21. Body A claimed proof of Riemann's hypothesis. http://www.coolissues.com/mathematics/riemann.htm

PROOF OF RIEMANN'S HYPOTHESIS James Constant math@coolissues.com Riemann's hypothesis is proved using Riemann's functional equation. Introduction The famous conjecture known as Riemann' s hypothesis is to classical analysis what Fermat's last theorem is to arithmetic. Euler (1737) noted that the formula the sum extending to all positive integers n, and the product to all positive primes p. The neces- sary conditions of convergence hold for complex values of s as a function of of the complex variable s , Riemann (1859) proved that satisfies a functional equation which led Riemann to the theorem that all the zeros of , except those at s=-2,-4,-6, . . . , lie in the strip of the s -plane for which where x is the real part of s . Riemann conjectured that all the zeros in the strip should lie on the line x = ½. Attempts to prove or disprove this conjecture have generated a vast and intricate department of analysis, especially since Hardy (1914) proved that has an infinity of zeros on x The question is still open in 2000. A prize is available to prove or disprove Riemann's hypothesis. Proof Using Riemann's Functional Equation It has already been shown that all zeros are in the critical strip and that they are symmetric about the critical line x Riemann's functional equation can be restated as =A( in which A( at all points in the critical strip. Since functions

22. The Gaia Hypothesis - Dr James Lovelock & Dr Lynn Margulis The Gaia hypothesis Resource Document Section 2 - Dr James Lovelock and theFormulation of the Gaia hypothesis - This document presents the research http://www.magna.com.au/~prfbrown/gaia_jim.html

The Gaia Hypothesis proposed by Dr. James Lovelock in collaboration with Dr. Lynn Margulis "Giants of Gaia" Diana Stanley Section 2: Dr James Lovelock: Formulation of the Gaia Hypothesis Web Publication by Mountain Man Graphics, Australia in the Southern Autumn of 1996 BACKGROUND: Primitive ExtraTerrestrial Glimpses ... In the search for the evidence of extra-terrestrial life, the closer - Earth's neighbouring planets - Venus and Mars were targetted by the NASA program. Of these, due to the unknown conditions of the planetary surface caused by the dense and aggitated Venusian atmosphere, the planet Mars was given priority. The first spacecraft to visit Mars was Mariner 4 in 1965, and several others followed including the two Viking landers in 1976. Dr James Lovelock, a British Chemist specialising in the atmospheric sciences, was a recognised leader in his field. He was to invent an electron capture detector, capable of tracing extremely small amounts of tracer elements in gases, which was used by the ozone monitoring research concerning the effect of CFC's in the early 1970's. Almost a decade before this, NASA and the Jet Propulsion Laboratory (JPL) requested the presence of Lovelock in their project teams relating to the scientific search for the evidence of life on Mars. In collaboration with other project researchers, Lovelock predicted the absence of life on mars based on the consideration of the Martian atmosphere and its state of being in a chemically

23. Gaia Hypothesis 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. 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.

24. Clay Mathematics Institute - Riemann Hypothesis RIEMANN hypothesis. The Riemann hypothesis asserts that all interestingsolutions of the equation. z(s) = 0. lie on a straight line. http://www.claymath.org/Millennium_Prize_Problems/Riemann_Hypothesis/

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 “ z (s)” called the Riemann Zeta function . The Riemann hypothesis asserts that all interesting solutions of the equation z (s) = lie on a 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. Lecture by Jeff Vaaler at UT.ram Official Problem Description.pdf Privacy Statement Help

25. The Continuum Hypothesis A workshop featuring a number of lectures surveying the current insights into the continuum problem and its variations. MSRI, Berkeley, CA, USA; 29 May 1 June 2001. http://zeta.msri.org/calendar/workshops/WorkshopInfo/94/show_workshop

Calendar The Continuum Hypothesis May 29, 2001 to June 1, 2001 Organized by: Hugh Woodin and John Steel The workshop will feature a number of lectures surveying the current insights into the continuum problem and its variations. Group Photo Group Photo (larger version) Continuum Hypothesis Schedule Lectures on Streaming Video: This event is now over. Resources from this event, including streaming video , may be available. MSRI Home Page Search the MSRI Website Subject and Title Index webmaster@msri.org

