Physical Sciences and Mathematics Commons^™

Pick Interpolation For Free Holomorphic Functions, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

We give necessary and sufficient conditions to solve an interpolation problem for free holomorphic functions bounded in norm on a free polynomial polyhedron. As an application, we prove that every bounded holomorphic function on a polynomial polyhedron extends to a bounded free function.

Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Mungia, Dambaru Bhatta

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions.

Generalized Cokähler Geometry And An Application To Generalized Kähler Structures, Ralph R. Gomez, Janet Talvacchia

Mathematics & Statistics Faculty Works

In this paper, we propose a generalization of classical coKähler geometry from the point of view of generalized contact metric geometry. This allows us to generalize a theorem of Capursi (1984), Goldberg (1968) and show that the product M1×M2M1×M2 of generalized contact metric manifolds (Mi,Φi,E±,i,Gi)(Mi,Φi,E±,i,Gi), i=1,2i=1,2, where M1×M2M1×M2 is endowed with the product (twisted) generalized complex structure induced from Φ1Φ1 and Φ2Φ2, is (twisted) generalized Kähler if and only if View the MathML source(Mi,Φi,E±,i,Gi),i=1,2 are (twisted) generalized coKähler structures. As an application of our theorem we construct new examples of twisted generalized Kähler structures on manifolds that do not admit …

Low-Rank Network Decomposition Reveals Structural Characteristics Of Small-World Networks, Victor J. Barranca, D. Zhou, D. Cai

Mathematics & Statistics Faculty Works

Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering …

Review: A Short Introduction To De Branges-Rovnyak Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Non-Commutative Holomorphic Functions On Operator Domains, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

We characterize functions of d-tuples of bounded operators on a Hilbert space that are uniformly approximable by free polynomials on balanced open sets.

Integrability And Regularity Of Rational Functions, Greg Knese

Mathematics Faculty Publications

Motivated by recent work in the mathematics and engineering literature, we study integrability and non-tangential regularity on the two-torus for rational functions that are holomorphic on the bidisk. One way to study such rational functions is to fix the denominator and look at the ideal of polynomials in the numerator such that the rational function is square integrable. A concrete list of generators is given for this ideal as well as a precise count of the dimension of the subspace of numerators with a specified bound on bidegree. The dimension count is accomplished by constructing a natural pair of commuting …

Maximal Class P-Groups With Large Character Degree Gaps, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

In Mann (More on normally monomial p-groups, 2015), he proves some bounds on the size of gaps between character degrees of maximal class p-groups. In this note we construct a family of examples that shows that one of these bounds is sharp.

Lower Bound For Ranks Of Invariant Forms, Harm Derksen, Zach Teitler

Mathematics Faculty Publications and Presentations

We give a lower bound for the Waring rank and cactus rank of forms that are invariant under an action of a connected algebraic group. We use this to improve the Ranestad-Schreyer-Shafiei lower bounds for the Waring ranks and cactus ranks of determinants of generic matrices, Pfaffians of generic skew-symmetric matrices, and determinants of generic symmetric matrices.

Extended Lindley Poisson Distribution, Mavis Pararai, Gayan Warahena-Liyanage, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

The Extended Lindley Poisson (ELP) distribution which is an extension of the extended Lindley distribution [2] is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density, hazard rate functions, moments, Bonferroni and Lorenz curves are explored. Entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally, we present applications …

Black Male Students And The Algebra Project: Mathematics Identity As Participation, Melva R. Grant, Helen Crompton, Deanna J. Ford

STEMPS Faculty Publications

In this article, the authors examine the mathematics identity development of six Black male students over the course of a 4-year The Algebra Project Cohort Model (APCM) initiative. Mathematics identity here is defined as participation through interactions and positioning of self and others. Data collection included nearly 450 minutes of video recordings of small-group, mathematics problem solving in which student actions, coded as acts of participation, were tallied. These tallied actions were conceptualized descriptively in terms of mathematics identity using the lenses of agency, accountability, and work practices. The analyses suggest that the APCM students’ confidence in self and peers …

The Mathematics And Applications Behind Image Warping And Morphing, Tanvir Prince, Maria Malik, Ildefonso Salva, Ariel Mazor, Sakhr Aldaylam

Publications and Research

This research is conducted in the summer of 2015 and is possible by the support of various agency, in particular, by the grant of Prof. Angulo Nieves and the New York City Research Initiative.

The purpose of this research is to reveal the mathematics and applications of the computer animation techniques of warping and morphing. A warp is a twist or distortion in the form of an object in an image while a morph is the smooth and gradual transformation of an object in one image into the object in another image. Linear algebra makes these computer animation techniques possible; …

Investigating The Role Of The Host Multidrug Resistance Associated Protein Transporter Family In Burkholderia Cepacia Complex Pathogenicity Using A Caenorhabditis Elegans Infection Model, Pietro Tedesco, Marco Visone, Ermenegilda Parrilli, Maria Luisa Tutino, Elena Perrin, Isabel Maida, Renato Fani, Francesco Ballestriero, Radleigh Santos, Clemencia Pinilla, Elia Di Schiavi, George Tegos, Donatella De Pascale

Mathematics Faculty Articles

This study investigated the relationship between host efflux system of the non-vertebrate nematode Caenorhabditis elegans and Burkholderia cepacia complex (Bcc) strain virulence. This is the first comprehensive effort to profile host-transporters within the context of Bcc infection. With this aim, two different toxicity tests were performed: a slow killing assay that monitors mortality of the host by intestinal colonization and a fast killing assay that assesses production of toxins. A Virulence Ranking scheme was defined, that expressed the toxicity of the Bcc panel members, based on the percentage of surviving worms. According to this ranking the 18 Bcc strains were …

Closed Range Composition Operators On Hilbert Function Spaces, Pratibha Ghatage, Maria Tjani

Mathematics and Statistics Faculty Publications

We show that a Carleson measure satisfies the reverse Carleson condition if and only if its Berezin symbol is bounded below on the unit disk D. We provide new necessary and sufficient conditions for the composition operator to have closed range on the Bergman space. The pull-back measure of area measure on D plays an important role. We also give a new proof in the case of the Hardy space and conjecture a condition in the case of the Dirichlet space.

