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THE RIEMANN HYPOTHESIS BERNARD RUSSO University Of
THE RIEMANN HYPOTHESIS BERNARD RUSSO University of California, Irvine PART I THE PRIME NUMBER THEOREM JULY 29, 2010 PACIFIC SUMMER UNSOLVED PROBLEMS SEMINAR PART II THE RIEMANN HYPOTHESIS SEPTEMBER 14, 2010 MATH COLLOQUIUM FULLERTON COLLEGE DEPARTMENT OF MATHEMATICS BEGINNING OF PART I “book report” “PRIME OBSESSION” JOHN DERBYSHIRE 2003 PRESENTATION OF CREDENTIALS Bernard Russo 1965 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 M. Riesz 1912 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 M. Riesz 1912 L. Fejer 1902 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 M. Riesz 1912 L. Fejer 1902 H. A. Schwarz 1864 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 M. Riesz 1912 L. Fejer 1902 H. A. Schwarz 1864 Karl Weierstrass 1854—E. E. Kummer 1831 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 M. Riesz 1912 L. Fejer 1902 H. A. Schwarz 1864 Karl Weierstrass 1854—E. E. Kummer 1831 C. Gudermann 1841—H. Scherk 1823 PRESENTATION OF CREDENTIALS Bernard Russo 1965 Henry Dye 1950 Irving Segal 1940 Einar Hille 1918 M. Riesz 1912 L. Fejer 1902 H. A. Schwarz 1864 Karl Weierstrass 1854—E. E. Kummer 1831 C. Gudermann 1841—H. -
Regal (Hastings) Ltd V Gulliver (1942)
This is a repository copy of Regal (Hastings) Ltd v Gulliver (1942). White Rose Research Online URL for this paper: https://eprints.whiterose.ac.uk/75080/ Version: Published Version Book Section: Nolan, Richard orcid.org/0000-0002-7134-5124 (2012) Regal (Hastings) Ltd v Gulliver (1942). In: Landmark Cases in Equity. Hart Publishing Limited , Oxford , pp. 499-528. Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ 17 Regal (Hastings) Ltd v Gulliver (1942) RICHARD NOLAN A. INTRODUCTION LMOST 70 YEARS have passed since the House of Lords’ decision in Regal (Hastings) Ltd v Gulliver,1 and over 40 years since it Afigured so prominently in Boardman v Phipps,2 yet little is known about the very strange course of the proceedings in Regal. At first instance, and in the Court of Appeal, Regal was argued and decided as a case at common law for negligence, money had and received, or misfeasance. -
Irving Kaplansky
Portraying and remembering Irving Kaplansky Hyman Bass University of Michigan Mathematical Sciences Research Institute • February 23, 2007 1 Irving (“Kap”) Kaplansky “infinitely algebraic” “I liked the algebraic way of looking at things. I’m additionally fascinated when the algebraic method is applied to infinite objects.” 1917 - 2006 A Gallery of Portraits 2 Family portrait: Kap as son • Born 22 March, 1917 in Toronto, (youngest of 4 children) shortly after his parents emigrated to Canada from Poland. • Father Samuel: Studied to be a rabbi in Poland; worked as a tailor in Toronto. • Mother Anna: Little schooling, but enterprising: “Health Bread Bakeries” supported (& employed) the whole family 3 Kap’s father’s grandfather Kap’s father’s parents Kap (age 4) with family 4 Family Portrait: Kap as father • 1951: Married Chellie Brenner, a grad student at Harvard Warm hearted, ebullient, outwardly emotional (unlike Kap) • Three children: Steven, Alex, Lucy "He taught me and my brothers a lot, (including) what is really the most important lesson: to do the thing you love and not worry about making money." • Died 25 June, 2006, at Steven’s home in Sherman Oaks, CA Eight months before his death he was still doing mathematics. Steven asked, -“What are you working on, Dad?” -“It would take too long to explain.” 5 Kap & Chellie marry 1951 Family portrait, 1972 Alex Steven Lucy Kap Chellie 6 Kap – The perfect accompanist “At age 4, I was taken to a Yiddish musical, Die Goldene Kala. It was a revelation to me that there could be this kind of entertainment with music. -
Six Great Advocates by Kylie Day
LEGAL HISTORY Six great advocates By Kylie Day At the swearing in of Fullerton J in the Supreme Court In short, the book is a delight. It is a quick afternoon’s of New South Wales earlier this year, Michael Slattery read, and Lord Birkett’s style is engaging and easy. QC referred to the extravagant compliment paid by There are a number of things that I particularly like Sir Patrick Hastings KC, the great English advocate about Six Great Advocates. One is Lord Birkett’s gift for of the 1920s, to friend and fellow advocate Norman making these advocates of a bygone era come to life. Birkett. Hastings is reported to have said of Birkett: The reader gets very close to the experience of seeing and hearing them in action in the courtroom, because ... if it had ever been my lot to decide to cut up a of Lord Birkett’s powers of description and attention lady into small pieces and put her in an unwanted to detail. No doubt the reality is heightened because suitcase, I should without hesitation have placed he knew a number of them personally. It helps that he my future in Norman Birkett’s hands. He would was briefed on the other side in some of the cases from have satisfied the jury (a) that I was not there, (b) which he plucks moments. Lord Birkett also understood that I had not cut up the lady and (c) that if I had well the difference between the written word, and she had thoroughly deserved it anyway. -
