# Belfer Graduate School of Science 1958-1978

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Item Restricted A circular model for an interacting Fermi gas(ProQuest Dissertations & Theses, 1969) Witteles, Eleonora Meira; Carmi, Gideon; Lebowitz, Joel L.; Landovitz, Leon F.In this work we study a circular one dimensional model for an interacting Fermi gas. We consider an interparticle potential having the properties that its Fourier transform has a functional form (-)k/k2, and."whose spatial form is such that it can be solved exactly in the thermodynamic limit using the Green's function technique. The results obtained from such an exact solution are compared with the conclusions reached, by studying the problem using three dimentional systems. It turns out however that the RPA brakes down for our model system. We therfore make a further approximation (which we call the Modified Random Phase Approximation (MRPA) ). _ l. __The study of the system in the MRPA shows that a :first order phase transition is possible. The thermodynamic properties of the system and the question of the possibility of a first order phase transition is also studied in the exact solution of our .model system. __Upon further study of our circular one dimensional model within the MRPA and using the BCS simplification and the BCS ansatz for the trial function for the system, we show that our system exhibits superconductive behavior in the sense that we show the existence of an energy gap in the single particle energy spectrum. We show the existence of a critical magnetic field and a discontinuity in the specific heat for the system. i.e. we show the existence of a second order phase transition.Item Restricted A history of finite group theory in the United States: 1888-1916(ProQuest Dissertations & Theses, 1975) Craig, Robert T.; Grosof, Miriam S.; Flatto, Leopold; Newman, Donald J.; Woodruff, Arthur E .The study of finite group theory in the United States at the end of the 19th century and beginning of the 20th century. (from Introduction)Item Restricted A history of relativity: The role of Henri Poincaré and Paul Langevin(ProQuest Dissertations & Theses, 1970) Cuvaj, CamilloAmong the goals followed in the present study are: first~' to do justice to the contributions to relativity by Poincaré, Langevin and other neglected work; secondly, to consider their work when it was interesting per se regardless of its external influence (or lack of it); thirdly, to concentrate frequently on mathematical aspects of problems, (following the method of E. Whittaker) since I am convinced of the inadequacy of all the qualitative treatments; fourthIy, to demolish the unwritten law that a thesis or a work on the history of science should be uniformly dull, without admitting humorous or entertaining passages. '__What is meant by relativity here? I shall not systematically discuss the work of earlier men such as Galileo, Huygens, Leibniz, Boskovich, Kant, Mach, E. Mascart and B. Russell. I shall start with Voigt and Lorentz. Confusion will be avoided by distinguishing13 or omitting the philosophical concept of relativity and the common concept of subjective relativity of observers or of sense-perception. __Finally, in analysing the original architecture of relativity one obtains a different structure on consideration of mutual influence rather than just simple chronology, as I have respectively drawn below (Fig. 1), with some crucial links mainly due to the efforts of Holton and Keswani. (from Introduction)Item Metadata only A NEW METHOD IN THE STUDY OF NONLINEAR FREDHOLM OPERATOR EQUATIONS(ProQuest Dissertations & Theses, 1974) PODOLAK, ESTHERItem Open Access An N-Dimensional Muntz-Jackson Theorem(ProQuest Dissertations & Theses, 1966) Passow, Eli Aaron; Newman, Donald J.The main theorem of approximation theory is that of Weierstrass, [7], which states that the closure of the monomials [l,x,x2, ••• }, on a compact set, X , is the set of all continuous function on X, C {X). There are many generalizations of this theorem, and two, in particular, are of concern in this paper.Item Open Access Analysis of an ultrafast discharge in air produced by a megavolt pulse system(ProQuest Dissertations & Theses, 1967) Shuchatowitz, JoshuaItem Open Access Approaches to the synthesis of macrolides(ProQuest Dissertations & Theses, 1971) Gross, Leonard; Borowitz, Irving J.; Snyder, James P.; Pomerantz, Martin; Fujimoto, George; Goldstein,Item Restricted Approximation by invertibles and extensions of the index(ProQuest Dissertations & Theses, 1972) Gartenberg, Michael; Coburn, Lewis A.; Berger, Charles A.; Lebow, ArnoldItem Open Access Approximation to separated functions on Cartesian product spaces(ProQuest Dissertations & Theses, 1966) Grosof, Miriam Schapiro; Rauch, Harry E.; Newman, Donald J·,; Flatto, Leopold; Koranyi, AdamIntroduction: The purpose of this paper is to generalize some results contained in _Some theorems of Chebyshev's approximations_, by D. J. Newman and H. S. Shapiro [3], and to exhibit the failure of certain other