# Belfer Graduate School of Science 1958-1978

Permanent URI for this communityhttps://hdl.handle.net/20.500.12202/8578

## Browse

# Browsing Belfer Graduate School of Science 1958-1978 by Issue Date

Now showing 1 - 20 of 51

- Results Per Page
- Sort Options

Item Open Access Solution of the Dirichlet problem in parallel slit domains(ProQuest Dissertations & Theses, 1963) Zuckerberg, Hyam L.Item Restricted Weak and electromagnetic interactions in quaternion quantum mechanics(ProQuest Dissertations & Theses, 1964) Tavel, Morton Allen; Bergmann, Peter G.; Finkelstein, David; Komar, Arthur; Landovitz, Leon; Behrends, RalphIn the following paragraphs we will review1 ,3 briefly the formalism required to crystallize the basic automorphic symmetry of the quaternions into an invariance principle within the Lagrangian framework and thence to a description of particle symmetries. We shall see that we are led to a theory where, in fact, isospin is not described by automorphisms because the isospin synmietry is not absolute whereas the automorphic symmetry is inviolate. (from Introduction)Item Restricted Special divisors, theta nulls and analytic subloci of Teichmueller space(ProQuest Dissertations & Theses, 1965) Farkas, Hershel Mark; Rauch, Harry E.; Newman, Donald J .; Flatto, LeopoldItem Restricted Conjugate points on homogeneous spaces(ProQuest Dissertations & Theses, 1966) Chavel, Isaac; Rauch, Harry E.; Newman, Donald J.; Flatto, Leopold; Koranyi, AdamItem 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 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 Restricted SU(3) SYMMETRY IN STRONG COUPLING THEORY(ProQuest Dissertations & Theses, 1966) Theumann, Alba Graciela; Landovitz, Leon F.; Behrends, Ralph E.; Horwitz, Gerald; Komar, ArthurAlthough the basic assumptions and results of the "Strong Coupling Theory" are very well known, we give here a brief review of the essential features of the model, that have helped in the understanding of some experimental results in pion-nucleon interaction .__ When mesons were first considered as interacting with nucleons in analogous way to the interaction of charged particles with the electromagnetic field the theoretical results obtained, the singular nature of nuclear forces and a very large cross section for meson-nucleon scattering, were very far from the experimental facts1__ This departure from agreement with electrodynamics was considered to be due to the difference in the value of the coupling constant. (From Introduction)Item Open Access Completeness Theorems for Special Classes of Trigonometric Polynomials(ProQuest Dissertations & Theses, 1967) FEINERMAN, ROBERT PHILIPItem Open Access Analysis of an ultrafast discharge in air produced by a megavolt pulse system(ProQuest Dissertations & Theses, 1967) Shuchatowitz, JoshuaItem Restricted Perturbation expansion for long-range potentials and spherical models(ProQuest Dissertations & Theses, 1967) THEUMANN, WALTER KARL; Lebowitz, Joel; Horwitz, Gerald; Mattis, DanielThe purpose of the present work is the investigation of the perturbation formalism developed by Lebowitz, Stell and Baer [l] for a classical fluid when expressed in a form suitable for lattice gases [2]. The main interest lies in the prediction of the properties of some simple systems when the systematic expansion of the formalism is carried through.Item Restricted The evolution of the mathematical concept of convergence(ProQuest Dissertations & Theses, 1968) Schommer, Mary Carol; Zlot, William L.; Lewittes, Joseph; Patt, Charles R.Item Open Access Intuitionistic logic model theory and forcing(ProQuest Dissertations & Theses, 1968) Fitting, Melvin Chris; Rauch, Harry E.; Davis, Martin D.; Smullyan, Raymond M.The independence proofs of Cohen for the axiom of choice, the continuum hypothesis, and the axiom of constructability are re-formulated using s. Kripke's intuitionistic logic model theory·. We define transfinite sequences of intuitionistic.models with a 'class' model limit in a manner exactly analogous to the definition of Godel in the classical case of a transfinite sequence of (domains of) classical models, M∞ , with a 'class' model limit, L. Classical independence results are established by working with the intuitionistic models themselves; no classical models are constructed, no countable classical models are required (though the definition of intuitionistic model is essentially the same as that of forcing.) ¶ An intuitionistic (or forcing) generalization of the R∞: sequence (sets with rank) is defined and some connections between it and Scott and Solovay's boolean valued models for set theory are established. ¶ For completeness sake, the first six chapters provide a complete treatment of s. Krlpke's intuitionistic logic model theory. Completeness proofs are given for tableau and axiomatic systems, compactness and Skolem-Lowenheim theorems ·are established, and relations with classical logic are shown. The connection between Kripke rmodel theory and algebraic model theory is shown in the propositional case.Item Restricted Invariants of finite reflection groups(ProQuest Dissertations & Theses, 1968) Wiener, Margaret Mary; Flatto, Leopold; Zlot, William; Newman, DonaldThe invariants of a finite reflection group acting on an n dimensional vector space over a field of characteristic zero have an integrity basis or n invariants. If the underlying field is real or complex this property is a characterization of the finite reflection groups. In this thesis the above statement is proved and we give a method for computing the degrees of the members of the basis. __The construction of a basic set of invariants is shown to be related to the solution of a certain mean value problem. Considerations of this mean value problem lead to a conjecture yielding an explicit construction of a basic set of invariants. The conjecture is verified for most of the irreducible finite reflection groups.