| Papers [1-15] of 100 :: [Page 1 of 7] | | Go to page : 1 2 3 4 5 6 7 —> | Search results on "EXISTENCE UNIQUENESS THEOREM": |
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Existence and Uniqueness Theorem, 2002.
A study of the relationship and accuracy of the existence and uniqueness theorems.
1,835 words (approx. 7.3 pages), 3 sources, MLA, $ 58.95
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Abstract
This paper aims to provide information on generalization of existence and uniqueness theorem for ordinary differential equations (ODE). This contains mathematical definitions, notations, symbolisms, formulas, graphics, and equations of the theorems mentioned. A few examples were also provided to illustrate and prove the definitions of the theorems.
From the Paper
The fundamental theorem of Existence and Uniqueness answer the questions does a solution exists and is it unique. If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of solutions (by means of a so-called existence theorem) and then investigate their uniqueness (by means of a so-called uniqueness theorem). The solutions to an ordinary differential equation (frequently abbreviated as ODE) satisfy the existence and uniqueness properties.
The foundation of the theory of differential equations is the theorem on the existence of solutions for the initial value problem
x = f ( x ), x ( t o ) = x o
for a function x: R - Rn and f: Rn - Rn The main tool that we will use in developing our theory is the reformation of the differential equation as an integral equation. Suppose that both x(t) and f(x) are continuous functions. Then we can formally integrate both sides with respect to t to obtain:
x ( t ) = x o + ....
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National Uniqueness in East Asia, 2002.
A discussion of how the national uniqueness in East Asia is hindered by Chinese domination over the years.
1,400 words (approx. 5.6 pages), 3 sources, $ 53.95
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Abstract
This essay will argue that national uniqueness in East Asia is rendered unstable due to the historical domination of China over the region. As will be seen, this domination - political, economic, cultural, and linguistic - renders national distinctions and boundaries in the region unstable by definition.
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The Uniqueness of Italian-Americans, 2002.
Discusses the unique ethnic culture of the Italian-Americans and how they have contributed to the American cutlure.
1,900 words (approx. 7.6 pages), 7 sources, $ 71.95
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Abstract
At the beginning of the 20th century, Italian immigrants began coming to America in ever-increasing numbers. For more than 100 years, they have been one of the most "visible" ethnic groups in this country and have firmly planted their seal of ethnicity in everything from their food to their intellectual achievements. Like all other ethnic groups, they have enriched the culture of America and contributed substantially to the diversity we know and love.
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The Uniqueness of Hawaii's Economic Geography and the Effects of the Growing Economy on the Land, 2000.
At look at Hawaii under the following headings: recreation, tourism, agriculture, industry, transport. Examines the urbanization that is occurring due to the growth of the economy.
1,185 words (approx. 4.7 pages), 3 sources, $ 40.95
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Abstract
This paper presents the uniqueness of Hawaii?s economic geography and how it?s growing economy is forever altering the land.
From the Paper
"The Hawaiian islands are unique. Of course, it can be said that all places and regions are unique, since each differs in some particular way from its? surroundings. The unique differences of places and regions are what make the Earth an intriguing planet. "
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The Uniqueness of Hong Kong, 2006.
A reflection on emigration and immigration since the 1997 hand over of Hong Kong to the PRC.
2,700 words (approx. 10.8 pages), 6 sources, $ 106.95
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Abstract
This paper stresses Hong Kong's uniqueness as it is not quite a British or Chinese locality. The paper discusses how among its distinctive features, has been the pattern of human transit from the 1840s to the present, in waves of immigration and emigration. At the same time, Hong Kong appears to bestow a strong identity. The 1997 hand over prompted especially high emigration to Canada after the late 1980s, where a third phenomenon is found in persons seeking to return to Hong Kong.
From the Paper
"Through the 1990s, East Asia awaited the momentous hand over of the British crown colony of Hong Kong to the People's Republic of China (PRC). Mass media reports stressed the emigration of thousands from Hong Kong in persons said to fear Communist oppression. Other reportage referred to Hong Kong activists trying to ensure that the colony would retain freedoms known under British authority. Less expected, after the British departure was migration to Hong Kong on the part of Mainland Chinese and persons of diverse other origin in Asia and beyond."
