Belfer Graduate School of Science 1958-1978No Descriptionhttps://hdl.handle.net/20.500.12202/8578https://repository.yu.edu/bitstreams/5e60627c-551a-47c7-95f3-b2872f1912dd/download2024-11-13T22:26:16Z2024-11-13T22:26:16Z511Existence and completeness of wave operators in two Hilbert spacesAltabet, Meryl J.https://hdl.handle.net/20.500.12202/91972023-09-13T00:50:16Z1984-06-01T00:00:00Zdc.title: Existence and completeness of wave operators in two Hilbert spaces
dc.contributor.author: Altabet, Meryl J.
dc.description.abstract: In 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.
dc.description: Doctoral dissertation, PhD / Open Access
1984-06-01T00:00:00ZDifference equation methods for solution of partial differential equationsKohn, Meryle Cherrickhttps://hdl.handle.net/20.500.12202/28042023-11-15T16:31:55Z1982-01-01T00:00:00Zdc.title: Difference equation methods for solution of partial differential equations
dc.contributor.author: Kohn, Meryle Cherrick
dc.description.abstract: Difference 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.
dc.description: Doctoral dissertation, PhD / YU only
1982-01-01T00:00:00ZTwo parallel queues created by arrivals with two demandsHahn, Susan Annhttps://hdl.handle.net/20.500.12202/28022023-11-15T16:17:48Z1982-01-01T00:00:00Zdc.title: Two parallel queues created by arrivals with two demands
dc.contributor.author: Hahn, Susan Ann
dc.description.abstract: In this thesis we consider the system of two unbounded single server queues in which a customer upon arrival joins both queues. The arrivals are assumed to form a Poisson process with mean interarrival time 1 and the servers have exponential service time distribution with means 1/(alpha) and 1/(beta) respectively. It is assumed 1 < (alpha) (LESSTHEQ) (beta) and hence the equilibrium probabilities p(,ij) are positive for all i,j and.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;The functional equation for the generating function.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;is obtained from the equilibrium equations. This equation exhibits a relation between the functions P(z,0), P(0,w) on the algebraic curve S = {lcub}(z,w): (zw)('2) - (1 + (alpha) + (beta))zw + (alpha)w + (beta)z = 0{rcub}. S is parametrized by a pair of elliptic functions z = z(t), w = w(t) and the functional equation is converted into automorphy conditions for A(t) = P(z(t),0) and B(t) = P(0,w(t)), which are then continued analytically to the whole t-plane. A(t) and B(t), and hence P(z,0), P(0,w), P(z,w) are obtained in closed form. Asymptotic formulas for p(,ij) as i,j (--->) (INFIN) are obtained from the expression for P(z,w).
dc.description: Doctoral dissertation, PhD / YU only
1982-01-01T00:00:00ZON THE COMPLETENESS OF (F(N THETA)) AND A RECIPROCAL THEOREM FOR ABSOLUTELY CONVERGENT DIRICHLET SERIESGOODMAN, ARTHURhttps://hdl.handle.net/20.500.12202/26652023-08-21T21:54:00Z1980-01-01T00:00:00Zdc.title: ON THE COMPLETENESS OF (F(N THETA)) AND A RECIPROCAL THEOREM FOR ABSOLUTELY CONVERGENT DIRICHLET SERIES
dc.contributor.author: GOODMAN, ARTHUR
dc.description.abstract: One of the basic questions in approximation theory is: given a Banach space B, and S a subset of B, under what conditions will S be "rich" enough to approximate any element of B by a finite linear combination of elements of S. The most important result of this type pertains to the case where B is the Banach space of continuous functions on a finite interval with the supremum norm, and S is the set of monomials {l,x,x 2, ••• }. In this case the famous Weierstrass Theorem asserts that any element of B can be uniformly approximated by a finite linear combination of elements of S, that is any continuous function on a finite interval can be uniformly approximated by a polynomial. (from Introduction)
dc.description: Doctoral dissertation, PhD / YU only
1980-01-01T00:00:00ZThe representation ring of some finite simple groupsRabinowitz, Aliza Dubinhttps://hdl.handle.net/20.500.12202/25612023-11-15T16:39:37Z1979-01-01T00:00:00Zdc.title: The representation ring of some finite simple groups
dc.contributor.author: Rabinowitz, Aliza Dubin
dc.description.abstract: This paper is concerned with some of the representations and
representation rings of PSL(n, p). • We show how Frobenius 's original
method of character computation can be applied to PSL(2,5), and
give derivations for all the characters of PSL(3,p). We find the
reprasentation ring of PSL(2,p) and PSL(3,p).
dc.description: Doctoral dissertation, PhD / YU only
1979-01-01T00:00:00ZPhase transitions in three-component fluid systemsSato, Makotohttps://hdl.handle.net/20.500.12202/24792023-10-06T14:01:49Z1978-01-01T00:00:00Zdc.title: Phase transitions in three-component fluid systems
dc.contributor.author: Sato, Makoto
dc.description.abstract: We prove the existence of phase segregation in a three component
Widom-Rowlinson fluid mixture with activities εA=εB=ε≥εc.
for sufficiently large ε. Integration
over the coordinates of one component in a three-component
Widom-Rowlinson Model yields a binary systems with hard core
plus attractive many body potentials. We investigate some
features of the phase diagram of such a binary mixture using
the results of mean field theory and of series expansion for
the three-component Widom-Rowlinson model. We also find a
general way of obtaining the equation of state of multi-component
one-dimensinal systems with non-additive hard
core diameters and nearest neighbor soft potentials.
dc.description: Doctoral dissertation / YU ONLY
1978-01-01T00:00:00ZInterpretation of molecular absorption in the atmosphere of JupiterSATO, MAKIKOhttps://hdl.handle.net/20.500.12202/24782023-08-22T14:38:26Z1978-01-01T00:00:00Zdc.title: Interpretation of molecular absorption in the atmosphere of Jupiter
dc.contributor.author: SATO, MAKIKO
dc.description: Doctoral dissertation, PhD / YU only
1978-01-01T00:00:00ZStrong Coupling Calculations Of The Nonlinear Sigma ModelHan, Daesoohttps://hdl.handle.net/20.500.12202/24412023-08-21T21:54:48Z1977-01-01T00:00:00Zdc.title: Strong Coupling Calculations Of The Nonlinear Sigma Model
dc.contributor.author: Han, Daesoo
dc.description: Doctoral dissertation, PhD / YU only
1977-01-01T00:00:00ZStates in separable algebrasCzarnocha, Bronislawhttps://hdl.handle.net/20.500.12202/23882023-08-21T21:45:23Z1976-01-01T00:00:00Zdc.title: States in separable algebras
dc.contributor.author: Czarnocha, Bronislaw
dc.description: Doctoral dissertation, PhD / Open Access
1976-01-01T00:00:00ZI. Pyrolysis of Dibenzotropilidene. Ii. Bicyclobutane-coupling constantsFink, Rinahttps://hdl.handle.net/20.500.12202/23492023-11-15T15:48:55Z1976-01-01T00:00:00Zdc.title: I. Pyrolysis of Dibenzotropilidene. Ii. Bicyclobutane-coupling constants
dc.contributor.author: Fink, Rina
dc.description: Doctoral dissertation, PhD / YU only
1976-01-01T00:00:00Z