141. 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

142. Fuel Cell Today - Event, HYPOTHESIS VI The global internet portal for companies and individuals with an interest in the commercialisation of fuel cells. http://www.fuelcelltoday.com/FuelCellToday/EventListings/EventListingsExternal/c

Home Events Event Details HYPOTHESIS VI http://www.hypothesis.ws/ Dates 08 May 2005 - 12 May 2005 Subject HYPOTHESIS VI Type Symposium Location La Habana, Cuba Description The sixth HYPOTHESIS (HYdrogen – POwer THeoretical and Engineering Solutions) International Symposium will cover again the following areas: National and International Hydrogen Projects, Strategies , Concepts, Visions Hydrogen Production from Fossil Fuels Hydrogen Production from Renewable Sources Hydrogen storage and distribution Safety, Standards, Regulations Hydrogen Thermal Conversion Contact: info@hypothesis.ws Printer friendly version e-mail this Page 17 September 2005 May 2005 s m t w t f s January February March April May June July August September October November December Event Options Register with site Submit your Event Search Events e-mail this Page Printer friendly version Featured Links: Receive our e-Newsletter subscribe View the Fuel Cell Today Industry Directory Related Links: Society of Automotive Engineers IQPC Opening doors to fuel cells commercialisation Home News Analysis Community ... Shop Please review our and

143. Quantum Physics (journal) Papers about the Smarandache hypothesis that there is no speed barrier in the universe, SRMTheory of constructing arbitrary speeds from zero to infinite, Smarandache Sorites Paradox. http://www.geocities.com/m_l_perez/QuantumPhysics.html

Quantum Physics Welcome to the miraculous micro-world of Quantum Physics! Read about: - Smarandache's Quantum Chromodynamics Formula; - A new form of matter: Unmatter [in "Infinite Energy" journal]; - Verifying Unmatter by Experiments, More Types of Unmatter [in "Progress in Physics" journal]; - Smarandache Hypothesis that there is no speed barrier in the universe: ... - Extension of the Bing Bang Theory to Cycles of Beginning and Ending [in "Bull. Pure Appl. Science" journal]. Your feedback is important to us. My Favorite Links: Progress in Physics journal Quantum Physics Minh Perez (Rehoboth, Box 141, NM 87322, USA) Name: Email: M_L_Perez@yahoo.com

144. THE HYPOTHESIS You must develop a hypothesis, or a possible explanation to answer your question. A hypothesis is a tentative explanation for what we observe (Campbell, http://www.lv.psu.edu/jxm57/irp/hypothes.html

145. Body Generalisations of the zeta function might provide a proof of Riemann's hypothesis. http://www.coolissues.com/mathematics/Zeta/zeta.htm

Some Extended Zeta Functions Provide Easy Proofs of Riemann's Hypothesis James Constant math@coolissues.com While extended zeta functions support investigations of Riemann's hypothesis and estimates for the Prime Number Theorem, some zeta functions offer better prospects for providing easy proofs. Definitions A first zeta function is defined by oo z(s)= s=x+jy n=1 A second zeta function is defined by oo z(1-s)= s=x+jy n=1 In 1859, Riemann had the idea to define z(s) for all complex numbers s by analytic extension. This extension is important in number theory and plays a central role in the distribution of prime numbers. One way of extending is by using the first f function alternating series defined by oo f(s)= s=x+jy n=1 1 by means of the formula f(s)=(1-2 )z(s) A second f function is defined by oo f(1-s)= s=x+jy n=1 1 by means of the formula f(1-s)=(1-2 )z(1-s) Equations (1) through (6) are analytic. Riemann's Extended Zeta Function and Functional Equation Euler (1737) noted that the formula n, and the product to all positive primes p.

