Physical Sciences and Mathematics Commons^™

The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh

Mathematics Faculty Publications

We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical d-dimensional Euclidean one.

Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres

Mathematics Faculty Publications

A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Caldeŕon-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.

Iterative Scheme For Solving Optimal Transportation Problems Arising In Reflector Design, Tilmann Glimm, Nick Henscheid

Mathematics Faculty Publications

We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it has been shown previously that this problem is equivalent to an infinite-dimensional linear programming (LP) problem. Here we investigate techniques for constructing the two reflectors numerically by considering the finite dimensional LP problems which arise as approximations to the infinite dimensional problem. A straightforward discretization has the disadvantage that the number of constraints increases rapidly with the mesh size, so only very coarse meshes are …

Anisotropic Classes Of Inhomogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik

Mathematics Faculty Publications

We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class S^m_γ,δ of inhomogeneous symbols. We extend a well-known L ²-boundedness result to the anisotropic class S⁰_δ,_δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S⁰_1,0(A) are bounded on L ^p spaces, 1 < p < ∞.

The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko

Mathematics Faculty Publications

We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in …

Solving Separable Nonlinear Equations Using Lu Factorization, Yun-Qiu Shen, Tjalling Ypma

Mathematics Faculty Publications

Separable nonlinear equations have the form F(y,z) ≡ A (y)z + b(y) = 0, where the matrix A(y)∈ R ^{m × N} and the vector b(y) ∈ R^mare continuously differentiable functions of y ∈ R^{n and} z ^∈ R^N. We assume that m ≥ N + n, and F'(y,z) has full rank. We present a numerical method to compute the solution (y∗, z∗) for fully determined systems (m = N+ n) and compatible overdetermined systems (m …

Secrecy Coverage, Amites Sarkar, Martin Haenggi

Mathematics Faculty Publications

Motivated by information-theoretic secrecy, geometric models for secrecy in wireless networks have begun to receive increased attention. The general question is how the presence of eavesdroppers affects the properties and performance of the network. Previously, the focus has been mostly on connectivity. Here we study the impact of eavesdroppers on the coverage of a network of base stations. The problem we address is the following. Let base stations and eavesdroppers be distributed as stationary Poisson point processes in a disk of area n. If the coverage of each base station is limited by the distance to the nearest eavesdropper, …

On The Nilpotent Graph Of A Ring, Mohammad Javad Nikmehr, Soheila Khojasteh

Turkish Journal of Mathematics

Let R be a ring with unity. The nilpotent graph of R, denoted by \Gamma_N(R), is a graph with vertex set Z_N(R)^* = {0 \neq x \in R \mid xy \in N(R) for some 0 \neq y \in R}; and two distinct vertices x and y are adjacent if and only if xy \in N(R), where N(R) is the set of all nilpotent elements of R. Recently, it has been proved that if R is a left Artinian ring, then diam(\Gamma_N(R)) \leq 3. In this paper, we present a new proof for the above result, where R is a finite …

On The Centroid Of Prime Semirings, Hasret Yazarli, Mehmet Ali̇ Öztürk

Turkish Journal of Mathematics

We define and study the extended centroid of a prime semiring. We show that the extended centroid is a semifield and give some properties of the centroid of a right multiplicatively cancellable prime semiring.

Products Of Conjugacy Classes And Products Of Irreducible Characters In Finite Groups, Mohammad Reza Darafsheh, Sajjad Mahmood Robati

Turkish Journal of Mathematics

Let G be a finite group. If A and B are two conjugacy classes in G, then AB is a union of conjugacy classes in G and \eta(AB) denotes the number of distinct conjugacy classes of G contained in AB. If \chi and \psi are two complex irreducible characters of G, then \chi\psi is a character of G and again we let \eta(\chi\psi) be the number of irreducible characters of G appearing as constituents of \chi\psi. In this paper our aim is to study the product of conjugacy classes in a finite group and obtain an upper bound for \eta …

Global Existence, Decay And Blow Up Solutions For Coupled Nonlinear Wave Equations With Damping And Source Terms, Erhan Pi̇şki̇n, Necat Polat

Turkish Journal of Mathematics

We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao's inequality. The nonexistence of global solutions is discussed under some conditions on the given parameters.