26. 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

27. 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/prize_problems/

28. The Dopamine Hypothesis Of Schizophrenia One page article that addresses the theory of increased levels of dopamine in patients who have symptoms of schizophrenia. Bibliography included. http://serendip.brynmawr.edu/bb/neuro/neuro98/202s98-paper2/Frederickson2.html

This paper was written by a student in a course at Bryn Mawr College, and reflects that student's research and thoughts at the time the paper was written. Like other things on Serendip , the paper is not intended to be "authoritative" but is instead provided to encourage others to themselves learn about and think through subjects of interest, and, by providing relevant web links, to serve as a "window" to help them do so. Web links were active as of the time the paper was posted but are not updated. Biology 202 1998 Second Web Reports On Serendip The Dopamine Hypothesis of Schizophrenia Anne Frederickson Schizophrenia is a disease that has plagued societies around the world for centuries, although it was not given its formal name until 1911. It is characterized by the presence of positive and negative symptoms. Positive symptoms are so named because of the presence of altered behaviors, such as delusions, hallucinations (usually auditory), extreme emotions, excited motor activity, and incoherent thoughts and speech. In contrast, negative symptoms are described as a lack of behaviors, such as emotion, speech, social interaction, and action.

29. 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

Cogprints Home About Browse Search ... Help The sexual competition hypothesis for eating disorders Abed, Riadh T (1998) 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 Deposited On: 01 March 1999 Cogprints Editor: cogprints@ecs.soton.ac.uk

30. COSMIC ANCESTRY: The Modern Version Of Panspermia. By Brig Klyce The Cosmic Ancestry hypothesis about which this site has a large amount of information - treats all of evolution, not just the origin of life on Earth, as due to interaction with cosmic microorganisms. http://www.panspermia.org/

Quick Guide Next Brig Klyce COSMIC ANCESTRY Life comes from space because life comes from life. Books: by Fred Hoyle by Hoyle and Wickramasinghe What'sNEW Index Introduction: More Than Panspermia Panspermia Asks New Questions ... FAQs and RAQs Where Does Life Come From? What is Life? Louis Pasteur The RNA World Bacteria: The Space Colonists ... Comets: The Delivery System How Does Life Evolve? Neo-Darwinism: The Current Paradigm Viruses and Other Gene Transfer Mechanisms Why Sexual Reproduction? Introns: a Mystery ... Gaia The Logic of Neo-Darwinism Evolution vs Creationism The Second Law of Thermodynamics ... Macroevolutionary Progress Redefined... Can Meaning Come From Nonmeaning? Hoyle and Wickramasinghe Analysis of Interstellar Dust and Selected Resources An Interview with Fred Hoyle, July 5, 1996 Chandra Wickramasinghe in Arkansas, 1981 Tests for Cosmic Ancestry Can The Theory Be Tested? 1996 Aug 7: Life on Mars! or Europa or Other Moons? 1996 Oct 25: Metazoan Genes Older Than Metazoa? 1996 Nov 7: Life Before 3850 Million Years Ago? 1997 Feb 14: Amino Acid Asymmetry in ...Meteorite ... Cosmic Ancestry From Science to Philosophy How Is It Possible?

31. An Evolutionary Hypothesis For Obsessive Compulsive Disorder: A Psychological Im Abed, Riadh T and de Pauw, Karel W (1999) An Evolutionary hypothesis for ObsessiveCompulsive Disorder A Psychological Immune System?. Behavioural Neurology 11245-250. http://cogprints.soton.ac.uk/documents/disk0/00/00/11/47/cog00001147-00/ocd-fina