generalizations. This problem was suggested by Professor Donald J. Newman ; I wish to acknowledge, with deep gratitude, his innumerable helpful suggestions and constant encouragement. ¶ The work has been carried out, in part, under N. S. F. Summer Fellowships for Graduate Teaching Assistants (1964 and 1965). ¶ Numbers in brackets refer to the bibliography at the end of the paper.Item Open Access Asymptotic Relations Between Differential And Difference Equations(ProQuest Dissertations & Theses, 1968) Gerber, Leon E.; Newman, Donald J.; Flatto, Leopold; Lewittes, JosephItem Restricted Boundary limits of h('p)-functions in tube domains(ProQuest Dissertations & Theses, 1972) Hughes, Anne; Korányi, Ádám; Sawyer, Stanley; Putz, Robert B.Item Open Access Completeness Theorems for Special Classes of Trigonometric Polynomials(ProQuest Dissertations & Theses, 1967) FEINERMAN, ROBERT PHILIPItem Restricted Conjugate points on homogeneous spaces(ProQuest Dissertations & Theses, 1966) Chavel, Isaac; Rauch, Harry E.; Newman, Donald J.; Flatto, Leopold; Koranyi, AdamItem Restricted Difference equation methods for solution of partial differential equations(ProQuest Dissertations & Theses, 1982) Kohn, Meryle Cherrick; Ehrenpreis, Leon; Lebow, Arnold; Rosenfeld, NormanDifference equation techniques are applied to determine sufficient conditions on polynomials P(x,y) for which the Fischer space related differential equation.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;has (a) no non-trivial solutions f(x,y); (b) locally convergent solutions; and (c) formal solutions; {lcub}where P(x,y) is a polynomial with complex coefficients,;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;is the differential operator whose coefficients are the complex conjugates of the coefficients of P, and.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;Solutions of a general difference equation in two dimensions, (SIGMA) K(,i)C(,m+ai, n+bi) = 0 with K(,i) non-vanishing, are analyzed. Particular emphasis is placed on solutions with C(,mn) = 0 in specified regions of the plane.;Difference equations corresponding to the differential equation.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;(where P and Q are polynomials) are examined to determine sufficient conditions on P and Q for which the equation has (a) no non-trivial solution; (b) polynomial solutions; and (c) formal solutions.Item Restricted Dual symmetric theory and the harmonic oscillator model of hadrons.(ProQuest Dissertations & Theses, 1970) Gallardo, Juan Carlo; Susskind, Leonard; Aharonov, Yakir; Frye, GrahamThe exciting activities the last two years :in the direction of dual resonance models,in particular the simple renormalization procedure £ow1d to eliminate the divergency :in loop graphs [12] and the symmetry properties encounter in the amplitudes which provides Ward-like identities [1.3] to be used to solve the problem of the ghost particles; and most of all the beautiful physical :interpretation discussed by Nielsen [14] and Susskind [15] exploting the conformal invariance of the theory,have :increased the hope of being on the right track for finding a general scheme to describe the physics or strong interactions. (from Introduction)Item Open Access Ergodic Theory and Infinite-Systems(ProQuest Dissertations & Theses, 1974) GOLDSTEIN, SHELDON; Lebowitz, Joel L.; Lanford, III, Oscar E.; Newman, Donald E.Item Open Access Ergodic theory in statistical mechanics(ProQuest Dissertations & Theses, 1975) Aizenman, Michael; Lebowitz, Joel L.; Landford, III, Oscar E.; Penrose, OliverItem Open Access Existence and completeness of wave operators in two Hilbert spaces(Yeshiva University, 1984-06) Altabet, Meryl J.; Schechter, Martin; Lebow, Arnold; Rosenfeld, NormanIn this thesis we consider an unperturbed self-adjoint operator H(,0) on a Hilbert space H(,0), the operators A, B mapping H(,0) to the Hilbert space K, and J a bounded linear operator mapping the Hilbert space H(,0) to the Hilbert space H.;Our first objective is to give conditions under which there exists a perturbed self-adjoint operator H such that R(z)J - JR(,0)(z) = -(BJ('*)R(z))*AR(,0)(z) and HJ(R-HOOK)J(H(,0) + B('*)A). We prove the existence of the operator H by actually constructing its resolvent R(z).(').;Our next objective is to consider two specific operators H(,0), the momentum operator and the kinetic energy operator, and to give examples of A, B, J for which the main conclusions of scattering theory hold. In obtaining conditions for the existence and completeness of the wave operator, we use a combination of time dependent and stationary methods.Item Restricted Formation and synthetic utility of enol phosphorylated species(ProQuest Dissertations & Theses, 1972) Crouch, Rosalie Kelsey; Pomerantz, Martin; Snyder, James P.; Goldstein, Martin; Seifter, EliItem Restricted General properties of dual models: Conformal invariance(ProQuest Dissertations & Theses, 1970) Galli, Alicia J. Couto; Susskind, Leonard; Frye, Graham; Behrends, Ralph

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