Mathematics Commons^™

Preface

Communications on Stochastic Analysis

No abstract provided.

Robin Hudson's Pathless Path To Quantum Stochastic Calculus, David Applebaum

Communications on Stochastic Analysis

No abstract provided.

Quantum Filtering In Coherent States, John E Gough, Claus Köstler

Communications on Stochastic Analysis

No abstract provided.

Quantum Quasi-Markov Processes, L-Dynamics, And Noncommutative Girsanov Transformation, V P Belavkin

Communications on Stochastic Analysis

No abstract provided.

On The Characteristic Function Of Random Variables Associated With Boson Lie Algebras, Luigi Accardi, Andreas Boukas

Communications on Stochastic Analysis

No abstract provided.

Cosine And Gaussian Transforms, Carlos Lizama, Rolando Rebolledo

Communications on Stochastic Analysis

No abstract provided.

E-Semigroups Subordinate To Ccr Flows, Stephen J Wills

Communications on Stochastic Analysis

No abstract provided.

Slider-Pinning Rigidity: A Maxwell-Laman-Type Theorem, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley’s direction networks.

The K-Cores Of A Graph, Allan Bickle

Dissertations

Full abstract attached as supplemental file.

Robust Interval Estimation Of A Treatment Effect In Observational Studies Using Propensity Score Matching, Scott F. Kosten

Dissertations

Estimating the treatment effect between a treatment group and a control group in an observational study is a challenging problem in statistics. Without random assignment of subjects, there are likely to be differences between the treatment group and control group on a set of baseline covariates. If one of these baseline covariates is correlated to the response variable, then the difference in sample means between the groups is likely to be a biased estimate of the true treatment effect.

Propensity score matching has become an increasingly popular strategy for reducing bias in estimates of the treatment effect. This reduction in …

Exact Solutions Of The Generalized- Zakharov (Gz) Equation By The Infinite Series Method, N. Taghizadeh, M. Mirzazadeh, F. Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

The infinite series method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the direct algebraic method is used to construct new exact solutions of generalized- Zakharov equation.

An Analytical Technique For Solving Nonlinear Heat Transfer Equations, Hossein Aminikhah, Milad Hemmatnezhad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytic technique, namely the New Homotopy Perturbation Method (NHPM) is applied for solving the nonlinear differential equations arising in the field of heat transfer. In this method, the solution is considered as an infinite series expansion where converges rapidly to the exact solution. The nonlinear convective–radioactive cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples and the exact solutions have been found for each case.

Duality In Fuzzy Linear Programming With Symmetric Trapezoidal Numbers, S. H. Nasseri, E. Ebrahimnejad, S. Mizuno

Applications and Applied Mathematics: An International Journal (AAM)

Linear programming problems with trapezoidal fuzzy numbers have recently attracted much interest. Various methods have been developed for solving these types of problems. Here, following the work of Ganesan and Veeramani and using the recent approach of Mahdavi-Amiri and Nasseri, we introduce the dual of the linear programming problem with symmetric trapezoidal fuzzy numbers and establish some duality results. The results will be useful for post optimality analysis.

Invariant And Coinvariant Spaces For The Algebra Of Symmetric Polynomials In Non-Commuting Variables, Francois Bergeron, Aaron Lauve

Mathematics and Statistics: Faculty Publications and Other Works

We analyze the structure of the algebra K⟨x⟩Sn of symmetric polynomials in non-commuting variables in so far as it relates to K[x]Sn, its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of K⟨x⟩Sn analogous to the classical theorems of Chevalley, Shephard-Todd on finite reflection groups.

Résumé. Nous analysons la structure de l'algèbre K⟨x⟩Sn des polynômes symétriques en des variables non-commutatives pour obtenir des analogues des résultats classiques concernant la structure de l'anneau K[x]Sn des polynômes symétriques en des variables …

Structures On A K3 Surface, Nathan P. Rowe

UNLV Theses, Dissertations, Professional Papers, and Capstones

In the first part of this paper, we examine properties of K3 surfaces of the form:

(x2 + 1)(y2 + 1)(z2 + 1) + Axyz − 2 = 0

We show the surface has Picard number q " 12 by finding 12 curves whose equivalence classes are linearly independent. These curves have self intersection −2. We find the lattice representations of the single-coordinate swapping automorphisms in x, y, and z. We show that we have enough of the Lattice to make accurate predictions of polynomial degree growth under the automorphisms. We describe these automorphisms in terms of operations on elliptic …

Rademacher-Type Formulas For Restricted Partition And Overpartition Functions, Andrew Sills

Mathematical Sciences: Faculty Publications

A collection of Hardy-Ramanujan-Rademacher type formulas for restricted partition and overpartition functions is presented, framed by several biographical anecdotes.

The Cohomology Of Modules Over A Complete Intersection Ring, Jesse Burke

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if one even self-extension module of M vanishes then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomposable is projectively connected.