146. The RNA World a general hypothesis was constructed from a few specific instances of a This hypothesis proved to be very effective in stimulating thought about the http://nobelprize.org/chemistry/articles/altman/

HOME SITE HELP ABOUT SEARCH ... EDUCATIONAL The RNA World by Sidney Altman 1989 Nobel Laureate in Chemistry On further reflection, many doubts have been raised about whether or not the original genetic/catalytic material could have been RNA as we know it today because extreme conditions on the primitive Earth might have led to the rapid chemical degradation of RNA. Nevertheless, even if the precise chemical nature of the early genetic/catalytic material differed from present-day RNA, it seems reasonable to conclude that the RNA World did exist at some time. If very primitive life on Earth did not arise until about 3.5 billion years ago, there was, perhaps, a period of 0.5 billion years in which to sample many polymer sequences that originally arose through non-biochemical mechanisms and that ultimately evolved directed the first self-replicating systems. My involvement in the discovery of the first catalytic RNA began in innocence during a study of tRNA biosynthesis in Escherichia coli. I was fortunate enough to isolate and characterize a precursor tRNA, one of the intermediates in the metabolic pathway leading to the synthesis of mature tRNA. As in all biochemical pathways, if one has an intermediate compound, there must be an intra-cellular enzyme that acts on this intermediate to take it to the next step in the pathway. This enzyme, ribonuclease P (RNase P), was readily identifiable. Its function was to cleave a phosphodiester bond at the start of the mature tRNA nucleotide sequence, thereby releasing the upstream extra or "precursor" nucleotides.

147. Proof Of Riemann's Hypothesis A claimed proof of Riemann's hypothesis. http://www.coolissues.com/mathematics/Riemann/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 necessary 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

148. Introductory Routes Of Rice To Japan An Examination Of The Southern Route Hypoth Asian Perspectives 40(2). The beginning of rice agriculture in Japan impacted every aspect of life in most parts of the archipelago. It was the Japanese version of the Neolithic Revolution. (PDF) http://muse.jhu.edu/journals/asian_perspectives/v040/40.2takamiya.pdf

149. The Riemann Hypothesis The Lindelof hypothesis and breaking convexity; Perspectives on RH Zeta Gallery; Anecdotes about the Riemann hypothesis http://www.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

150. Evaluating Descartes' Dreaming Hypothesis -- Essay At PhilosophyClassics.com An assessment of Descartes' skeptical arguments in the first Meditation, especially his argument on dreams. http://www.philosophyclassics.com/essays/941/

Start your day with a thought-provoking quote from the world's greatest thinkers and writers. Sign up to The Daily Muse for free. Evaluating Descartes' Dreaming Hypothesis By Andrew Nicol , Student A critical evaluation of a slightly modified version of Descartes' argument. An essay hosted at PhilosophyClassics.com Descartes’ dreaming hypothesis appears, at first glance, to be a very compelling argument. The argument in question, which is a modification of Descartes’ hypothesis, initially appears to be almost irrefutable. However, I will argue that although it is deductively valid, the argument is not cogent. The first premiss is not acceptable, and equivocation makes the conclusion of the argument ambiguous in its meaning and deceptive in its implications. The claim that the argument is deductively valid requires some justification. It can be argued that, assuming the premisses are true, there are circumstances in which the conclusion would be false. For example, it may be suggested that the statement ‘I know that I am thinking’ could be true regardless of whether I am awake or asleep. However, relies on the assumption that thought in dreams is essentially the same as thought in everyday life. I will argue later that this is not true, and that it is impossible for someone who is dreaming to be conscious of the fact that she is thinking. Other claims like ‘I know that I exist’, are similarly problematic. Given that there are no other imaginable circumstances in which the conclusion would not follow from the premisses, the main argument must be valid.

