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Infinite Matrices

Description: This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.
Date: August 1957
Creator: Smallwood, James D.
Partner: UNT Libraries
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Oracle inequalities for SVMs that are based on random entropy numbers

Description: In this paper we present a new technique for bounding local Rademacher averages of function classes induced by a loss function and a reproducing kernel Hilbert space (RKHS). At the heart of this technique lies the observation that certain expectations of random entropy numbers can be bounded by the eigenvalues of the integral operator associated to the RKHS. We then work out the details of the new technique by establishing two new oracle inequalities for SVMs, which complement and generalize or… more
Date: January 1, 2009
Creator: Steinwart, Ingo
Partner: UNT Libraries Government Documents Department
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A Classification of the Homogeneity of Countable Products of Subsets of Real Numbers

Description: Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And f… more
Date: August 2017
Creator: Allen, Cristian Gerardo
Partner: UNT Libraries
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Finite Element Solutions to Nonlinear Partial Differential Equations

Description: This paper develops a numerical algorithm that produces finite element solutions for a broad class of partial differential equations. The method is based on steepest descent methods in the Sobolev space H¹(Ω). Although the method may be applied in more general settings, we consider only differential equations that may be written as a first order quasi-linear system. The method is developed in a Hilbert space setting where strong convergence is established for part of the iteration. We also prov… more
Date: August 1981
Creator: Beasley, Craig J. (Craig Jackson)
Partner: UNT Libraries
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Strings in AdS{sub 3} and the SL(2,R) WZW Model. Part 1: The spectrum

Description: In this paper we study the spectrum of bosonic string theory on AdS{sub 3}. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with non-zero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the repre… more
Date: May 19, 2000
Creator: Maldacena, Juan & Ooguri, Hirosi
Partner: UNT Libraries Government Documents Department
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Quantum mechanical coherence, resonance, and mind

Description: Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in nat… more
Date: March 26, 1995
Creator: Stapp, Henry P.
Partner: UNT Libraries Government Documents Department
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Compact Operators and the Schrödinger Equation

Description: In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The pape… more
Date: December 2006
Creator: Kazemi, Parimah
Partner: UNT Libraries
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Interpolation and Approximation

Description: In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and… more
Date: May 1977
Creator: Lal, Ram
Partner: UNT Libraries
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Quantum entanglement of baby universes

Description: We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in type IIA string theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G=1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is their coherent super… more
Date: December 7, 2006
Creator: Essman, Eric P.; Aganagic, Mina; Okuda, Takuya & Ooguri, Hirosi
Partner: UNT Libraries Government Documents Department
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Full- and Half-Range Theory of Indefinite Sturm-Liouville Problems

Description: This report is concerned with eigenvalue problems of the form Au = lambda Tu, where A is a selfadjoint positive differential operator and T a selfadjoint indefinite multiplicative operator on a Hilbert space H. Three particular cases are discussed in detail. In the first case, A is positive definite and T is unitary; in the second case, A is positive definite and T is bounded, but T⁻¹ is unbounded; in the third case, A is positive, dim ker(A) = 1, and T is bounded, but T⁻¹is unbounded. Emphasis… more
Date: September 1983
Creator: Kaper, Hans G.; Kwong, Man Kam; Lekkerkerker, C. G. & Zettl, A.
Partner: UNT Libraries Government Documents Department
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Truncated Hilbert space approach to models of high-{Tc} superconductivity

Description: In this talk the author introduces a method of diagonalization in a systematically expanded Hilbert space. The author shows some applications of this procedure to several models of relevance to high-Tc superconductivity like the t-J, the t-J{sub z} and Hubbard models. Finally, the author discusses the relation of this method of diagonalization in a reduced Hilbert space with perturbation theory and with variational methods.
Date: July 1, 1995
Creator: Riera, J.
Partner: UNT Libraries Government Documents Department
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Mesh independent convergence of the modified inexact Newton method for a second order nonlinear problem

Description: In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced… more
Date: September 20, 2004
Creator: Kim, T; Pasciak, J E & Vassilevski, P S
Partner: UNT Libraries Government Documents Department
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Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory

Description: Ordinary quantum theory is a statistical theory without an underlying probability space. The Wiener-Siegel theory provides a probability space, defined in terms of the usual wave function and its ``stochastic coordinates``; i.e., projections of its components onto differentials of complex Wiener processes. The usual probabilities of quantum theory emerge as measures of subspaces defined by inequalities on stochastic coordinates. Since each point {alpha} of the probability space is assigned valu… more
Date: February 1, 1996
Creator: Warnock, R.L.
Partner: UNT Libraries Government Documents Department
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Exhaustive geographic search with mobile robots along space-filling curves

Description: Swarms of mobile robots can be tasked with searching a geographic region for targets of interest, such as buried land mines. The authors assume that the individual robots are equipped with sensors tuned to the targets of interest, that these sensors have limited range, and that the robots can communicate with one another to enable cooperation. How can a swarm of cooperating sensate robots efficiently search a given geographic region for targets in the absence of a priori information about the t… more
Date: March 1998
Creator: Spires, S. V. & Goldsmith, S. Y.
Partner: UNT Libraries Government Documents Department
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On the Convergence of Stochastic Finite Elements

Description: We investigate the rate of convergence of stochastic basis elements to the solution of a stochastic operator equation. As in deterministic finite elements, the solution may be approximately represented as the linear combination of basis elements. In the stochastic case, however, the solution belongs to a Hilbert space of functions defined on a cross product domain endowed with the product of a deterministic and probabilistic measure. We show that if the dimension of the stochastic space is n, a… more
Date: October 1, 2001
Creator: DELAURENTIS, JOHN M. & MOSHESH, IRENE
Partner: UNT Libraries Government Documents Department
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Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups

Description: Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the pr… more
Date: May 2008
Creator: Atim, Alexandru Gabriel
Partner: UNT Libraries
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Quantum Monte Carlo Calculations Applied to Magnetic Molecules

Description: We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing… more
Date: August 9, 2006
Creator: Engelhardt, Larry
Partner: UNT Libraries Government Documents Department
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Single-Atom Gating of Quantum State Superpositions

Description: The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space - or Hilbert space - is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hil… more
Date: April 28, 2010
Creator: Moon, Christopher
Partner: UNT Libraries Government Documents Department
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