The Hopf-Laplace Equation, Jan Cristina, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such solutions are harmonic maps. Nevertheless, minimization of the Dirichlet energy among homeomorphisms often leads to nonharmonic solutions. We investigate the Hopf-Laplace equation for a certain class of topologically well behaved mappings which are almost homeomorphisms, called Hopf deformations. We establish Lipschitz continuity of Hopf deformations, the best possible regularity one can get. Thus in particular we show that the minimal-energy deformations are Lipschitz continuous, a result of considerable interest in the theory of minimal …

Building Graphs From Colored Trees, Rachel M. Esselstein, Peter Winkler

Dartmouth Scholarship

We will explore the computational complexity of satisfying certain sets of neighborhood conditions in graphs with various properties. More precisely, fix a radius $\rho$ and let $N(G)$ be the set of isomorphism classes of $\rho$-neighborhoods of vertices of $G$ where $G$ is a graph whose vertices are colored (not necessarily properly) by colors from a fixed finite palette. The root of the neighborhood will be the unique vertex at the "center" of the graph. Given a set S of colored graphs with a unique root, when is there a graph G with N (G) = S? Or N (G) ⊂ …

Fixed Point Theorems For Ws-Compact Mappings In Banach Spaces, Ravi P. Agarwal, Donal O'Regan, Mohamed-Aziz Taoudi

Mathematics and System Engineering Faculty Publications

We present new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii, Leray-Schauder, Rothe, Altman, Petryshyn, and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results.

On The Construction Of Explicit Solutions To The Matrix Equation X2ax = Axa, Aihua Li, Edward Mosteig

Department of Mathematics Faculty Scholarship and Creative Works

In a previous article by Aihua Li and Duane Randall, the existence of solutions to certain matrix equations is demonstrated via nonconstructive methods. A recurring example appears in that work, namely the matrix equation AXA = X2AX, where A is a fixed, square matrix with real entries and X is an unknown square matrix. In this paper, the solution space is explicitly constructed for all 2×2 complex matrices using Gröbner basis techniques. When A is a 2×2 matrix, the equation AXA = X2AX is equivalent to a system of four polynomial equations. The solution space then is the variety defined …

Rethinking Geometrical Exactness, Marco Panza

MPP Published Research

A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should not be allowed into it. According to Bos, this is the exactness concern. I argue that Descartes’s way of responding to this concern was to suggest an appropriate conservative extension of Euclid’s plane geometry (EPG). In Section 2, I outline the exactness concern as, I think, it appeared to Descartes. In Section 3, I account for Descartes’s views on exactness and for his attitude towards the most common sorts of constructions in classical geometry. I also explain in …

Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza

MPP Published Research

A review of Paolo Mancosu (ed.): The Philosophy of Mathematical Practice.

Lipchitzian Stability Of Parametric Variational Inequalities Over Generalized Polyhedra In Banach Spaces, Liqun Ban, Boris S. Mordukhovich, Wen Song

Mathematics Research Reports

This paper concerns the study of solution maps to parameterized variational inequalities over generalized polyhedra in reflexive Banach spaces. It has been recognized that generalized polyhedral sets are significantly different from the usual convex polyhedra in infinite dimensions and play an important role in various applications to optimization, particularly to generalized linear programming. Our main goal is to fully characterize robust Lipschitzian stability of the aforementioned solutions maps entirely via their initial data. This is done on the base of the coderivative criterion in variational analysis via efficient calculations of the coderivative and related objects for the systems under consideration. …

Can Telomere Shortening Explain Sigmoidal Growth Curves?, Peter Olofsson

Mathematics Faculty Research

A general branching process model is proposed to describe the shortening of telomeres in eukaryotic chromosomes. The model is flexible and incorporates many special cases to be found in the literature. In particular, we show how telomere shortening can give rise to sigmoidal growth curves, an idea first expressed by Portugal et al. [A computational model for telomere-dependent cell-replicative aging, BioSystems 91 (2008), pp. 262–267]. We also demonstrate how other types of growth curves arise if telomere shortening is mitigated by other cellular processes. We compare our results with published data sets from the biological literature.

Teaching Research: Encouraging Discoveries, Francis E. Su

All HMC Faculty Publications and Research

What does it take to turn a learner into a discoverer? Or to turn a teacher into a co-adventurer? A handful of experiences—from teaching a middle-school math class to doing research with undergraduates—have changed the way that I would answer these questions. Some of the lessons I’ve learned have surprised me.

Correspondences Of Hypersurfaces In Hyperbolic Poincaré Manifolds And Conformally Invariant Pdes, Vincent Bonini, José M. Espinar, Jie Qing

Mathematics

On a hyperbolic Poincaré manifold, we derive an explicit relationship between the eigenvalues of Weyl-Schouten tensor of a conformal representative of the conformal infinity and the principal curvatures of the level sets of the associated geodesic defining function. This considerably simplifies the arguments and generalizes the results of Gálvez, Mira and the second author. In particular, we obtain the equivalence between Christoffel-type problems for hypersurfaces in a hyperbolic Poincar´e manifold and scalar curvature problems on the conformal infinity.

The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li

Mathematics and Statistics Faculty Publications

This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as a characterization of the different solutions. The emphasis lies on the study of the M …

Asymptotically Linear Solutions For Some Linear Fractional Differential Equations, Dumitru Baleanu, Octavian G. Mustafa, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We establish here that under some simple restrictions on the functional coefficient at the fractional differential equation 0Dα t tx − x x0 at x 0,t> 0, has a solution expressible as ct d o1 for t → ∞, where 0Dα t designates the Riemann-Liouville derivative of order α ∈ 0, 1 and c, d ∈ R.

Powerpack: Energy Profiling And Analysis Of High-Performance Systems And Applications, Rong Ge, Xizhou Feng, Shuaiwen Song, Hung-Ching Chang, Dong Li, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Energy efficiency is a major concern in modern high-performance computing system design. In the past few years, there has been mounting evidence that power usage limits system scale and computing density, and thus, ultimately system performance. However, despite the impact of power and energy on the computer systems community, few studies provide insight to where and how power is consumed on high-performance systems and applications. In previous work, we designed a framework called PowerPack that was the first tool to isolate the power consumption of devices including disks, memory, NICs, and processors in a high-performance cluster and correlate these measurements …