Members of Parliament Disqualified Since 1900 This Document Provides Information About Members of Parliament Who Have Been Disqu
Members of Parliament Disqualified since 1900 This document provides information about Members of Parliament who have been disqualified since 1900. It is impossible to provide an entirely exhaustive list, as in many cases, the disqualification of a Member is not directly recorded in the Journal. For example, in the case of Members being appointed 5 to an office of profit under the Crown, it has only recently become practice to record the appointment of a Member to such an office in the Journal. Prior to this, disqualification can only be inferred from the writ moved for the resulting by-election. It is possible that in some circumstances, an election could have occurred before the writ was moved, in which case there would be no record from which to infer the disqualification, however this is likely to have been a rare occurrence. This list is based on 10 the writs issued following disqualification and the reason given, such as appointments to an office of profit under the Crown; appointments to judicial office; election court rulings and expulsion. Appointment of a Member to an office of profit under the Crown in the Chiltern Hundreds or the Manor of Northstead is a device used to allow Members to resign their seats, as it is not possible to simply resign as a Member of Parliament, once elected. This is by far the most common means of 15 disqualification. There are a number of Members disqualified in the early part of the twentieth century for taking up Ministerial Office. Until the passage of the Re-Election of Ministers Act 1919, Members appointed to Ministerial Offices were disqualified and had to seek re-election. -
Irving Ezra Segal (1918–1998)
mem-segal.qxp 5/12/99 12:57 PM Page 659 Irving Ezra Segal (1918–1998) John C. Baez, Edwin F. Beschler, Leonard Gross, Bertram Kostant, Edward Nelson, Michèle Vergne, and Arthur S. Wightman Irving Segal died suddenly on August 30, 1998, After the war while taking an evening walk. He was seventy-nine Segal spent two and was vigorously engaged in research. years at the Insti- Born on September 13, 1918, in the Bronx, he tute for Advanced grew up in Trenton and received his A.B. from Study, where he Princeton in 1937. What must it have been like to held the first of the be a member of the Jewish quota at Princeton in three Guggenheim the 1930s? He told me once that a fellow under- Fellowships that he graduate offered him money to take an exam in his was to win. Other stead and was surprised when Irving turned him honors included down. election to the Na- He received his Ph.D. from Yale in 1940. His the- tional Academy of sis was written under the nominal direction of Sciences in 1973 Einar Hille, who suggested that Segal continue his and the Humboldt Award in 1981. At and Tamarkin’s investigation of the ideal theory the University of of the algebra of Laplace-Stieltjes transforms ab- Chicago from 1948 solutely convergent in a fixed half-plane. But, Segal to 1960, he had fif- wrote, “For conceptual clarification and for other teen doctoral stu- reasons, an investigation of the group algebra of dents, and at MIT, a general [locally compact] abelian group was of where he was pro- Irving Segal interest.” And the thesis was not restricted to fessor from 1960 abelian groups. -
The Legacy of Norbert Wiener: a Centennial Symposium
http://dx.doi.org/10.1090/pspum/060 Selected Titles in This Series 60 David Jerison, I. M. Singer, and Daniel W. Stroock, Editors, The legacy of Norbert Wiener: A centennial symposium (Massachusetts Institute of Technology, Cambridge, October 1994) 59 William Arveson, Thomas Branson, and Irving Segal, Editors, Quantization, nonlinear partial differential equations, and operator algebra (Massachusetts Institute of Technology, Cambridge, June 1994) 58 Bill Jacob and Alex Rosenberg, Editors, K-theory and algebraic geometry: Connections with quadratic forms and division algebras (University of California, Santa Barbara, July 1992) 57 Michael C. Cranston and Mark A. Pinsky, Editors, Stochastic analysis (Cornell University, Ithaca, July 1993) 56 William J. Haboush and Brian J. Parshall, Editors, Algebraic groups and their generalizations (Pennsylvania State University, University Park, July 1991) 55 Uwe Jannsen, Steven L. Kleiman, and Jean-Pierre Serre, Editors, Motives (University of Washington, Seattle, July/August 1991) 54 Robert