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Mathematics: Fermat's Last Theorem, 2002.
This paper describes the interesting phenomenon called Fermat's Last Theorem, written in layman's terms.
613 words (approx. 2.5 pages), 5 sources, MLA, $ 21.95
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Abstract
Fermat's Last Theorem (FLT) has been one of the most fascinating theorems in mathematics. This paper looks at the conformities and the disparities of this statement. It assesses the theorem and the problem it comes to solve as well as the theorem's proof. It gives a detailed mathematical exercise which he solves using the theorem.
From the Paper
"Pierre de Fermat was born near Montauban in 1601. He was born in a family reared by a leather-merchant who was his father and was educated at home. He was essentially a lawyer and was an amateur mathematician. Throughout his life, Fermat published only one mathematical paper, which was written anonymously and appeared as an appendix to a book. He died in 1655."
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Godel's Theorem, 2007.
A review of Godel's theorem and the limitations of an allegory in trying to understand it.
1,495 words (approx. 6.0 pages), 5 sources, MLA, $ 49.95
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Abstract
This paper discusses Godel's theorem and how it is sometimes used to imply that all machine logic can eventually become self-aware. The paper also discusses the criticisms of the theorem and its limitations. The paper then provides an allegory to explain Godel's theorem and discusses the advantages of this explanation, as well as the limitations in using an allegory to try to understand the theorem.
Table of Contents:
Allegory and Godel: Oil and Water
From the Paper
"Godel recognizes that his theory in fact could not be fully described in human language and concepts and this is a fact that Hofstadter completely misses. When Godel is quoted as saying the epistemological descriptions in a given language cannot be restated in that same language, he directly disallows the use of allegory in retelling his theory. The unfortunate aspect of Hofstadter's allegory is that most readers get lost in trying to decide what the various characters represent, what is meant by the way the dialogue is spoken and, ultimately, what the Omega record player looks like. None of which, of course, has anything to do with Godel's Theorem."
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Godel's Theorem, 2008.
An analysis of the advantages of Godel's theorem within mathematics.
1,596 words (approx. 6.4 pages), 5 sources, MLA, $ 52.95
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Abstract
This paper explains Godel's theorem and its application to the machine mind. It describes the advantages of Godel's theorem in mathematics and how it is used in practice by mathematicians who lack understanding of a specific principle. The paper also provides the writer's opinion of the use of the theorem and suggests that it is almost commonsensical in nature.
Table of Contents:
Response to Postings
Discussion
From the Paper
"This could in fact be yet another referral to Cherniak's Riddle but that fact would only be left to the literary critic to decide and because human language is a series of referential signs and symbols that always refer to something else this could never be known absolutely. Here is the key difference in the two languages in question. When a mathematical principle is discovered and proven it is self evident to all and taken as fact. When a literary concept is created it is, conversely, always up for debate and its meaning always at play. Thus, Godel's theorem is both an apologetic and a principle best left explained in the language it was conceived in--mathematics."
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Fermat?s Last Theorem, 2001.
This paper takes a look at this mathematical theorem and how it has fascinated mathematicians for hundreds of years.
650 words (approx. 2.6 pages), 5 sources, MLA, $ 23.95
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Abstract
This paper briefly gives a background of Pierre de Fermat and states this famous theorem - FLT. It looks at a few working examples of problems related to the theorem and how mathematicians think that they have finally solved them.
From the Paper
"Pierre de Fermat was born near Montauban in 1601. He was born in a family reared by a leather-merchant who was his father and was educated at home. He was essentially a lawyer and was an amateur mathematician. Throughout his life, Fermat published only one mathematical paper, which was written anonymously and appeared as an appendix to a book. He died in 1655. (Ball) Fermat?s Last Theorem (FLT) has been one of the most fascinating theorems in mathematics. This theorem has been one the great, unsolved problems in this field for three hundred and fifty some years. Some experts believe, however, that the problem has been solved."
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Free Will in Godel's Theorem, 2006.
