21. Clay Mathematics Institute Article by Enrico Bombieri (PDF) and video by Jeff Vaaler (.ram) from the Clay Mathematics Institute. http://www.claymath.org/millennium/Riemann_Hypothesis/

Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME ABOUT CMI PROGRAMS AWARDS ... PUBLICATIONS Riemann Hypothesis Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 - 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function s s s called the Riemann Zeta function . The Riemann hypothesis asserts that all interesting solutions of the equation lie on a certain vertical straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers. The Millennium Problems Lecture by Jeff Vaaler at the University of Texas (video) Facsimile of Riemann's 1859 manuscript Return to top Contact Search Clay Mathematics Institute

22. Louis De Branges: Home Purdue University. Proposed solution for the Riemann hypothesis (pdf format). http://www.math.purdue.edu/~branges/

Department of Mathematics About Us Faculty Emeritus Faculty ... Home Louis de Branges Home Papers Publications PhD: Cornell University 1957 Title: Edward C. Elliott Distinguished Professor of Mathematics Professional Interests: complex analysis, Fourier analysis, functional analysis Office: MATH 800 Phone: Email: Homepage: http://www.math.purdue.edu/~branges/ Home Papers Publications Department of Mathematics, Purdue University 150 N. University Street, West Lafayette, IN 47907-2067 Phone: (765) 494-1901 - FAX: (765) 494-0548 Contact the Webmaster West Lafayette, IN 47907 USA, 765-494-4600 An equal access/equal opportunity university Contact the Webmaster to address accessibility issues.

23. Hypothesis Explanation hypothesis invites authors to submit new and thoughtprovoking predictions based on scientific findings or theories from any field. http://hypothesisjournal.com/

User Username Password Remember me Journal Content Search All Authors Title Abstract Index terms Full Text Browse By Issue By Author By Title Font Size Home About Log In Register ... Vol 8, No 1 (2010) Hypothesis Mission: To elicit healthy scientific thought by disseminating stimulating and novel scientific progress and hypotheses in any field. Explanation: Hypothesis invites authors to submit new and thought-provoking predictions based on scientific findings or theories from any field. We aim to establish an interdisciplinary journal that swiftly publishes new, provocative, and sometimes currently untestable ideas, while preserving the free-thinking nature of the earliest scientific publications. Thus, Hypothesis favours publication of articles that go beyond reporting data or summarizing a body of work, providing a vessel for thoughtful speculation and healthy debate where authors can freely articulate their most exciting ideas. Moreover, by challenging authors to create intriguing hypotheses concerning their reviewed or original research, Hypothesis is committed to publishing entertaining articles suitable for all readers.

24. Hypothesis Encyclopedia Topics | Reference.com Copy paste this link to your blog or website to reference this page http://www.reference.com/browse/hypothesis

25. The Riemann Hypothesis A short article by Kimon Spiliopoulos. http://users.forthnet.gr/ath/kimon/Riemann/Riemann.htm

The Riemann Hypothesis Riemann's Hypothesis was one of the 23 problems - milestones that David Hilbert suggested in 1900, at the 2nd International Conference on Mathematics in Paris, that they should define research in mathematics for the new century (and indeed, it is not an exaggeration to say that modern mathematics largely come from the attempts to solve these 23 problems). It is the most famous open question today, especially after the proof of Fermat's Last Theorem The Riemann zeta function is of central importance in the study of prime numbers. In its first form introduced by Euler, it is a function of a real variable x: This series converges for every x > 1 (for x=1 it is the non-corvergent harmonic series). Euler showed that this function can also be expressed as an infinite product which involves all prime numbers p n , n=1,… Riemann studied this function extensively and extended its definition to take complex arguments z. So the function bears his name. Of particular interest are the roots of Trivial zeros are at z= -2, -4, -6, …

26. Hypothesis - What Is A Hypothesis A hypothesis is a tentative statement about the relationship between two or more variables http://psychology.about.com/od/hindex/g/hypothesis.htm

zWASL=1;zGRH=1 zGCID=this.zGCID?zGCID+" test11":" test11" zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') zDO=0 Home Education Psychology Psychology Search Psychology Basics Theories Experiments ... Share w(x2+zWl+'?p=1" zT="18/1[N" rel="nofollow">Print') Free Psychology Newsletter! Sign Up Discuss in my Forum By Kendra Cherry , About.com Guide See More About: hypothesis theory psychology research methods zSB(3,3) Definition: Definition: A hypothesis is a tentative statement about the relationship between two or more variables . A hypothesis is a specific, testable prediction about what you expect to happen in your study. For example, a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states, "This study is designed to assess the hypothesis that sleep deprived people will have perform worse on a test than individuals who are non sleep deprived." Unless you are creating a study that is exploratory in nature, your hypothesis should always explain what you expect to happen during the course of your experiment or research.

