Physical Sciences and Mathematics Commons^™

The Aronsson-Euler Equation For Absolutely Minimizing Lipschitz Extensions With Respect To Carnot-Carathéodory Metrics, Thomas Bieske, Luca Capogna

Mathematics Sciences: Faculty Publications

We derive the Euler-Lagrange equation (also known in this setting as the Aronsson-Euler equation) for absolute minimizers of the L ∞ variational problem inf∥∇ 0u∥L∞(Ω), u = g ε Lip(∂Ω) on ∂Ω, where Ω ⊂ G is an open subset of a Carnot group, ∇ 0u denotes the horizontal gradient of u: Ω ℝ R, and the Lipschitz class is defined in relation to the Carnot-Carathéodory metric. In particular, we show that absolute minimizers are infinite harmonic in the viscosity sense. As a corollary we obtain the uniqueness of absolute minimizers in a large class of groups. This result extends …

A Modular Integer Gcd Algorithm, Kenneth Weber, Vilmar Trevisan, Luiz Felipe Martins

Mathematics and Statistics Faculty Publications

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U-bV)/p, where …

Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy

Faculty Publications

Let F be a finite field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with p^t elements, p does not = 2, it is shown that mr(F,G) ≤ 2 if and only if the complement of G is the join of a complete graph with either the union of at most …

Scattering Matrix Analysis Of Photonic Crystals, Valeriy Lukyanov

Dissertations

Using a scattering matrix approach we analyze and study the scattering and transmission of waves through a two-dimensional photonic crystal which consists of a periodic array of parallel rods with circular cross sections. Without making any assumptions about normal incidence, single mode propagation, and sufficient inter-scatter separation in the direction of propagation, we show how to compute the transmission and reflection coefficients of these periodic structures. The method is based on the computation of a generalized scattering matrix for one column of the periodic structure.

We also develop an analytical method to analyze and to study the scattering and transmission …

Balanced Scaling Vectors Using Linear Combinations Of Existing Scaling Vectors, Bruce Kessler

Mathematics Faculty Publications

The majority of the research done into creating balanced multiwavelets has involved establishing a series of conditions on the mask of the new scaling vector by solving a large nonlinear system. The result is a completely different new function vector solution to the dilation equation with the new matrix coefficients. The research presented here will show a way to use previously-constructed orthonormal scaling vectors to generate equivalent orthonormal scaling vectors that are balanced up to the approximation order of the previous scaling vector. The technique uses linear combinations of the integer translates of the previous-constructed scaling vector.

On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr.

Doctoral Theses

In this thesis, we propose two new subband transforms entitled ISITRA and YKSK transforms and their possible applications in image compression and encryption. Both these transforms are developed based on a common model of multiplication known as Bino’s model of multiplication. ISITRA is a convolution based transforms i.e., that both forward and inverse transform of ISITRA is based on convolution as in DWT or 2-channel filter bank. However, it is much more general than the existing DWT or 2-channel filter bank scheme in the sense that it we can get different kinds of filters in addition to the filters specified …

Essays On Dynamic Disequilibrium Models., Arpita Dhar Dr.

Doctoral Theses

The present dissertation is devoted to the analysis of some problems of economic growth in the framework of what has been called Disequilibrium model.Studies on economic growth have been mostly confined, with few exceptions, to the analysis of equilibrium models. But in reality there are cases where the concept of equilibrium may not be relevant and hence a disequilibrium approach is needed. The present thesis is concerned with analysing some theoretical and empirical aspects of the problem of economic growth in a disequilibrium framework. At the theoretical level, the objective has been to re-examine the conclusions of some existing equilibrium …

An Introduction To Hellmann-Feynman Theory, David Wallace

Electronic Theses and Dissertations

The Hellmann-Feynman theorem is presented together with certain allied theorems. The origin of the Hellmann-Feynman theorem in quantum physical chemistry is described. The theorem is stated with proof and with discussion of applicability and reliability. Some adaptations of the theorem to the study of the variation of zeros of special functions and orthogonal polynomials are surveyed. Possible extensions are discussed.