Greene and S. T. Yau, Editors, Differential geometry (University of California, Los Angeles, July 1990) 53 James A. Carlson, C. Herbert Clemens, and David R. Morrison, Editors, Complex geometry and Lie theory (Sundance, Utah, May 1989) 52 Eric Bedford, John P. D'Angelo, Robert E. Greene, and Steven G. Krantz, Editors, Several complex variables and complex geometry (University of California, Santa Cruz, July 1989) 51 William B. Arveson and Ronald G. Douglas, Editors, Operator theory/operator algebras and applications (University of New Hampshire, July 1988) 50 James Glimm, John Impagliazzo, and Isadore Singer, Editors, The legacy of John von Neumann (Hofstra University, Hempstead, New York, May/June 1988) 49 Robert C. Gunning and Leon Ehrenpreis, Editors, Theta functions - Bowdoin 1987 (Bowdoin College, Brunswick, Maine, July 1987) 48 R. -
Quantization, Nonlinear Partial Differential Equations,And Operator
http://dx.doi.org/10.1090/pspum/059 Other Titles in This Series 59 William Arveson, Thomas Branson, and Irving Segal, editors, Quantization, nonlinear partial differential equations, and operator algebra (Massachusetts Institute of Technology, Cambridge, June 1994) 58 Bill Jacob and Alex Rosenberg, editors, K-theory and algebraic geometry: Connections with quadratic forms and division algebras (University of California, Santa Barbara, July 1992) 57 Michael C. Cranston and Mark A. Pinsky, editors, Stochastic analysis (Cornell University, Ithaca, July 1993) 56 William J. Haboush and Brian J. Parshall, editors, Algebraic groups and their generalizations (Pennsylvania State University, University Park, July 1991) 55 Uwe Jannsen, Steven L. Kleiman, and Jean-Pierre Serre, editors, Motives (University of Washington, Seattle, July/August 1991) 54 Robert Greene and S. T. Yau, editors, Differential geometry (University of California, Los Angeles, July 1990) 53 James A. Carlson, C. Herbert Clemens, and David R. Morrison, editors, Complex geometry and Lie theory (Sundance, Utah, May 1989) 52 Eric Bedford, John P. D'Angelo, Robert E. Greene, and Steven G. Krantz, editors, Several complex variables and complex geometry (University of California, Santa Cruz, July 1989) 51 William B. Arveson and Ronald G. Douglas, editors, Operator theory/operator algebras and applications (University of New Hampshire, July 1988) 50 James Glimm, John Impagliazzo, and Isadore Singer, editors, The legacy of John von Neumann (Hofstra University, Hempstead, New York, May/June 1988) 49 Robert C. Gunning and Leon Ehrenpreis, editors, Theta functions - Bowdoin 1987 (Bowdoin College, Brunswick, Maine, July 1987) 48 R. O. Wells, Jr., editor, The mathematical heritage of Hermann Weyl (Duke University, Durham, May 1987) 47 Paul Fong, editor, The Arcata conference on representations of finite groups (Humboldt State University, Arcata, California, July 1986) 46 Spencer J. -
Publications of Irving Segal Papers
Publications of Irving Segal Papers [1] Fiducial distribution of several parameters with application to a normal system, Proc. Camb. Philos. Soc. , 34 (1938), 41–47. Zbl 018.15703 [2] The automorphisms of the symmetric group, Bull. Amer. Math. Soc. 46 (1940), 565. MR 2 #1c Zbl 061.03301 [3] The group ring of a locally compact group. I, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 348–352. MR 3 #36b Zbl 063.06858 [4] The span of the translations of a function in a Lebesgue space, Proc. Nat. Acad. Sci. U. S. A. 30 (1944), 165–169. MR 6 #49c Zbl 063.06859 [5] Topological groups in which multiplication of one side is differen- tiable, Bull. Amer. Math. Soc. 52 (1946), 481–487. MR 8 #132d Zbl 061.04411 [6] Semi-groups of operators and the Weierstrass theorem, Bull. Amer. Math. Soc. 52 (1946), 911–914. (with Nelson Dunford) MR 8 #386e Zbl 061.25307 [7] The group algebra of a locally compact group, Trans. Amer. Math. Soc. 61 (1947), 69–105. MR 8 #438c Zbl 032.02901 [8] Irreducible representations of operator algebras, Bull. Amer. Math. Soc. 53 (1947), 73–88. MR 8 #520b Zbl 031.36001 [9] The non-existence of a relation which is valid for all finite groups, Bol. Soc. Mat. S˜aoPaulo 2 (1947), no. 2, 3–5 (1949). MR 13 #316b [10] Postulates for general quantum mechanics, Ann. of Math. (2) 48 (1947), 930–948. MR 9 #241b Zbl 034.06602 [11] Invariant measures on locally compact spaces, J. Indian Math. Soc. -
The 3-Fold Way and Consciousness Studies K. Korotkov, A. Levichev
