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. Introduction To The Scientific Method 3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

23. The Riemann Hypothesis Here we define, then discuss the Riemann hypothesis. We provide several related links. http://primes.utm.edu/notes/rh.html

The Riemann Hypothesis (Another of the Prime Pages ' resources) Home Search Site Largest The 5000 ... Submit primes Summary: When studying the distribution of prime numbers Riemann extended Euler's zeta function (defined just for s with real part greater than one) to the entire complex plane ( sans simple pole at s = 1). Riemann noted that his zeta function had trivial zeros at -2, -4, -6, ... and that all nontrivial zeros were symmetric about the line Re( s The Riemann hypothesis is that all nontrivial zeros are on this line. In 1901 von Koch showed that the Riemann hypothesis is equivalent to: The Riemann Hypothesis: Euler studied the sum for integers s >1 (clearly (1) is infinite). Euler discovered a formula relating k ) to the Bernoulli numbers yielding results such as and . But what has this got to do with the primes? The answer is in the following product taken over the primes p (also discovered by Euler): Euler wrote this as Riemann later extended the definition of s ) to all complex numbers s (except the simple pole at s =1 with residue one). Euler's product still holds if the real part of

24. Willkommen Bei Hypothesis Social Programme. HyWeb the Hydrogen and Fuel Cell Information System is Official Information Carrier of hypothesis IV http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

25. Introduction The Two Gospel hypothesis (2GH), formerly known as the Griesbach hypothesis, First given its name by Bernard Orchard, the Two Gospel hypothesis proposes http://www.colby.edu/rel/2gh/

A Web Site for the Two Gospel Hypothesis The Two Gospel Hypothesis (2GH), formerly known as the Griesbach Hypothesis, presents a comprehensive solution to the Synoptic Problem. First given its name by Bernard Orchard, the Two Gospel Hypothesis proposes that the Gospel of Matthew was the earliest gospel, that the author of the Gospel of Luke used the Gospel of Matthew as a source, and that the author of the Gospel of Mark wrote using both the Gospels of Matthew and Luke as sources. This page has been created to provide interested parties with basic information about this solution and its advantages. Links to detailed evidence and work in progress will be provided for those who wish to explore the solution further. We strongly recommend that you set your browser to view these pages at "full screen" configuration.

26. Introdution To The Theory A theory of human evolution which seeks to understand how humans evolved from animals that were similar to the great apes. http://www.geocities.com/Athens/Acropolis/4314/intromhh.html

The Amphibious-Generalist Hypothesis of Human Evolution 'Why are there human beings?' or 'What caused them to evolve?' must be two of the most fundamental questions in science, and indeed form the whole raison d'etre of anthropology. Robert Foley The Amphibious-Generalist Hypothesis seeks to understand how humans evolved from animals that were similar to the great apes. My view is that they were hyper-generalists, adaptable and capable of exploiting different habitats, including aquatic habitats. go to outline of theory

27. The Riemann Hypothesis Here we define, then discuss the Riemann hypothesis. We provide several related links. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

28. Fermi's Paradox And Extraterrestrial Visitation Suggests that aliens might be preparing mankind for the eventuality of meeting species from other worlds. http://www.ufoskeptic.org/contact.html

ufoskeptic.org Fermi's Paradox and the Preparation for Contact Hypothesis The famous physicist, Enrico Fermi, was referring to such an argument when he asked: "Where are they?" Since he was a prominent (and very smart) scientist, his simple question has been given a duly profound name: Fermi's paradox. The paradox is resolved, of course, if the answer is: "Well, they are already here!" (and possibly have been for a very long time and perhaps have even been involved in the rather sudden emergence of homo sapiens sapiens, but that may be over the top, so ignore that last conjecture if it is too much, though I seem to recall that even Sagan considered that possibility at some point). Their being here but surreptitiously would answer Fermi and at the same time address a second common objection to the UFO phenomenon by scientists: that the observations indicate such utterly nonsensical, bizarre behaviour that it just could not possibly be real. Intelligent visitors just would not pull such disreputable antics as have been reported. It is tempting to argue, as some do, that since the visitors are not behaving like proper alien explorers, there are no visitors in the first place. (For some reason this logic brings to mind Galileo attempting to get the Cardinals to look through his telescope.) To counter this argument, I would like to suggest one possible rationale that might, in principle at least (no real world guarantees), account for the widespread, disjoint kind of behavior that the UFO phenomenon has manifested over 50 years. The reason for proposing this "preparation for contact hypothesis" (which is certainly no original idea of mine) is simply to facilitate a "suspension of disbelief" so that the UFO evidence can be confronted on its own terms without the mental roadblock that the phenomenon violates all common sense, or more precisely the common sense of modern western society, and that of the scientific community in particular, and hence cannot be real.