The Scintillation Index In Moderate To Strong Turbulence For The Gaussian Beam Wave Along A Slant Path, Fredrick Eugene Thomas

Electronic Theses and Dissertations

Scintillation is one of the most common statistics in the literature of mathematical modeling of laser propagation through random media. One approach to estimating scintillation is through the Rytov approximation, which is limited to weak atmospheric turbulence. Recently, an improvement of the Rytov approximation was developed employing a linear filter function technique. This modifies the Rytov approximation and extends the validity into the moderate to strong regime. In this work, an expression governing scintillation of a Gaussian beam along an uplink slant path valid in all regimes of turbulence is presented, as well as results for the limiting cases of …

Decision Theory Classification Of High-Dimensional Vectors Based On Small Samples, David Bradshaw

Electronic Theses and Dissertations

In this paper, we review existing classification techniques and suggest an entirely new procedure for the classification of high-dimensional vectors on the basis of a few training samples. The proposed method is based on the Bayesian paradigm and provides posterior probabilities that a new vector belongs to each of the classes, therefore it adapts naturally to any number of classes. Our classification technique is based on a small vector which is related to the projection of the observation onto the space spanned by the training samples. This is achieved by employing matrix-variate distributions in classification, which is an entirely new …

Disko Solution In Braille, Jeremiah Farrell

Scholarship and Professional Work - LAS

A copy of a 4x4 DISKO solution in Braille. Constructed by students at the Indiana School for the Blind on magnetized squares on a "toasted", i.e. raised grid.

The Expected Variation Of Random Bounded Integer Sequences Of Finite Length, Rudolfo Angeles, Don Rawlings, Lawrence Sze, Mark Tiefenbruck

Mathematics

From the enumerative generating function of an abstract adjacency statistic, we deduce the mean and variance of the variation on random permutations, rearrangements, compositions, and bounded integer sequences of finite length.

Reversals And Transpositions Over Finite Alphabets, A. J. Radcliffe, A. D. Scott, E. L. Wilmer

Department of Mathematics: Faculty Publications

Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition, or signed reversal distance between two strings over a finite alphabet is NP-hard, while for “dense” instances we give a polynomial-time approximation scheme. We also give a number of extremal results, as well as investigating the distance between random strings and the problem of sorting a string over a finite alphabet.

Pseudo-Codewords Of Cycle Codes Via Zeta Functions, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker

Department of Mathematics: Faculty Publications

Cycle codes are a special case of low- density parity-check (LDPC) codes and as such can be decoded using an iterative message-passing decod- ing algorithm on the associated Tanner graph. The existence of pseudo-codewords is known to cause the decoding algorithm to fail in certain instances. In this paper, we draw a connection between pseudo- codewords of cycle codes and the so-called edge zeta function of the associated normal graph and show how the Newton polyhedron of the zeta function equals the fundamental cone of the code, which plays a crucial role in characterizing the performance of iterative de- coding …

Weak Solutions To The Cauchy Problem Of A Semilinear Wave Equation With Damping And Source Terms, Petronela Radu

Department of Mathematics: Faculty Publications

In this paper we prove local existence of weak solutions for a semilinear wave equation with power-like source and dissipative terms on the entire space ℝⁿ. The main theorem gives an alternative proof of the local in time existence result due to J. Serrin, G. Todorova and E. Vitillaro, and also some extension to their work. In particular, our method shows that sources that are not locally Lipschitz in L² can be controlled without any damping at all. If the semilinearity involving the displacement has a “good” sign, we obtain global existence of solutions.

Matrix Model Superpotentials And Calabi–Yau Spaces: An A-D-E Classification, Carina Curto

Department of Mathematics: Faculty Publications

We use F. Ferrari’s methods relating matrix models to Calabi-Yau spaces in order to explain Intriligator and Wecht’s ADE classification of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. The connection between matrix models and N = 1 gauge theories can be seen as evidence for the Dijkgraaf–Vafa conjecture. We find that ADE superpotentials in the Intriligator–Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau’s with corresponding ADE singularities. Moreover, in the additional Ô, Â, Dˆ and Ê cases we find new singular geometries. These ‘hat’ geometries are …

On Properties Of Group Closures Of One-To-One Transformations., Inessa Levi

Faculty Bibliography

For a permutation group H on an infinite set X and a transformation / of X, let (/:// ) = ({hfh'1 : h € //)) be a group closure of / . We find necessary and sufficient conditions for distinct normal subgroups of the symmetric group on X and a one-to-one transformation / of X to generate distinct group closures of / . Amongst these group closures we characterize those that are left simple, left cancellative, idempotent-free semigroups, whose congruence lattice forms a chain and whose congruences are preserved under automorphisms.

The Cohomology Of Right Angled Artin Groups With Group Ring Coefficients, Craig A. Jensen

Mathematics Faculty Publications

The cohomology of a right-angled Artin group with group ring coefficients is explicitly presented in terms of the cohomology of its defining flag complex. 2000 Mathematics Subject Classification 20F36 (primary), 57M07 (secondary).