An Evolutionary Hypothesis For Obsessive Compulsive Disorder: A Psychological Immune System? *Riadh T. Abed, MBChB, MRCPsych, DPM, Consultant Psychiatrist, Rotherham District General Hospital, Moorgate Road, Rotherham S60 2UD , UK; and Honorary Clinical Lecturer, University of Sheffield. Karel W. de Pauw, MBChB, MD, MRCPsych, Consultant Psychiatrist and Senior Clinical Lecturer , St James’s University Hospital, Leeds LS9 7TF, UK. * Correspondence : E-mail abed@globalnet.co.uk An Evolutionary Hypothesis for Obsessive Compulsive Disorder: A Psychological Immune System? Abstract: A new hypothesis is presented within the framework of evolutionary psychology that attempts to explain the origins of obsessive-compulsive disorder. It is suggested that obsessions and compulsions originate from the overactivity of a mental module that the majority of humans possess and has the function of generating risk scenarios without voluntary intervention. It is hypothesised that obsessional phenomena function as an off-line risk avoidance process, designed to lead to risk avoidance behaviour at a future time, thus distinguishing it from anxiety and related phenomena as

32. JAMA -- Page Not Found Review of book by Sheldon Krimsky in Journal of the American Medical Association (JAMA). http://jama.ama-assn.org/issues/v284n18/ffull/jbk1108-1.html

Select Journal or Resource JAMA Archives of Dermatology Facial Plastic Surgery Family Medicine (1992-2000) General Psychiatry Internal Medicine Neurology Ophthalmology Surgery MSJAMA Science News Updates Meetings Peer Review Congress The page you requested was not found. The JAMA Archives Journals Web site has been redesigned to provide you with improved layout, features, and functionality. The location of the page you requested may have changed. To find the page you requested, click here HOME CURRENT ISSUE PAST ISSUES ... HELP Error 404 - "Not Found"

33. The Two Source Hypothesis Summary of the dominant synoptic theory by Stephen Carlson. http://www.mindspring.com/~scarlson/synopt/2sh/index.htm

The Two Source Hypothesis Abstract Mark was a source for Matthew and Luke, both of whom also independently used a now lost sayings source called Q. Overview The Two Source Hypothesis ( ) has been the predominant source theory for the synoptic problem for almost a century and half. Originally conceived in Germany by Ch. H. Weisse in 1838, the came to dominate German protestant scholarship after the fall of the Tübingen school with H. J. Holtzmann's endorsement of a related variant in 1863. In the latter part of the 19th century, the Oxford School brought the to English scholarship, culminating in B. H. Streeter's 1924 treatment of the synoptic problem. Now, the commands the support of most biblical critics from all continents and denominations. The derives its name from its postulation of two main sources for the synoptic gospels: a narrative source for the triple tradition and a sayings source for the double tradition. The triple tradition comprises the subject matter jointly related by Matthew, Mark, and Luke. Generally, the triple tradition is characterized by substantial agreements in arrangement and wording among all three gospels with frequent agreements between Mark and Matthew against Luke and between Mark and Luke against Matthew, but a near absence of agreements of Matthew and Luke against Mark. The

34. Riemann Hypothesis In A Nutshell The Riemann hypothesis in a Nutshell. The Riemann Zeta Function. image source. (in Unix/Linux anyway). Verifying the Riemann hypothesis. Basic Strategy. http://www.math.ubc.ca/~pugh/RiemannZeta/RiemannZetaLong.html

Home Z(t) Plotter Verifying RH ... More Applets The Riemann Hypothesis in a Nutshell The Riemann Zeta Function image source In his 1859 paper On the Number of Primes Less Than a Given Magnitude , Bernhard Riemann (1826-1866) examined the properties of the function for s a complex number. This function is analytic for real part of s greater than and is related to the prime numbers by the Euler Product Formula again defined for real part of s greater than one. This function extends to points with real part s less than or equal to one by the formula (among others) The contour here is meant to indicate a path which begins at positive infinity, descends parallel to and just above the real axis, circles the origin once in the counterclockwise direction, and then returns to positive infinity parallel to and just below the real axis. This function is analytic at all points of the complex plane except the point s = 1 where it has a simple pole. This last function is the Riemann Zeta Function ( the zeta function The Riemann Hypothesis The zeta function has no zeros in the region where the real part of s is greater than or equal to one. In the region with real part of

35. No Longer Available A hypothesis which examines man's detrimental interaction with the environment as a natural process. http://www.biophage.org/

The Web site you were trying to reach is no longer available at GoBizGo

36. Power Of A Hypothesis Test Applet (24-Mar-1997) Power of a hypothesis Test Applet. This applet and then rejecting thenull hypothesis if the appropriate condition is satisfied. In the http://www.stat.sc.edu/~ogden/javahtml/power/power.html