Bbm Equation With Non-Constant Coefficients, Amutha Senthilkumar

Turkish Journal of Mathematics

In this article, a model for the propagation of long waves over an uneven bottom is considered. We provide both theoretical and numerical results for this model. We also discuss the changes which occur in a solitary wave solution of the BBM equation as it travels through a channel of decreasing depth.

Second Order Approximations In Sequential Point Estimation Of The Probability Of Zero In Poisson Distribution, Eisa Mahmoudi, Mohammad Hatami Kamin

Turkish Journal of Mathematics

In the analysis of the count data, the Poisson model becomes overtly restrictive in the case of over-dispersed or under-dispersed data. When count data are under-dispersed, specific models such as generalized linear models (GLM) are proposed. Other examples are the zero-inflated Poisson model (ZIP) and zero-truncated Poisson model (ZTP), which have been used in literature to deal with an excess or absence of zeros in count data. Thus having a knowledge of the probability of zeros and its estimation in Poisson distribution can be significant and useful. Some estimation problems with unknown parameter cannot attain minimum risk where the sample …

Generalized Derivations Of Prime Rings On Multilinear Polynomials With Annihilator Conditions, Nurcan Argaç, Çağri Demi̇r

Turkish Journal of Mathematics

Let K be a commutative ring with unity, R be a prime K-algebra with characteristic not 2, U be the right Utumi quotient ring of R, C the extended centroid of R, I a nonzero right ideal of R and a a fixed element of R. Let g be a generalized derivation of R and f(X_1,..., X_n) a multilinear polynomial over K. If ag(f(x_1,...,x_n))f(x_1,...,x_n)=0 for all x_1,...,x_n \in I, then one of the following holds: (1) aI=ag(I)=0; (2) g(x)=bx+[c,x] for all x\in R, where b,c\in U. In this case either [c,I]I=0=abI or aI=0=a(b+c)I; (3) [f(X_1,...,X_n),X_{n+1}]X_{n+2} is an identity for I.

Strongly Gorenstein Flat And Gorenstein Fp-Injective Modules, Chunhua Yang

Turkish Journal of Mathematics

In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use them to prove that the global strongly Gorenstein flat dimension and the global Gorenstein FP-injective dimension of a ring R are identical when R is n-FC or commutative coherent. Finally, we show that if R is a commutative Noetherian ring, then, for any R-module M, SGfd_RM=Gpd_RM, and hence SGfd_RM< \infty if and only if Gfd_RM

Some Properties On The Baer-Invariant Of A Pair Of Groups And V_G-Marginal Series, Mohammad Reza Rismanchian, Mehdi Araskhan

Turkish Journal of Mathematics

The aim of this paper is to present some properties of the Baer-invariant of a pair of groups with respect to a given variety of groups V. We derive some equalities and inequalities of the Baer-invariant of a pair of finite groups, as long as V is considered to be a Schur-Baer variety. Moreover, we present a relative version of the concept of lower marginal series and give some isomorphisms among V_G-marginal factor groups. Also, we conclude a generalized version of the Stallings' theorem.

(P,\\Lambda)-Koszul Algebras And Modules, Ii, Jiafeng Lu

Turkish Journal of Mathematics

This paper is a continuous work of [14], where the notions of (p,\lambda)-Koszul algebra and (p,\lambda)-Koszul module were first introduced. More precisely, some new criteria for a positively graded algebra to be (p,\lambda)-Koszul are provided. We also generalize (p,\lambda)-Koszul objects to the nongraded case and define the so-called quasi-(p,\lambda)-Koszul objects. Further, the relationships between (quasi-) (p,\lambda)-Koszul modules and minimal Horseshoe Lemma are established.

