1 
Serializability: concurrency control in databasesPhilyaw, Remona Joyce 01 July 1985 (has links)
This paper examines concurrency control in databases beginning with some basic terminology and issues that will be used throughout the paper, and an informal intuitive description of serializability. This paper later provides a comprehensive mathematical theory. This theory forms the basis for the development of the various algorithmic tests for serializability which guarantee the consistency of a database which permits concurrency.

2 
On the identity of Weierstrass' factortheorem and MittagLeffler's partial fractions theoremSimmons, Grover Cleveland, Jr. 01 June 1963 (has links)
No description available.

3 
On orthogonal functions with applications to the Legendre equation and the Bessel equationPerkins, Joe Melvin 01 August 1964 (has links)
No description available.

4 
The theory of Hestenes Ternary Rings and Complex Ternary AlgebrasRay, Isadore 01 May 1979 (has links)
The Theory of Hestenes Ternary Rings and Complex Ternary Algebras were discussed and applications were presented for Hestenes Ternary Rings and *reciprocal of Complex Ternary Algebras. Specifically, the author presented the traditional algebraic theory of rings and algebra. This presentation was followed by the basic theory of Hestenes Ternary Rings and Hestenes Complex Ternary Algebras. The culmination of the paper was Chapter IV where the author presented applications of the latter theory, the most distinguished being the generalization of the ChevalleyJacobson Density Theorem to the Theory of Hestenes Ternary Rings and Algebras.

5 
Long Time Behavior for ReactionDiffusion Population ModelsWu, Yixiang 24 February 2016 (has links)
<p> In this work, we study the long time behavior of reactiondiffusion models arising from mathematical biology. First, we study a reactiondiffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions, prove the existence/uniqueness result for the model, and show the global asymptotic behavior of the model by constructing successive improved upper/lower solutions. Next, we consider a reactiondiffusion equation with continuous delay and spatial variable coefficients. We prove the global attractivity of the positive steady state by showing that the omega limit set is a singleton. Finally, we study an SIS reactiondiffusion model with spatial heterogeneous disease transmission and recovery rates. We define a basic reproduction number and obtain some existence and nonexistence results of the endemic equilibrium of the model. We then study the global attractivity of the steady state for two special cases.</p>

6 
Classification of FiveDimensional Lie Algebras with OneDimensional Subalgebras Acting as Subalgebras of the Lorentz AlgebraRozum, Jordan 24 February 2016 (has links)
<p> Motivated by A. Z. Petrov's classification of fourdimensional Lorentzian metrics, we provide an algebraic classification of the isometryisotropy pairs of fourdimensional pseudoRiemannian metrics admitting local slices with fivedimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebrasubalgebra pairs. This method yields an algorithm for identifying isometryisotropy pairs subject to the aforementioned constraints.</p>

7 
An I/OComplexity Lower Bound for All Recursive Matrix Multiplication Algorithms by PathRoutingScott, Jacob N. 08 April 2016 (has links)
<p> Via novel pathrouting techniques we prove a lower bound on the I/Ocomplexity of all recursive matrix multiplication algorithms computed in serial or in parallel and show that it is tight for all square and nearsquare matrix multiplication algorithms. Previously, tight lower bounds were known only for the classical Θ (<i>n</i><sup>3</sup>) matrix multiplication algorithm and those similar to Strassen's algorithm that lack multiple vertex copying. We first prove tight lower bounds on the I/Ocomplexity of Strassenlike algorithms, under weaker assumptions, by constructing a routing of paths between the inputs and outputs of sufficiently small subcomputations in the algorithm's CDAG. We then further extend this result to all recursive divideandconquer matrix multiplication algorithms, and show that our lower bound is optimal for algorithms formed from square and nearly square recursive steps. This requires combining our new pathrouting approach with a secondary routing based on the LoomisWhitney Inequality technique used to prove the optimal I/Ocomplexity lower bound for classical matrix multiplication.</p>