29. Louis De Branges Professor of Mathematics at Purdue University. Contact information, papers on the Bieberbach Conjecture, the Riemann hypothesis, and related topics. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

30. Continuum Hypothesis -- From MathWorld 282) recount a generalized version of the continuum hypothesis The continuum hypothesis follows from generalized continuum hypothesis, so ZF+GCH CH . http://mathworld.wolfram.com/ContinuumHypothesis.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Set Theory Cardinal Numbers ... Szudzik Continuum Hypothesis The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers and the "large" infinite set of real numbers (the " continuum "). Symbolically, the continuum hypothesis is that showed that no contradiction would arise if the continuum hypothesis were added to conventional Zermelo-Fraenkel set theory . However, using a technique called forcing , Paul Cohen (1963, 1964) proved that no contradiction would arise if the negation of the continuum hypothesis was added to set theory set theory being used, and is therefore undecidable (assuming the Zermelo-Fraenkel axioms together with the axiom of choice Conway and Guy (1996, p. 282) recount a generalized version of the continuum hypothesis originally due to

31. Millennium Prize Problems The seven problems proposed by the Clay Mathematics Institute P versus NP; Hodge Conjecture; Poincar© Conjecture; Riemann hypothesis; YangMills Existence and Mass Gap; Navier-Stokes Existence and Smoothness; Birch and Swinnerton-Dyer Conjecture. Resources include articles on each problem by leading researchers. http://www.claymath.org/millennium/

Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME ABOUT CMI PROGRAMS AWARDS ... PUBLICATIONS Millennium Problems In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven Prize Problems . The Scientific Advisory Board of CMI selected these problems, focusing on important classic questions that have resisted solution over the years. The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each. During the Millennium Meeting The Importance of Mathematics , aimed for the general public, while John Tate and Michael Atiyah spoke on the problems. The CMI invited specialists to formulate each problem. One hundred years earlier, on August 8, 1900, David Hilbert delivered his famous lecture about open mathematical problems at the second International Congress of Mathematicians in Paris. This influenced our decision to announce the millennium problems as the central theme of a Paris meeting. The rules for the award of the prize have the endorsement of the CMI Scientific Advisory Board and the approval of the Directors. The members of these boards have the responsibility to preserve the nature, the integrity, and the spirit of this prize.

32. ZetaGrid Homepage Numerical verification of the Riemann hypothesis by a collaborative computing effort, with downloadable software. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

33. Are You Living In A Computer Simulation? Site examining the hypothesis that we are currently living in an ancestor simulation run by a future, posthuman society. Includes papers and research links. http://www.simulation-argument.com/

Are You Living In a Computer Simulation? The Simulation Argument Nick Bostrom Director, Future of Humanity Institute, Oxford University On this website you can follow the debate that followed the paper presenting the Simulation argument. The original paper is here, as are popular synopses, and scholarly papers commenting on the first paper, and a reply to these comments. The Simulation argument has attracted a great deal of attention, and I regret that I can usually not respond to individual queries about the argument. The original paper presenting the Simulation Argument: Are You Living In a Computer Simulation? Nick Bostrom. Philosophical Quarterly , 2003, Vol. 53, No. 211, pp. 243-255. [ html pdf ] (An earlier draft was circulated in 2001 ABSTRACT. This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

34. Riemann Hypothesis In A Nutshell Riemann hypothesis http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

35. Gaia Hypothesis This will serve as an introduction to the Gaia hypothesis; What is the hypothesis of Gaia ? Stated simply, the idea is that we may have discovered a http://erg.ucd.ie/arupa/references/gaia.html