27. Riemann A short article with some graphical and numerical evidence in the critical strip. http://www.mathpuzzle.com/riemann.html

The Riemann Hypothesis is currently the most famous unsolved problem in mathematics. Like the Goldbach Conjecture (all positive even integers greater than two can be expressed as the sum of two primes), it seems true, but is very hard to prove. I did some playing around with the Riemann Hypothesis, and I'm convinced it is true. My observations follow. The Zeta Function Euler showed that z p 6 , and solved all the even integers up to z (26). See the Riemann Zeta Function in the CRC Concise Encyclopedia of Mathematics for more information on this. It is possible for the exponent s to be Complex Number ( a + b I). A root of a function is a value x such that f x The Riemann Hypothesis : all nontrivial roots of the Zeta function are of the form (1/2 + b I). Mathematica can plot the Zeta function for complex values, so I plotted the absolute value of z b I) and z b I). z b I) for b = to 85. Note how often the function dips to zero. z b I) for b = to 85. Note how the function never dips to zero. The first few zeroes of z b I) are at b = 14.1344725, 21.022040, 25.010858, 30.424876, 32.935062, and 37.586178. Next, I tried some 3D plots, looking dead on at zero. The plot of the function looked like this:

28. Hypotheses Oct 20, 2006 An hypothesis is a specific statement of prediction. It describes in concrete ( rather than theoretical) terms what you expect will happen in http://www.socialresearchmethods.net/kb/hypothes.php

SEARCH: Previous Home Next Home ... Language Of Research Hypotheses An hypothesis is a specific statement of prediction. It describes in concrete (rather than theoretical) terms what you expect will happen in your study. Not all studies have hypotheses. Sometimes a study is designed to be exploratory (see inductive research ). There is no formal hypothesis, and perhaps the purpose of the study is to explore some area more thoroughly in order to develop some specific hypothesis or prediction that can be tested in future research. A single study may have one or many hypotheses. Actually, whenever I talk about an hypothesis, I am really thinking simultaneously about two hypotheses. Let's say that you predict that there will be a relationship between two variables in your study. The way we would formally set up the hypothesis test is to formulate two hypothesis statements, one that describes your prediction and one that describes all the other possible outcomes with respect to the hypothesized relationship. Your prediction is that variable A and variable B will be related (you don't care whether it's a positive or negative relationship). Then the only other possible outcome would be that variable A and variable B are not related. Usually, we call the hypothesis that you support (your prediction) the

29. PAH World Hypothesis - Wikipedia, The Free Encyclopedia Artist Vangelis Rating Release Date 1978 Genre Electronica Review A 1971 experimental jazz performance featuring Vangelis and a small band. The music appears to wander in http://en.wikipedia.org/wiki/PAH_world_hypothesis

PAH world hypothesis From Wikipedia, the free encyclopedia Jump to: navigation search The PAH world hypothesis is a speculative theory that proposes that polycyclic aromatic hydrocarbons (PAH), assumed to be abundant in the primordial soup of the early Earth , played a major role in the origin of life by mediating the synthesis of RNA molecules, leading into the RNA world . As yet it is untested. A PAH stack assembling Contents Background Polycyclic aromatic hydrocarbons Attachment of nucleobases to PAH scaffolding Attachment of oligomeric backbone ... edit Background The Miller–Urey experiment showed that organic compounds can be readily produced under the presumed conditions of the early Earth The Miller–Urey experiment in 1952, and others since, demonstrated the synthesis of organic compounds , such as nucleobases amino acids formaldehyde and sugars , from the original inorganic precursors presumed to have been present in the primordial soup . The RNA world hypothesis shows how RNA can become its own catalyst (a ribozyme ), and so become the basis for evolution of life. In between there are some missing steps such as how the first RNA molecules could be formed. The PAH world hypothesis was proposed by Simon Nicholas Platts in May 2004 to try to fill in this missing step.