Power of a Hypothesis Test Applet This applet illustrates the fundamental principles of statistical hypothesis testing through the simplest example: the test for the mean of a single normal population, variance known (the Z test). The basic set-up of the test is this: using only n independent observations from a normal distribution with unknown mean (but known variance), the task is to decide whether to accept a null hypothesis for a specified value of , or to reject the null hypothesis in favor of some alternative hypothesis. In most applications, there are only three alternative hypotheses of interest: respectively, ``upper-tailed,'' ``lower-tailed,'' and ``two-tailed.'' The testing framework consists of computing a ``test statistic'' and then rejecting the null hypothesis if the appropriate condition is satisfied. In the order the alternative hypotheses are given above, the null hypothesis is rejected if where represents the upper critical point of the standard normal distribution. This hypothesis testing procedure is set up to give the null hypothesis ``the benefit of a doubt;'' that is, to accept the null hypothesis unless there is strong evidence to support the alternative. If

37. Hypothesis On MATTER hypothesis on. M A T T E R. This hypothesis on matter provides simple andlogical explanation to all physical phenomena related to the matter. http://physicsweb.org/resources/follow/3145

Hypothesis on M A T T E R (A preliminary study) By Nainan.K.Varghese TABLE OF CONTENTS: Chapter 1 (HTML) (PDF) INTRODUCTION 1.1. General 1.2. Aim of this text 1.3. Salient features of this hypothesis 1.4. Scope of this text 1.5. Interaction Chapter ONE gives a general introduction on the "Hypothesis on MATTER". Few important conclusions are given in brief. Limitations and aim of this preliminary study is briefly described. Reader is requested to give only a passing reference to conclusions mentioned in this chapter and not to form any opinion based on them without reading through the text. Chapter 2A (HTML) (PDF) SPACE SYSTEMS AND ENERGY FIELDS 2.1. Fundamental dimensions 2.2. Dimensional space system 2.3. Quantum of energy 2.4. Formation of 2D energy fields 2.5. Equilibrium of 2D energy field 2.6. Field force 2.7. Properties of 2D energy fields 2.8. Disturbance 2.9. Gravitational pressure Chapter 2B (HTML) (PDF) SPACE SYSTEMS AND ENERGY FIELDS (Contd) 2.10. Gravitational force on a point disturbance 2.11. Gravitational pressure on a disturbance

38. Christianity And The Mathematical Sciences - The Heliocentric Hypothesis Religious influences on Copernicus, Galileo, Brahe and Kepler. http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Heliocentric.html

39. Index Of /b.vermeulen Site van Baptist Vermeulen, met cursusdata en online teksten van de cursus. http://home.wanadoo.nl/b.vermeulen/

Index of /b.vermeulen Parent Directory

40. The Gaia Hypothesis The Gaia hypothesis is the theory is that living organisms and inorganicmaterial are part of a dynamic homeostatic system. The Gaia hypothesis. http://www.kheper.auz.com/gaia/Gaia_Hypothesis.htm

Life in the Cosmos Gaia Hypothesis Dr James Lovelock Biosphere Evolution New/Updated ... The Goddess Earth The Gaia Hypothesis "The entire range of living matter on Earth from whales to viruses and from oaks to algae could be regarded as constituting a single living entity capable of maintaining the Earth's atmosphere to suit its overall needs and endowed with faculties and powers far beyond those of its constituent parts...[Gaia can be defined] as a complex entity involving the Earth's biosphere, atmosphere, oceans, and soil; the totality constituting a feedback of cybernetic systems which seeks an optimal physical and chemical environment for life on this planet." Dr James Lovelock Gaia - A New Look at Life on Earth The Gaia Hypothesis is the theory is that living organisms and inorganic material are part of a dynamic system that shape Earth's biosphere , in Lynn Margulis 's words, a "super organismic system" The earth is a self-regulating environment; a single, unified, cooperating and living system - a superorganism that regulates physical conditions to keep the environment hospitable for life Evolution therefore is the result of cooperative not competitive processes.

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