Gaia Hypothesis This will serve as an introduction to the Gaia hypothesis; It is a review (published in 1989) of James Lovelock's The Ages of Gaia What is the hypothesis of Gaia ? Stated simply, the idea is that we may have discovered a living being bigger, more ancient, and more complex than anything from our wildest dreams. That being, called Gaia, is the Earth. More precisely: that about one billion years after it's formation, our planet was occupied by a meta-life form which began an ongoing process of transforming this planet into its own substance. All the life forms of the planet are part of Gaia. In a way analogous to the myriad different cell colonies which make up our organs and bodies, the life forms of earth in their diversity coevolve and contribute interactively to produce and sustain the optimal conditions for the growth and prosperity not of themselves, but of the larger whole, Gaia. That the very makeup of the atmosphere, seas, and terrestrial crust is the result of radical interventions carried out by Gaia through the evolving diversity of living creatures. Encountering the Earth from space, a witness would know immediately that the planet was alive. The atmosphere would give it away. The atmospheric compositions of our sister planets, venus and mars, are: 95-96% carbon dioxide, 3-4% nitrogen, with traces of oxygen, argon and methane. The earth's atmosphere at present is 79% nitrogen, 21% oxygen with traces of carbon dioxide, methane and argon. The difference is Gaia, which transforms the outer layer of the planet into environments suitable to its further growth. For example, bacteria and photosynthetic algae began some 2.8 billions of years ago extracting the carbon dioxide and releasing oxygen into the atmosphere, setting the stage for larger and more energetic creatures powered by combustion, including, ultimately, ourselves.

36. Axiom Of Choice And Continuum Hypothesis Part of the Frequently Asked Questions in Mathematics. http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node34.html

Next: The Axiom of Choice Up: Frequently Asked Questions in Mathematics Previous: Master Mind Axiom of Choice and Continuum Hypothesis The Axiom of Choice Cutting a sphere into pieces of larger volume The Continuum Hypothesis Alex Lopez-Ortiz Fri Feb 20 21:45:30 EST 1998

37. Power Of A Hypothesis Test Applet (24-Mar-1997) Power of a hypothesis Test Applet http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

38. Logic Of Hypothesis Testing Ruling out chance as an explanation The null hypothesis Steps in hypothesis testing Why the null hypothesis is not accepted The precise meaning of http://www.ruf.rice.edu/~lane/hyperstat/logic_hypothesis.html

Chapter 9: Logic of Hypothesis Testing Other Sites Contents Instructional Demos Tests of proportions by Charles Stanton Text Hypothesis testing by Gene Glass Hypothesis testing: Does chance explain the results? by P. B. Stark Hypothesis testing part 1 Hypothesis testing part 2 by Keith Dear Testing statistical hypotheses by H. J. Newton, J. H. Carroll, N. Wang, and D. Whiting Hypothesis testing by David Stockburger Interpreting p values by TexaSoft Main Contents Search Glossary Ruling out chance as an explanation ... Following a nonsignificant finding

39. Cogprints - The Sexual Competition Hypothesis For Eating Disorders A hypothesis that suggests eating disorders stem from intense female intrasexual competition for mates. http://cogprints.soton.ac.uk/documents/disk0/00/00/08/00/index.html

@import url(http://cogprints.org/eprints.css); @import url(http://cogprints.org/eprints.css); @import url(http://cogprints.org/print.css); Cogprints Home About by Year by Subject ... Help The sexual competition hypothesis for eating disorders Abed, Riadh T The sexual competition hypothesis for eating disorders British Journal of Medical Psychology Full text available as: HTML Abstract A hypothesis is presented for eating disorders that contends that these syndromes together with the phenomenon of the pursuit of thinness are manifestations of female intra-sexual competition. It is argued that the present-day environment of Western coutries presnts a range of conditions that have led to the overactivation or disruption of the archaic female sexual strategy of maximising 'mate value'. The hypothesis deals with the ultimate level of causation and is therefore compatible with a range of theories dealing with the proximate level of causation. Keywords: eating disorders, anorexia nervosa, bulimia nervosa, intra-sexual competition, thinness Subjects: Psychology Evolutionary Psychology Psychology Psychobiology ID Code: Deposited By: Abed, Riadh T

40. The Self-Medication Hypothesis A theory of the causation of addictions. This site explores both Khantzian's psychoanalytic model and Duncan's behavioral model of the hypothesis. http://self-med-hypothesis.tripod.com/

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Tripod Movie Clips Share This Page Report Abuse Edit your Site ... Next The Self-Medication Hypothesis Home Review Khantzian's Model Duncan's Model ... Links Welcome to our web site! The purpose of this web site is to provide basic information about the Self-Medication Hypothesis one of the most influential theories of the causation of drug abuse and addictions. The self-medication hypothesis proposes that addiction to alcohol and other drugs results from their use for relief from dysphoria resulting from an underlying disorder or condition such as stress. It was proposed in 1974 in separate publications by Edward J. Khantzian and David F. Duncan. This site is a member of WebRing. To browse visit here The Drug Abuse And Legalization SiteRing This ring owned by TinMan SiteRing by Bravenet.com

Page 2     21-40 of 184    Back | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | Next 20