8 
RiemannHilbert Formalism in the Study of Crack Propagation in Domains with a BoundarySmirnov, Aleksandr 14 April 2016 (has links)
The WienerHopf technique is a powerful tool for constructing analytic solutions for a wide range of problems in physics and engineering. The key step in its application is solution of the RiemannHilbert problem, which consists of finding a piecewise analytic (vector) function in the complex plane for a specified behavior of its discontinuities. In this dissertation, the applied theory of vector RiemannHilbert problems is reviewed. The analytical solution representing the problem on a Riemann surface, and a numerical solution that reduces the problem to singular integral equations, are considered, as well as a combination of the numerical and analytical techniques (partial WienerHopf factorization) is proposed.
In this work, we begin with a brief survey of the RiemannHilbert problem: constructing solution of the scalar RiemannHilbert problem for a class of Holder continuous functions; considering classes of matrices that admit the closedform solution of the vector RiemannHilbert problem; discussing numerical and analytical techniques of constructing solutions of vector RiemannHilbert problems.
We continue with applications of the WienerHopf technique to problems of Dynamic fracture mechanics: reviewing wellknown solutions to problems on propagation of a semiinfinite crack in an unbounded plane in the cases of a stationary crack, a crack propagating at a constant speed, and a crack propagating at a nonuniform arbitrary speed. Based on those, we derive solutions to new problems on a semiinfinite crack propagation in a halfplane (steadystate and transient problems for subsonic speeds) as well as in a composite strip (for intersonic speeds). These latter results are new and were first derived by Y. Antipov and the author.

9 
Quantization in Signal Processing with Frame TheoryJiang, Jiayi 08 April 2016 (has links)
Quantization is an important part of signal processing. Several issues influence the performance
of a quantization algorithm. One is the âbasisâ we choose to represent the signal, another is how
we quantize the âbasisâ coefficients. We desire to explore these two things in this thesis. In the first chapter, we review frame theory and fusion frame theory. In the second chapter, we introduce a
popular quantization algorithm known as SigmaDelta quantization and show how to apply it
to finite frames. Then we give the definition and properties of Sobolev duals which are optimized
duals associated to SigmaDelta quantization. The contraction Sobolev duals depends on the frame, and in chapter 3, we prove that for any finite unitnorm frame, the best error bound that can be achieved
from the reconstruction with Sobolev duals in rth SigmaDelta quantization is equal to order O(N????^(r)), where the error bound can be related to both operator norm and Frobenius norm. In the final chapter, we develop SigmaDelta quantization for fusion frames. We construct stable firstorder and highorder SigmaDelta algorithms for quantizing fusion frame projections of f onto W_n, where W_n is an M_n dimension subspace of R^d. Our stable 1storder quantizer uses only log2(Mn+1) bits per subspace. Besides, we give an algorithm to calculate the Kashin representations for fusion frames to improve the performance of the highorder SigmaDelta quantization algorithm. Then by defining the left inverse and the canonical left inverse for fusion frames, we prove the property that the canonical left inverse has the minimal operator norm and Frobenius norm. Based on this property, we give the idea of Sobolev left inverses for fusion
frames and prove it leads to minimal squared error.

10 
BalianLow Type Theorems for ShiftInvariant SpacesNorthington V, Michael Carr 09 April 2016 (has links)
Shiftinvariant spaces and Gabor systems are frequently used in approximation theory and signal processing. In these settings, it is advantageous for the generators of such spaces to be localized and for the spaces to be representative of a large class of functions. For Gabor systems, the celebrated BalianLow Theorem shows that if the integer translations and modulations of a function in $L^2(R)$ form an orthonormal basis for $L^2(R)$, then either the function or its fourier transform must be poorly localized. The present work shows that similar results hold in certain shiftinvariant spaces. In particular, if the integer translates of a welllocalized function in $L^2(R^d)$ form a frame for the shiftinvariant space, $V$, generated by the function then $V$ cannot be invariant under any noninteger shift. Similar results are proven under a variety of different basis properties, for finitely many generating functions, and with the extrainvariance property replaced with redundancy in the translates of the generator. Examples are given showing the sharpness of these results.

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