in the act The importance of this act is that it makes it easier to balance family, work and other obligations without fearing losing their jobs If you have a child, adopt a child, or if you yourself become sick or have a sick parent, child, or spouse you may be eligible to take unpaid time off to be with them without the job loss. Privacy Act of 1974 protects certain federal government records pertaining to individuals. In particular, the Act covers systems of records that an agency maintains and retrieves by an individual’s name or other personal identifier Individuals have the right to look at their employee file to make sure that information is accurate Drug-Free Workplace Act of 1988 This act requires some federal contractors and all federal grantees agree that they will provide drug free workplaces as a precondition of receiving a contract or grant from the Federal Government Enacted by Congress as part of an anti-drug legislation in 1988 The importance of this act is that it ensures the safety of all employees by ensuring that no one will be working while under the influence of drugs Drug testing as part of an application process and if an employee is hurt on the job most companies require a drug test when they go to the hospital Polygraph Protection Act of 1988 Prohibits employers to use polygraph tests in a job application process On June 27, 1988, Congress enacted the Employee Polygraph Protection Act 1 to regulate the use of lie detector devices in the workplace The importance of this act is that it protects employees from violating privacy issues by  asking non job related It is unreasonable for employers to give potential employees polygraph test Worker Adjustment and Retraining Notification Act (WARN) of 1988 Makes sure that employers give notification to employees about plant closings or lay-offs This became law without President Ronald Reagan’s signature through the use of veto-proof Democratic majority in Congress The importance of this law is to protect employees because of a shut down or layoff, requiring employees be given a 60-day notice ease the burden of losing their jobs, some companies give severance packages based on the employees years of service with the company

History Of Burger Fuel Restaurant And Restaurant Services...

LINGUIS INTERNATIONAL INSTITUTE NAME:- MANPREET KAUR ASSIGNMENT NO.: - 23912 SUBMITTED TO :- MONA RANI DIPLOMA IN BUSINESS LEVEL -6 The history of Burger Fuel restaurants in New Zealand Who are we?- In 1995, the first Burger Fuel was opened in Auckland. In 2007, the company Burger Fuel Worldwide publicly floated on the syringe Eileen. On 5 May 2008, the company Burger Fuel Worldwide has announced that it has agreed its first master franchise agreement with Al Khayyat Dubai-based investment group investing LLC. They will set up and operate stores in Dubai, UAE at the end of this year. Dubai is considered as high a profile for Burger Fuel. Today, The World Burger Fuel is a restaurant and restaurant services, which provides an opportunity for firms with significant growth and other benefits combined. 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