151. Alzforum: Hypothesis Factory The Alzheimer Research Forum is an online scientific community dedicated to developing treatments and preventions for Alzheimer s disease. http://www.alzforum.org/res/adh/hyp/default.asp

Home Contact Us How to Cite Become a Member ... Hypothesis Factory Hypothesis Factory Updated 21 August 2005 Important Notice : Alzheimer Research Forum does not provide medical advice nor promote any product or service. The contents are for informational purposes only and are not intended to substitute for professional medical advice, diagnosis or treatment. Always seek advice from a qualified physician or health care professional about any medical concern, and do not disregard professional medical advice because of anything you may read on this web site. The views of individuals quoted on this site are not necessarily those of the Alzheimer Research Forum. This page is devoted to the presentation and exchange of ideas regarding novel hypotheses, hunches, theories-in-progress, etc. All established hypotheses started out as someone's wild notion, and this page pays tribute to them by creating a forum where people with original or unconventional ideas can publicly present and discuss them. See also our AD Hypotheses page.

152. THE RIEMANN HYPOTHESIS Web article by Aldo Peretti. http://www.cuatrovientos.com.ar/_vti_z/

THE RIEMANN HYPOTHESIS By Aldo Peretti Download all the text 1– Introduction In 1859, G.F.B.Riemann published a most famous paper concerning the distribution of prime numbers, with the title: “On the quantity of prime numbers below a given quantity”, where, for the first time were used the methods of complex variable functions in order to determine (x) x. His starting formula was the product decomposition that Euler had found for the zeta function i.e. the formula where p stands for the prime numbers. (Riemann used the letter s to denote the variable, s + it ; and this way of notation was unanimously used after him) In the first part of the memoir, he proves the functional equation of the zeta function, and after this he deduces the formula valid for f(x) This formula had been obtained formerly in 1848 by Tchebychev (whose work on the subject very likely was known to Riemann). But he was unable to make the inversion of this formula, that Riemann succeeded to do, obtaining thus: f(x) = The remaining part of Riemann’s paper is very obscure and confusing because of its excessive brevity. Fortunately

153. Synoptic Problem Website: Two-Source Hypothesis The TwoSource hypothesis (2SH) has been the predominant source theory for Sometimes, the 2SH is more precisely called the two-document hypothesis to http://www.hypotyposeis.org/synoptic-problem/2004/09/two-source-hypothesis.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=8390144"); Synoptic Problem Website by Stephen C. Carlson My Sites Synoptic Problem Website Old Synoptic Problem Home Page My Hypotyposeis weblog New Testament Stemmatics Introduction Synoptic Problem FAQ Annotated Bibliography Chronology Tools Detailed Bibliography Table of Synoptic Parallels Synopsis Synoptic Theories Overview Two-Source Enumeration of 1488 viable synoptic theories. External Evidence Contents Archives September 2004 October 2004 November 2004 January 2005 ... March 2005 Colophon Site Feed 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 (2SH) 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 2SH came to dominate German protestant scholarship after the fall of the T¼bingen 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 2SH to English scholarship, culminating in B. H.

154. Naval History Magazine: The Earhart Tragedy: Old Mystery, New Hypothesis, By Joh John P. Riley considers the role of military officials in the mystery of the disappearance of Amelia Earhart and Fred Noonan. http://www.usni.org/NavalHistory/articles00/nhriley.htm

dqmcodebase = "../../js/" //script folder location Home Naval History Magazine August Issue Products Site Content COURTESY OF JOHN HANCOCK FINANCIAL SERVICES The Earhart Tragedy Old Mystery, New Hypothesis By John P. Riley, Jr. Naval History, August 2000 Over the decades since Amelia Earhart and Fred Noonan disappeared in the Pacific Ocean on 2 July 1937 while attempting to fly around the world, many authors have focused on the fliers' alleged incompetence as the reason they did not find Howland Island. Earhart, despite having achieved numerous aviation firsts, often is portrayed as unqualified, even though she was the first woman to fly the Atlantic Ocean and the first person of either sex to fly from Hawaii to the mainland of North America. In contrast with the sniping at the Earhart-Noonan team, Commander Warner K. Thompson, U.S. Coast Guard, commanding the USCGC