This paper discusses the concept and assertions of free will in Godel's Theorem.
1,125 words (approx. 4.5 pages), 4 sources, $ 44.95
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Abstract
This document discusses the Smullyan text, "Is God a Taoist?". The writer examines how its concept of free will is substantiated or invalidated by Godel's Theorem. The conclusion provided in this article is that this dialogue by Smullyan erroneously relies on Godel's Theorem to support his argument in that the reader is required to make assumptions regarding which characters are still undecided and at play.
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Godel's Theorem, 2005.
An analysis of the implications of Kurt Godel's theorem on mathematics.
900 words (approx. 3.6 pages), 3 sources, $ 35.95
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Abstract
This paper discusses Godel's theory on mathematical truths as being that they cannot be found in any set of axioms or rules and ultimate truth cannot be achieved. The paper suggests that Kurt Godel's incompleteness theorem encompasses the fact that all formal systems turn out to be incomplete by their very nature and it discusses the implications of this theory.
From the Paper
"Godel stated that there can be no proof of any statement (P). If P is true, there is no proof of it. If P is false, there is a proof that P is true. This is a contradiction. It cannot be decided whether P is true in a symbolic system."
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Godel's Theorem, 2008.
A discussion as the to the proof or lack thereof in support of Godel's theorem of the self-awareness of machines.
1,358 words (approx. 5.4 pages), 3 sources, MLA, $ 45.95
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Abstract
This paper discusses Godel's theorem and its lack of proof, absolute or otherwise, that machines do or may in the future experience self-awareness of one type or another. It discusses the assertions of the theory and the problems with it. The paper then provides a personal response, by the writer, to the issue of the present and future self-consciousness of machines.
Table of Contents:
Discussion
Response
From the Paper
"Free will is a concept that cannot be even remotely defined with any degree of consensus. Talking about free will with religious groups results in completely different concepts of free will than when talking with political groups or academic groups or any number of different types of groups. Conversely, arithmetic calculations are easy to quantify and easy to define within the confines of the overall system. Somehow Smullyan would like his readers to believe that defining free will is as self-apparent as 2 plus 2 or similar arithmetic equation. Some researchers have described Godel's Theorem as being some type of alternate description of a value system: "The system of values could be part of the program the computer followed in making its choices. The computer system would then appear to have those values, and be guided by them (Machina 3). Thus Smullyan's entire argument regarding free will is based on a number of unfounded and unproven assertions that have no basis except in extreme positives or negatives. These equate to a world that is either black or white and all decisions are, ultimately, yes or no questions."
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Godel and the "Theorem on Incompleteness", 2002.
Review of R. Rucker's discussion of the concept of infinity and how it relates to Godel's "Theorem on Incompleteness".
650 words (approx. 2.6 pages), 4 sources, $ 26.95
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Abstract
R. Rucker helps us better understand Godel's "Theorem on Incompleteness" by discussing infinity and whether it can be seen as a real entity. In his view, infinity can be seen as a tangible reality. He argues that it is quite possible that time may actually continue forever - and that is precisely what infinity is. Rucker also sees the possibility of the potential infinite divisibility of space into smaller and smaller pieces.
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Pythagoras and the Pythagorean Theorem, 2002.
This paper discusses the ancient Greek philosopher Pythagoras of Samos and the Pythagorean School
650 words (approx. 2.6 pages), 3 sources, $ 26.95
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Abstract
.The author examines the influence Pythagoras had on ancient learning, the Pythagorean Theorem, and the Pythagorean School, and notes that that the Pythagorean School was inspired by Pythagoras's genius. It was half religious and half scientific, and followed a code of secrecy which served its purpose in ancient times, but which has prevented historians from obtaining much information about Pythagoras other than through later second-hand sources.
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The Cultivation of a Unique Black Voice, 2002.
A look at the work of twentieth century Afro-American writers.
900 words (approx. 3.6 pages), 4 sources, $ 35.95
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Abstract
This paper discusses the dilemma faced by twentieth century Afro-American writers to either embrace or reject Anglo literary traditions and devices in their works. Gwendolyn Brooks and Zora Neale Hurston are used as examples.
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