© K. Korotkov, A. Levichev The 3-fold Way and Consciousness Studies K. Korotkov, A. Levichev Contents Part I. Biological fields and Quantum Mechanical representations I.1. Conventional Quantum Mechanical representations. I.2. Chronometric development of QM and the DLF-perspective. I.3. Fields of biological subjects. Part II. Penrose-Hameroff approach to quantum mechanics as the foundation for a theory of consciousness II.1. Discussion of some quantum-mechanical topics involved II.2. Quantum coherence, quantum computation, and where to seek the physical basis of mind II.3. The Penrose-Hameroff Orchestrated Objective Reduction model II.4. DLF-approach implanted into Penrose-Hameroff model Part III. Segal’s Chronometry and its LF-development III.1. Segal’s Chronometric Theory: a brief overview. III.2. Space-times L, F are on equal footing with D; the list is now complete III.3. Can the New Science be based on the DLF-triad? Part IV. Emergence of New Science and the GDV Bioelectrography IV.1. The three worlds have been known to humanity since ancient times IV.2. Is Direct Vision an example of L-phenomenon? I.1. Conventional Quantum Mechanical representations. Accordingly to quantum mechanics, each object is described by its state, or wave function. We prefer to use “state”, since (initially, at least) it is neither numerical-, nor vector-valued. Rather, it is a section of an induced vector bundle over space- time. It can be converted into a function (with values in a prescribed “spin space”) but one needs to go through the “parallelization” procedure (see our III.2, III.3 for more details). -
The Measure Algebra of the Heisenberg Group* L
Journal of Functional Analysis 161, 509525 (1999) Article ID jfan.1998.3354, available online at http:ÂÂwww.idealibrary.com on The Measure Algebra of the Heisenberg Group* L. A. Coburn Department of Mathematics, State University of New York, Buffalo, New York 14214 Communicated by Irving Segal Received June 16, 1998; revised August 28, 1998; accepted August 28, 1998 Irreducible representations of the convolution algebra M(Hn) of bounded regular complex Borel measures on the Heisenberg group Hn are analyzed. For the SegalBargmann representation \, the C*-algebra generated by \[M(Hn)] is just the C*-algebra generated by BerezinToeplitz operators with positive-definite ``symbols.'' This algebra is a deformation of the sup norm algebra generated by n View metadata,positive-definite citation and functions similar on papers complex at core.ac.ukn-space C . 1999 Academic Press brought to you by CORE provided by Elsevier - Publisher Connector 1. INTRODUCTION The Heisenberg group Hn is a nilpotent Lie group which plays a critical role in quantum mechanics and a significant role in representation theory. The irreducible infinitedimensional unitary representations of Hn satisfy the ``canonical commutation relations.'' Recently, [BC1 ,BC2 ,BC3 ,] provided an analysis of the C*-algebra generated by these unitary operators using the complex-function theory tools available in the SegalBargmann repre- sentation space. This work suggests an interesting connection between the convolution algebra M(Hn) of bounded regular Borel measures on Hn and the BerezinToeplitz quantization. In particular, for the SegalBargmann representation \, the C*-algebra generated by \[M(Hn)] is just the C*- algebra generated by BerezinToeplitz operators with positive-definite ``symbols.'' This algebra is a deformation of the sup norm algebra generated by positive-definite functions on complex n-space Cn. -
Projective Loop Quantum Gravity II. Searching for Semi-Classical States
Projective Loop Quantum Gravity II. Searching for1,2 Semi-Classical States1 Suzanne Lanéry and homas hiemann 1 Institute for Quantum Gravity, Friedrich-Alexander University Erlangen-Nürnberg, Germany 2 Mathematics and #heoretical Physics Laboratory, François-Rabelais University of #ours, France October 7, 2015 Abstract In [13] an extension of the Ashtekar-Lewandowski (AL) state space [2] of %oop Quantum Gravity was set up with the help a projective formalism introduced by 5ijowski [12, 21, 15]. #he motivation for this work was to achieve a more balanced treatment of the position and momentum variables (aka. holonomies and fluxes). Indeed, states in the AL Hilbert spaces describe discrete quantum excitations on top of a vacuum which is an eigenstate of the flux variables (a ‘no-geometry’ state): in such states, most holonomies are totally spread, making it difficult to approximate a smooth, classical 4-geometry. However, going beyond the AL sector does not fully resolve this difficulty: one uncovers a deeper issue hindering the constructionSU of states semi-classical with respect to a full set of observables. In the present article, we analyze this issue in the case of real-valued holonomies 1we will briefly comment on the heuristic implications for other gauge groups, eg. (2) 26 Specifically, we sho 0 that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomies and fluxes observables would all be finite, let alone small6 It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself: as there are too many (uncountably many) non-vanishing commutators between the holonomy and flux operators, the corresponding Heisenberg inequalities force the quantum uncertainties to blow up uncontrollably.