155. The Music Of The Primes A popular article by Marcus du Sautoy on the Riemann hypothesis; Science Spectra, Issue 11. http://www.dpmms.cam.ac.uk/~dusautoy/2soft/music.htm

1.-When the British mathematician Andrew Wiles told the world about his proof of the Last Theorem of the seventeenth century French lawyer, Pierre de Fermat, it looked as if the Holy Grail had been grasped. Fermat's Last Theorem has often been called the greatest unsolved riddle of mathematics. But many mathematicians would argue that this name belongs rather to an idea first put forward in the middle of the nineteenth century by the German mathematician Bernhard Riemann: The Riemann Hypothesis. 2.-PRIME NUMBERS It remains unresolved but, if true, the Riemann Hypothesis will go to the heart of what makes so much of mathematics tick: the prime numbers. These indivisible numbers are the atoms of arithmetic. Every number can be built by multiplying prime numbers together. The primes have fascinated generations of mathematicians and non-mathematicians alike, yet their properties remain deeply mysterious. Whoever proves or disproves the Riemann Hypothesis will discover the key to many of their secrets and this is why it ranks above Fermat as the theorem for whose proof mathematicians would trade their soul with Mephistopheles. 3.-Although the Riemann Hypothesis has never quite caught on in the public imagination as Mathematics' Holy Grail, prime numbers themselves do periodically make headline news. The media love to report on the latest record for the biggest prime number so far discovered. In November 1996 the Great Internet Prime Search announced their discovery of the current record, a prime number with 378,632 digits. But for mathematicians, such news is of only passing interest. Over two thousand years ago Euclid proved that there will be infinitely many such news stories, for the primes never run dry.

156. How To Plan A Grant Application: Develop A Solid Hypothesis -- NIAID Research Fu How to Plan a Grant Application Develop a Solid hypothesis. Developed and maintained by the National Institute of Allergy and Infectious Diseases (NIAID), http://www.niaid.nih.gov/ncn/grants/plan/plan_c1.htm

Search Help Site Index Contact Us NIAID ... Latest Updates Develop a Solid Hypothesis Search in Research Funding tutorial index Many top-notch NIH grant applications are driven by strong hypotheses rather than advances in technology. Think of your hypothesis as the foundation of your application the conceptual underpinning on which the entire structure rests. Generally applications should ask questions that prove or disprove a hypothesis rather than use a method to search for a problem or simply collect information. However, a new trend is pushing us toward more applied research. Especially in key areas, such as studies of organisms used for bioterrorism, we will be turning more to applications seeking to discover basic biology or develop or use a new technology. If your application is not hypothesis-based, state this in your cover letter and give the reasons why the work is important. Choose an important, testable, focused hypothesis that increases understanding of biologic processes, diseases, treatments, or preventions. It should be based on previous research. State your hypothesis in both the

157. Nam Tran Arizona State University. Knowledge representation, hypothesis generation, causal modelling in AI, bioinformatics. http://www.public.asu.edu/~nhtran/

Nam Tran ( CV Arizona State University Tempe , AZ 85281 Tel Advisor Professor C. Baral Research Group : KR Lab at ASU Research Knowledge Representation and Reasoning (KRR). Biochemical Networks - Statistical and Causal Modeling in AI. Research Assistant, PhD student, ASU Researcher, Mindmaker Inc Research Assistant, CIM Lab SZTAKI MS in Computer Science, Roland Eotvos University Hungarian language school, Budapest Paradise , Vietnam. Papers ( DBLP Knowledge-based framework for hypothesis formation in biochemical networks N. Tran, C. Baral, V. Nagaraj, L. Joshi To be presented in the European Conference on Computational Biology ( ECCB-05 To appear in a special issue of Bioinformatics Issues in Reasoning about Interaction Networks in Cells: Necessity of Event Ordering Knowledge N. Tran, C. Baral, C. Shankland To be presented in AAAI-05 Knowledge-Based Integrative Framework for Hypothesis Formation in Biochemical Networks N. Tran, C. Baral, V. Nagaraj, L. Joshi To be presented in the 2nd Workshop on Data Integration in the Life Sciences ( DILS 2005 Reasoning about the ERK signal transduction pathway using BioSigNet-RR C. Shankland