Proper Actions Of Automorphism Groups Of Free Products Of Finite Groups, Craig A. Jensen, Yuqing Chen, Henry H. Glover

Mathematics Faculty Publications

If G is a free product of finite groups, let ΣAut₁(G) denote all (necessarily symmetric) automorphisms of G that do not permute factors in the free product. We show that a McCullough–Miller and Gutiérrez–Krstić derived (also see Bogley–Krstić) space of pointed trees is an EΣAut₁(G)-space for these groups.

A Platform-Independent Software Suite For Statistical Analysis Of High Dimensional Biology Data, David B. Allison, Jacob P. L. Brand, Jode W. Edwards, Gary L. Gadbury, Kyoungmi Kim, Tapan Mehta, Grier P. Page, Amit Patki, Vinodh Srinivasasainagendra, Prinal Trivedi, Jelai Wang, Stanislav O. Zakharkin

Mathematics and Statistics Faculty Research & Creative Works

Many efforts in microarray data analysis are focused on providing tools and methods for the qualitative analysis of microarray data. HDBStat! (High-Dimensional Biology-Statistics) is a software package designed for analysis of high dimensional biology data such as microarray data. It was initially developed for the analysis of microarray gene expression data, but it can also be used for some applications in proteomics and other aspects of genomics. HDBStat! provides statisticians and biologists a flexible and easy-to-use interface to analyze complex microarray data using a variety of methods for data preprocessing, quality control analysis and hypothesis testing.

Maximal Regular Boundary Value Problems In Banach-Valued Weighted Space, Ravi P. Agarwal, Veli B. Shakhmurov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to …

Second Order Dynamic Inclusions, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The theory of dynamic inclusions on a time scale is introduced, hence accommodating the special cases of differential inclusions and difference inclusions. Fixed point theory for set-valued upper semicontinuous maps, Green's functions, and upper and lower solutions are used to establish existence results for solutions of second order dynamic inclusions.

Existence And Comparison Principles For General Quasilinear Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness and extremality results.

Existence, Comparison, And Compactness Results For Quasilinear Variational-Hemivariational Inequalities, Vy Khoi Le, Dumitru Motreanu, Siegfried Carl

Mathematics and Statistics Faculty Research & Creative Works

We consider quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of sub- and supersolutions, on the basis of which we then develop the sub-supersolution method for variational-hemivariational inequalities, including existence, comparison, compactness, and extremality results.

A Quasilinearization Approach For Two Point Nonlinear Boundary Value Problems On Time Scales, Elvan Akin, Ferhan Atici. Merdivenci

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Gap Labeling, Claude Schochet

Mathematics Faculty Research Publications

This joint review covers:

Moulay-Tahar Benameur and Hervé Oyono-Oyono, Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard). (English summary) Operator algebras and mathematical physics, (Constanţa, 2001), 11-22, Theta, Bucharest, 2003.

Jerome Kaminker and Ian Putnam, A proof of the gap labeling conjecture, Michigan Mathematical Journal 51(3) (2003), 537-546.

Jean Bellisard, Riccardo Benedetti and Jean-Marc Gambaudo, Spaces of tilings, finite telescopic approximations, and gap-labeling, Communications in Mathematical Physics 261(1) (2006), 1-41.

The gap labeling theorem was originally conjectured by Bellissard [in From number theory to physics (Les Houches, 1989), 538-630, Springer, Berlin, 1992; MR1221111 (94e:46120)]. …

Assimilation Of Simulated Float Data In Lagrangian Coordinates, J. L. Mead

Mathematics Faculty Publications and Presentations

We implement an approach for the accurate assimilation of Lagrangian data into regional general ocean circulation models. The forward model is expressed in Lagrangian coordinates and simulated float data are incorporated into the model via four dimensional variational data assimilation. We show that forward solutions computed in Lagrangian coordinates are reliable for time periods of up to 100 days with phase speeds of 1 m/s and deformation radius of 35 km. The position and depth of simulated floats are assimilated into the viscous, Lagrangian shallow water equations. The weights for the errors in the model and data are varied and …

Fast Multilevel Evaluation Of 1-D Piecewise Smooth Radial Basis Function Expansions, Oren E. Livne, Grady B. Wright

Grady Wright

No abstract provided.

Fibonacci In Contextures, An Application, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Contextures. Programming Dynamic Complexity, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.