Bayesian Approach For Inconsistent Information, M. Stein, Michael Beer, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the {\it exact} sample values, that the prior distribution is {\it exactly} known, etc. In reality, the data is imprecise due to measurement errors, the …

From P-Boxes To P-Ellipsoids: Towards An Optimal Representation Of Imprecise Probabilities, Konstantin K. Semenov, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the most widely used ways to represent a probability distribution is by describing its cumulative distribution function (cdf) F(x). In practice, we rarely know the exact values of F(x): for each x, we only know F(x) with uncertainty. In such situations, it is reasonable to describe, for each x, the interval [F(x)] of possible values of x. This representation of imprecise probabilities is known as a p-box; it is effectively used in many applications.

Similar interval bounds are possible for probability density function, for moments, etc. The problem is that when we transform from one of such representations …

Aggregation Operations From Quantum Computing, Lidiane Visintin, Adriano Maron, Renata Reiser, Ana Maria Abeijon, Vladik Kreinovich

Departmental Technical Reports (CS)

Computer systems based on fuzzy logic should be able to generate an output from the handling of inaccurate data input by applying a rule based system. The main contribution of this paper is to show that quantum computing can be used to extend the class of fuzzy sets. The central idea associates the states of a quantum register to membership functions (mFs) of fuzzy subsets, and the rules for the processes of fuzzyfication are performed by unitary qTs. This paper introduces an interpretation of aggregations obtained by classical fuzzy states, that is, by multi-dimensional quantum register associated to mFs on …

Relation Between Polling And Likert-Scale Approaches To Eliciting Membership Degrees Clarified By Quantum Computing, Renata Hax Sander Reiser, Adriano Maron, Lidiane Visintin, Ana Maria Abeijon, Vladik Kreinovich

Departmental Technical Reports (CS)

In fuzzy logic, there are two main approaches to eliciting membership degrees: an approach based on polling experts, and a Likert-scale approach, in which we ask experts to indicate their degree of confidence on a scale -- e.g., on a scale form 0 to 10. Both approaches are reasonable, but they often lead to different membership degrees. In this paper, we analyze the relation between these two approaches, and we show that this relation can be made much clearer if we use models from quantum computing.

Why Inverse F-Transform? A Compression-Based Explanation, Vladik Kreinovich, Irina Perlieva, Vilém Novák

Departmental Technical Reports (CS)

In many practical situations, e.g., in signal processing, image processing, analysis of temporal data, it is very useful to use fuzzy (F-) transforms. In an F-transform, we first replace a function x(t) by a few local averages (this is called forward F-transform), and then reconstruct the original function from these averages (this is called inverse F-transform). While the formula for the forward F-transform makes perfect intuitive sense, the formula for the inverse F-transform seems, at first glance, somewhat counter-intuitive. On the other hand, its empirical success shows that this formula must have a good justification. In this paper, we provide …

A Symmetry-Based Approach To Selecting Membership Functions And Its Relation To Chemical Kinetics, Vladik Kreinovich, Olga Kosheleva, Jorge Y. Cabrera, Mario Gutierrez, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

In many practical situations, we encounter physical quantities like time for which there is no fixed starting point for measurements: physical properties do not change if we simply change (shift) the starting point. To describe knowledge about such properties, it is desirable to select membership functions which are similarly shift-invariant. We show that while we cannot require that each membership function is shift-invariant, we can require that the linear space of all linear combinations of given membership functions is shift-invariant. We describe all such shift-invariant families of membership functions, and we show that they are naturally related to the corresponding …

Summer Land Surface Temperature: Small-Local Variation In Intro-Urban Environment In El Paso, Tx, Mactar Mohamed

Open Access Theses & Dissertations

ABSTRACT

It has been well documented that rapid urbanization and population growth have led to the transformation of the natural landscape into anthropogenic urban land and changed such surface physical properties as albedo, energy balance, and surface roughness. Cities, therefore, will be warmer at the urban areas than the rural lands; this situation creates a phenomenon called Urban Heat Island (UHI).