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 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 Open Access Weighted l('2) approximation of entire functions and related topics(ProQuest Dissertations & Theses, 1970) Wohlgelernter, Devora Kasachkoff; Newman, Donald J.; Berger, Charles A.; Flatto, LeopoldIn Chapter 1, sufficient conditions for polynomials to be dense in the space of entire functions of· L2 (dm) are examined, where dm is a positive, absolutely continuous measure defined on the complex plane. Let S be the space of entire functions such that [] Write dm(z) as K(z)dxdym K(r,0)rdrd6. The main theorems are: 1) Suppose In inf f K(r,8) is asymptotic to in s6up K(r,6) (together with other mild restrictions). Then polynomials are dense in S. 2) Let K(z) = e-$(z) where ♦(z) is a convex function of z such that et z belongs to S for all complex t. Then the exponentials are complete ins. (Corollary: Polynomials are dense ins.) l) is extended to the several-variable case. 2) was recently proven by B. A. Taylor for the many-variable situation. our proof does not extend beyond the case of one variable, but for this it is simpler and more direct than Taylor's. Examples of spaces in which polynomials are not dense are also given. (from Introduction)Item Open Access Numerical experiments on lattice gas models(ProQuest Dissertations & Theses, 1970) Plischke, Michael; Mattis, Daniel; Landovitz, Leon; Langer, W.D.The two dimensional Ising Model bas never been solved in a finite field.- The critical point exponents,1 however, have all been inferred from the exact solution of Onsager2 in zero field or determined by series expansions.8 It remains to determine the magnetization m(H,T ) for finite H. Recently Mattis and Plischk3 derived rigorous analytic lower bounds to m(H,T ) in terms of the zero field internal energy u(O,T) and the spontaneous magnetization of Yang4 mo(T). As the zero field susceptibility could not be rigorously incorporated into this expression the response to · small fields was much too weak and these analytic bounds do not lie very close to the correct answer. ¶ In this chapter we present the results of numerical computations giving a lower bound to m(H,T) which, except for a small region of the H-T plane, lies within .1% of the correct answer. This lower bound is obtained by dividing the infinite lattice into strips of infinite length and ·width M spins. This is achieved by removing .ferromagnetic bonds and can only lower the magnetization as has been shown by Griffiths .-5. The Kramers-Wannier transfer matrix for . such a strip is a 2N x 2N matrix whose largest eigenvalue, as well as the corresponding eigenvector, we obtain by a simple iterative process described in Section II. ¶ In Section III we introduce a new approximation to the transfer matrix, solvable in zero field, which reproduces co?:completely the critical point behavior of the full Ising Model in zero field. This pseudo transfer matrix has a feature which makes it easier to study numerically.Item Restricted General properties of dual models: Conformal invariance(ProQuest Dissertations & Theses, 1970) Galli, Alicia J. Couto; Susskind, Leonard; Frye, Graham; Behrends, RalphItem Restricted Tableau systems for first order number theory and certain higher order theories(ProQuest Dissertations & Theses, 1970) Walker, Sue Ann; Smullyan, Raymond; Coburn, Lewis; Korányi, ÁdámThis work will examine various topics in higher order logic and proof theory ·from the point of view of tableau systems similar to those developed by Smuilyan in [1]. __Chapter I presents constructive consistency proofs for first: order number theory that are closely related to those of Gentzen [l] ancl Schütte [2]. The development follows that of Schütte. __Chapter II considers topics in pure second order logic and the theory, with an emphasis on the former for the sake of convenience. Here no constructive consistency proofs arc known. I have found, however, a theorem similar to the Hauptsatz hut with a more elegant classical proof, a constructive proof of which would yield a constructive consistency proof for the formal systems discussed. (On the other hand there is at present no reason to assume that this theorem would be likely to have a constructive proof that would be simpler than one for a Hauptsstz.) The higher order logics are considered briefly within the context of a generalized abstract framework similar to those considered by Smullyan in [2]. In particular, a Henkin completeness proof is given which is simultaneously a completeness proof for first-order logic, the usual higher order logics and type theory. __Chapter III completes the proof-theoretic treatment of systems equivalent to those considered by Schütte in [2] that was begun in chapter I. __The first appendix explores further the constructivity of the constructive cut-elimination proof for first order logic. It shows that when we eliminate cuts from a first order proof, we form a new proof which preserves the "arguments" of the first proof although these arguments may be intertwined and some may be deleted, The second appendix illustrates translation procedures for going from a proof in a Schütte system to one in a (Smullyan) tableau system and vice-versa. Such a procedure is presented only for· the first order systems since the modifications for higher order systems ·are easily made.Item Open Access The mean spherical approximation for the primitive model of electrolytes(ProQuest Dissertations & Theses, 1970) WAISMAN, EDUARDO MARIO; Lebowitz, Joel L.; Stell, George; Horowitz, Gerald; Groeneveld, JohannesThe mean spherical model approximate integral equation applied to the primitive model for electrolytes is investigated. The primitive model for electrolytes considers tire solvent only insofar as using the dieletric constant E of the medium in the Coulomb interaction between ions, which have additive hard core diameters. The solution is electrically neutral.

- «
- 1 (current)
- 2
- 3
- »