30. Hypothesis hypothesis is at the core of research and needs careful understanding. Here's some handy notes. http://changingminds.org/explanations/research/initiation/hypothesis.htm

Changing Minds .org How we change what others think, feel, believe and do Disciplines Techniques Principles Explanations ... Links Now, you can buy the real book! Look inside Can you easily help the site? Add/share/save this page: addthis_pub = 'dmstraker'; Save the rain Hypothesis Explanations Social Research Initiation Definition ... See also Hypotheses are are the heart of much social research. Here's some useful notes about them. Definition A hypothesis is a predictive statement. A researcher starts with a hypothesis and determines whether it is true or false, and the conditions for truth or falsehood. Where there are several hypotheses, they are often abbreviated with a capital 'H' and a subscript (often a number). Primary hypothesis The primary (or alternative hypothesis (or just the first in a long list) is often written as H Experiments often seek to prove the primary hypothesis to be true and may be considered to have 'failed' if this is not achieved. In reality, an experiment succeeds when it correctly concludes that the primary hypothesis is true or false. It only fails when its conclusions are incorrect (or that a correct conclusion is incorrectly reached). Null hypothesis The null hypothesis (often written as H ) is the opposite of the primary hypothesis in that it includes all other outcomes.

31. The Riemann Hypothesis Some of the conjectures and open problems concerning RH, compiled by the AIM. http://aimath.org/WWN/rh/

The Riemann Hypothesis This web page highlights some of the conjectures and open problems concerning The Riemann Hypothesis. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. What is an $L$-function? Terminology and basic properties Functional equation Euler product ... Examples Dirichlet series associated with Maass forms Higher rank L-functions The Selberg class Dirichlet series Analytic Continuation Functional Equation ... Selberg Conjectures Analogues of zeta-functions Dynamical zeta-functions Spectral zeta functions Riemann Hypotheses Riemann Hypotheses for global L-functions The Riemann Hypothesis The Generalized Riemann Hypothesis The Extended Riemann Hypothesis ... The vertical distribution of zeros The Lindelof hypothesis and breaking convexity Perspectives on RH Analytic number theory Physics Probability Fractal geometry Equivalences to RH Primes The error term in the PNT More accurate estimates ... The Farey series Mikolas functions Amoroso's criterion Weil's positivity criterion Li's criterion Bombieri's refinement Complex function theory Speiser's criterion Logarithmic integrals An inequality for the logarithmic derivative of xi Function spaces ... Salem's criterion Other analytic estimates M. Riesz series

32. Writing Hypotheses What Is a Real hypothesis? A hypothesis is a tentative statement that proposes a possible explanation to some phenomenon or event. A useful hypothesis is a testable statement which http://www.accessexcellence.org/LC/TL/filson/writhypo.php

33. Hypothesis - New World Encyclopedia A hypothesis in the empirical disciplines (e.g. physics, chemistry, and biology) is a proposition proposed to predict or explain a reoccurring phenomenon, and in the a priori http://www.newworldencyclopedia.org/entry/Hypothesis

Hypothesis From New World Encyclopedia Jump to: navigation search Previous (Hypothalamus) Next (H�ryū-ji) A hypothesis in the empirical disciplines (e.g. physics, chemistry , and biology ) is a proposition proposed to predict or explain a reoccurring phenomenon, and in the a priori disciplines (e.g. mathematics, statistics, and logic ) it is a proposition proposed as the basis of an argument . The term derives from the ancient Greek, hypotithenai meaning "to put under" or "to suppose." The nature of the hypothesis is a topic of study primarily reserved for philosophy of science Contents Usage Types of Hypotheses Empirical Hypotheses A Priori Hypothesis ... Credits Usage In early usage, scholars often referred to a clever idea or to a convenient mathematical approach that simplified cumbersome calculations as a hypothesis . St. Robert Bellarmine (1542-1621) gave a famous example of the older sense of the word in the warning issued to Galileo in the early seventeenth century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis. During the eighteenth century, physicists (or “natural philosophers� as they were called) began to use the term ‘hypothesis’ in a pejorative sense, suggesting that hypothetico-deduction (explained later) was an inferior form of scientific reasoning. For example

34. Hypothesis Definition - Dictionary - MSN Encarta hy poth e sis hī p thəssiss (plural hy poth e ses hī p thə sz) noun Definition 1. theory needing investigation a tentative explanation for a phenomenon http://encarta.msn.com/dictionary_1861619718/hypothesis.html

35. Hypothesis - Simple English Wikipedia, The Free Encyclopedia A hypothesis is something that can explain a event. It can propose or suggest how two events relate to each other. The term comes from the Greek, hypotithenai meaning to put under or http://simple.wikipedia.org/wiki/Hypothesis