In the recent decades, numerous approaches to study the variation of land surface temperature during daytime have emerged; however, little is known about the variation during nighttime. This study addressed the spatial variation of Summer Nighttime Land Surface Temperature …

Impact Of Cerium Oxide Nanoparticles On Cilantro (Coriandrum Sativum), Maria Isabel Morales

Open Access Theses & Dissertations

Studies have shown that plants exposed to ENPs suffer different types of stress. Other studies have revealed that plants can take up and accumulate CeO2 NPs without modification. Thus, these NPs could enter the food chain through edible plants, posing a threat for human health. Cilantro (Coriandrum sativum) is a worldwide culinary and medicinal plant consumed either as a fresh herb or a spice. In this research, cilantro plants were germinated and cultivated for 30 days in organic soil treated with CeO2 NPs at concentrations varying from 0 to 500 mg kg!1. Subsequently, plant organs were analyzed by using spectroscopic …

Strong Coupled Quark Matter And Drawbacks Of Its Bcs-Bec Crossover, Israel Portillo Vazquez

Open Access Theses & Dissertations

It was found many years ago, that the ground state wave functions of the Bardeen-Cooper-Schrieer (BCS) superconductivity in a degenerate Fermi gas and the Bose-Einstein condensation (BEC) of composite molecules are essentially the same, and those two states can be smoothly connected through a crossover. This BCS-BEC crossover has being recently extended to relativistic Fermi System. This thesis is dedicated to exploring the possible crossover from BEC to BCS phase on strong-interacting matter and its implications for the system Equation of State. The study will be concentrated on dierent phases of dense quark-matter for vanishing temperatures and densities beyond hadronic …

Novel Copper (Ii) Mediated Transfection Nano-Systems And Biological Properties Of Pyridinium Surfactants, Sarit Pal

Open Access Theses & Dissertations

Efficacy of gene therapy is relied upon the improvement of gene delivery vectors into mammalian cells. Although viral-based polynucleotide carriers are still considered as the most common method for gene delivery but the cost effectiveness, nonspecific lethal immune response has evoked the renaissance of non-viral synthetic delivery systems. An initial discovery by Felgnar et al showed Cationic Liposomes (CLs) (having an overall positive charge) when mixed with DNA to form CL-DNA complexes can enhance the transfer of polynucleotides into cells followed by its expression. Presently, a flurry of experimental works is taking place for the better understanding of structural characterization …

Two-Photon Microscopy Of Nanoparticles And Biotissues, Judith Noemi Rivera

Open Access Theses & Dissertations

Biomedical Imaging is an important tool in medical research and clinical practice. From understanding the fundamental processes involved in our biological makeup to its use in diagnostics in helping determine what ails us, the advancements in imaging and microscopy have helped shape our view of the world and nature. Microscopy in particular is often used to study the smallest of cells and their dynamical properties while attempting to minimally change the sample being studied. My research objective is largely divided into two parts. The first part consists of designing a video-rate raster scanning two-photon microscope that is faster than current …

A Convex Optimization Algorithm For Sparse Representation And Applications In Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. Any test sample is represented in an overcomplete dictionary with the training sample as base elements. A given test sample can be expressed as a linear combination of only those training …

On Different Techniques For The Calculation Of Bouguer Gravity Anomalies For Joint Inversion And Model Fusion Of Geophysical Data In The Rio Grande Rift, Azucena Zamora

Open Access Theses & Dissertations

Density variations in the Earth result from different material properties, which reflect the tectonic processes attributed to a region. Density variations can be identified through measurable material properties, such as seismic velocities, gravity field, magnetic field, etc. Gravity anomaly inversions are particularly sensitive to density variations but suffer from significant non-uniqueness. However, using inverse models with gravity Bouguer anomalies and other geophysical data, we can determine three dimensional structural and geological properties of the given area. We explore different techniques for the calculation of Bouguer gravity anomalies for their use in joint inversion of multiple geophysical data sets and a …