158. ZetaGrid Homepage Numerical verification of the Riemann hypothesis by a collaborative computing effort, with downloadable software. http://www.zetagrid.net/

ZetaGrid ZetaGrid Acknowledgement Performance characteristics Riemann Hypothesis Prizes ... Links This site is owned by Sebastian Wedeniwski Sponsors IBM Deutschland Entwicklung GmbH Webhosting powered by EDIS.at Do you need help? Try the ZetaGrid forum What is ZetaGrid? ZetaGrid is a platform independent grid system that uses idle CPU cycles from participating computers. Grid computing can be used for any CPU intensive application which can be split into many separate steps and which would require very long computation times on a single computer. ZetaGrid can be run as a low-priority background process on various platforms like Windows, Linux, AIX, Solaris, HP-UX, and Mac OSX. On Windows systems it may also be run in screen saver mode. ZetaGrid in practice: Riemann's Hypothesis is considered to be one of modern mathematics most important problems. This implementation involves more than 11,000 workstations and has a peak performance rate of about 7056 GFLOPS. More than 1 billion zeros for the zeta function are calculated every day. To learn more about ZetaGrid, you have two options:

159. Scientific Method: Hypothesis For A Science Fair Project The hypothesis What do you think may be the answer to your question? The hypothesis is the possible answer you will try to prove or disprove. Examples http://sciencefairproject.virtualave.net/hypothesis.htm

Home Links Email The Steps of a Science Fair Project ... Judging Sheet Example The Steps of a Science Fair Project 1.Observation 2.Question 3.Hypothesis 4.Method ... 7.Presentation The Hypothesis: What do you think may be the answer to your question? The hypothesis is the possible answer you will try to prove or disprove Examples: Are rocks classified according to hardness, color, density? Do pillbugs prefer moist surroundings? Are people's left and right feet the same size? Does the moon always rise at the same time? Do all fluids weigh the same? How much salt will dissolve in a cup of water- and what about sugar? How do matches work? If you get this far and realize your question cannot be answered by the scientific method, return to step 2 and figure out whether any part of your question involves something which can be measured. If not, it is a question science can't answer. If yes, rephrase your question accordingly and continue. Related Links

160. Selected Classic Papers From The History Of Chemistry Historically important papers in the fields of Atomic hypothesis and discrete nature of matter Electricity, electrochemistry, and electrolyte solutions The electron and electronic structure of matter Elements nature, number, and discovery Environmental chemistry Gases Periodic table and periodic law Radioactivity and the nucleus Thermodynamics http://web.lemoyne.edu/~giunta/papers.html

Selected Classic Papers from the History of Chemistry The following papers from the history of chemistry are available as html files. Many are seminal papers in their fields. Some are interesting curiosities. Papers are arranged by subject below, or alphabetically Most of the entries reside either at the Classic Chemistry site at Le Moyne College or on the historical papers section of John Park's ChemTeam site. Links to classic papers outside the Classic Chemistry site are clearly credited. Analytical, instrumental, and spectroscopic techniques Atomic hypothesis and discrete nature of matter Biochemistry Bonding and Structure ... Others Analytical, instrumental, and spectroscopic techniques Gustav Kirchhoff and Robert Bunsen (1860): bright-line flame spectra (applied to alkali metals and alkaline earths). This paper is at the ChemTeam site. (Link to biographical data on Bunsen and Kirchhoff Chandrasekhara V. Raman and K. S. Krishnan : 1928 paper on the Raman effect (posted by Jim Holler , Department of Chemistry, University of Kentucky). View a biographical sketch of Raman.

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