Hypothesis From Wikipedia, the free encyclopedia Jump to: navigation search A hypothesis is something that can explain a event . It can propose or suggest how two events relate to each other. The term comes from the Greek hypotithenai meaning "to put under" or "to suppose." The scientific method requires that a scientific hypothesis can be tested. Scientists sometimes create hypotheses on events that have been seen before or on extensions of scientific theories Contents Usage Other pages References Other websites ... change Usage At first, educated people often referred to an idea or to an approach to math that made hard math easier as a hypothesis ; when used this way, the word did not necessarily have any specific meaning. Cardinal Bellarmine gave a well known example of the older sense of the word in the warning issued to Galileo in the early 17th century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis. In common usage in the 21st century, a hypothesis refers to a idea that needs to be tested. A hypothesis needs more work by the researcher in order to check it. A tested hypothesis that works, may become part of a theory or become a theory itself. Normally, scientific hypotheses have the form of a

36. Definition Of Hypothesis A supposition; a proposition or principle which is supposed or taken for granted, in order to draw a conclusion or inference for proof of the point in question; something not http://www.brainyquote.com/words/hy/hypothesis175474.html

37. Scientific Hypothesis, Theory, Law Definitions Learn about the difference between a scientific law, hypothesis, and theory. http://chemistry.about.com/od/chemistry101/a/lawtheory.htm

zWASL=1;zGRH=1 zGCID=this.zGCID?zGCID+" test11":" test11" zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') zDO=0 Home Education Chemistry Chemistry Search Chemistry Chem 101 Science Projects Science Fair ... Share w(x2+zWl+'?p=1" zT="18/1[N" rel="nofollow">Print') Free Chemistry Newsletter! Sign Up Discuss in my Forum Scientific Hypothesis, Theory, Law Definitions By Anne Marie Helmenstine, Ph.D. , About.com Guide See More About: chemistry definitions hypothesis scientific laws zSB(3,3) Words have precise meanings in science. For example, 'theory', 'law', and 'hypothesis' don't all mean the same thing. Outside of science, you might say something is 'just a theory', meaning it's supposition that may or may not be true. In science, a theory is an explanation that generally is accepted to be true. Here's a closer look at these important, commonly misused terms. Hypothesis A hypothesis is an educated guess, based on observation. Usually, a hypothesis can be supported or refuted through experimentation or more observation. A hypothesis can be disproven, but not proven to be true. Example: If you see no difference in the cleaning ability of various laundry detergents, you might hypothesize that cleaning effectiveness is not affected by which detergent you use. You can see this hypothesis can be disproven if a stain is removed by one detergent and not another. On the other hand, you cannot prove the hypothesis. Even if you never see a difference in the cleanliness of your clothes after trying a thousand detergents, there might be one you haven't tried that could be different.

38. Mathematical Constants Notes by Steven Finch. http://algo.inria.fr/bsolve/constant/apery/riemhyp.html

39. Language, Thought & Sapir-Whorf - Speaking Out - UsingEnglish.com A discussion hosted by UsingEnglish.com about the Sapir-Whorf hypothesis, and whether language shapes thought or thought shapes language. http://www.usingenglish.com/speaking-out/linguistic-whorfare.html

Home Members Students Teachers ... Share Polls: Does Language Shape Thought? Further Reading: Sapir-Whorf Concerning the Sapir-Whorf hypothesis The Sapir-Whorf hypothesis has been the object of a serious and, at times, nasty debate. Whorf has been accused of being a racist and of distorting his evidence to fit his theory. One American educational course began with a discussion of whether these theories were racist. Interestingly enough, this was before any discussion of what the ideas were. Linguistic relativism has been given an unfair press because some believe it is the path towards suggesting that one language is superior to another. However, it would be hard to justify this by reference to their writings. I think there has been too much concentration on elements of language such as the number of words used by the Inuit for snow. If language does control thought, it does so at a very basic level, shaping the possible structures of thought and not the individual instances. I think the Universal Grammar aspects of the question are more important here- thought is controlled by concepts such as negation, question, the order of argument leading to conclusion, justification, etc., and not by the number of ways of talking about a local weather conditions. Once language has superseded the non-linguistic thought processes of animals, then it imposes an inevitability of its own logic and, I believe, replaces anything that came before it- like overwriting an old operating system in effect.

40. Hypothesis - Definition Of Hypothesis At YourDictionary.com an unproved theory, proposition, supposition, etc. tentatively accepted to explain certain facts or (working hypothesis) to provide a basis for further investigation, argument, etc http://www.yourdictionary.com/hypothesis

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