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.

Models Describing The Sea Level Rise In Key West, Florida, Karm-Ervin Jean

FIU Electronic Theses and Dissertations

Lately, we have been noticing an unusual rise in the sea level near many Floridian cities. By 2060, scientists believe that the sea level in the city of Key West will reach between 22.86 to 60.96 centimeters (Strauss et al. 2012). The consequences of sea level rise are unpleasant by gradually tearing away our beaches and natural resources, destroying our homes and businesses, etc. Definitively, a continual increase of the sea level will affect everyone either directly or indirectly.

In this study, the sea level measurements of four Floridian coastal cities (including Key West) are collected in order to describe …

A Note On Practical Approximate Projection Schemes In Signal Space Methods, Xiaoyi Gu, Deanna Needell, Shenyinying Tu

CMC Faculty Publications and Research

Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many socalled signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has …

Gis-Integrated Mathematical Modeling Of Social Phenomena At Macro- And Micro- Levels—A Multivariate Geographically-Weighted Regression Model For Identifying Locations Vulnerable To Hosting Terrorist Safe-Houses: France As Case Study, Elyktra Eisman

FIU Electronic Theses and Dissertations

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to …

Fusion Algebras & Accidental Trigonometry, Christopher D. Goff

College of the Pacific Faculty Presentations

Have you ever been working in one area of math, and another area arises unexpectedly? While working on a problem in 2008, we inadvertently discovered some trigonometric identities. This talk will explain fusion algebras, which are relatively simple algebraic objects that demonstrate nice algebraic applications of linear algebra. Then we will see how trigonometry can arise in even this most algebraic of settings.

Convergence Properties Of The Randomized Extended Gauss-Seidel And Kaczmarz Methods, Anna Ma, Deanna Needell, Aaditya Ramdas

CMC Faculty Publications and Research

The Kaczmarz and Gauss-Seidel methods both solve a linear system Xβ=y by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized Gauss-Seidel algorithm. However, the behavior of both methods depends heavily on whether the system is under or overdetermined, and whether it is consistent or not. Here we provide a unified theory of both methods, their variants for these different settings, and draw connections between …

Review: The Classical Hom-Yang-Baxter Equation And Hom-Lie Bialgebras, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Sexually Dimorphic Gene Expression In The Lateral Eyes Of Euphilomedes Carcharodonta (Ostracoda, Pancrustacea), Andrea Sajuthi, Brenna Carrillo-Zazueta, Briana Hu, Anita Wang, Logan Brodnansky, John Mayberry, Ajna S. Rivera

College of the Pacific Faculty Articles

Background: The evolution and development of sexual dimorphism illuminates a central question in biology: How do similar genomes produce different phenotypes? In an XX/XO system especially the state of a sexually dimorphic trait is determined by differences in gene expression, as there are no additional genetic loci in either sex. Here, we examine the XX/XO ostracod crustacean species Euphilomedes carcharodonta. This species exhibits radical sexual dimorphism of their lateral eyes, females have only a tiny simple lateral eye while males have elaborate ommatidial eyes. Results: We find that males express three of nine eye-development gene homologs at significantly higher levels …

On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete

Mathematics Faculty Publications

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. …

Molecular Network Control Through Boolean Canalization, David Murrugarra, Elena S. Dimitrova

Mathematics Faculty Publications

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges …

2015: "Go With The Flow", Paul Nebres '16, Kushagra Gupta '16, Jason Chen '16, Noor Michael '16

Distinguished Student Work

In a famous incident in August 2010, a Chinese traffic jam stretched for over 100 kilometers and stranded drivers took over two weeks to get from one side to the other. Stemming from a routine lane closure for road maintenance, the traffic jam soon spiraled out of control, as cars piling up at the jam greatly outnumbered those leaving the other end. Sadly, in todays overpopulated world, these sorts of nightmare scenarios are only becoming more and more common, from chronic traffic jams in congested Chinese cities to Carmageddon in Los Angeles. For drivers, these extensive traffic jams can be …

From Equations To Tri-Quations And Multi-Quations, Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, an equation A(x₁, ..., x_n)= B(x₁, ..., x_n) corresponds to the situation when we have two quantities A(x₁, ..., x_n) and B(x₁, ..., x_n) which are known to be equal, we know how each of these quantities depends on the unknown parameters x₁, ..., x_n, and we want to find the values of the unknowns x_i from this equality -- and from other similar equalities. In some practical situations, instead of two equal values, we have three …

Maximum Entropy Approach Is Not As Arbitrary As It May Seem At First Glance, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we only have partial information about the probability distribution, i.e., when several different probability distributions are consistent with our knowledge, then it makes sense to select a distribution with the largest entropy. In particular, when we only know that the quantity is located within a certain interval -- and we have no information about the probability of different values within this intervals -- then it is reasonable to assume that all these values are equally probable, i.e., that we have a uniform distribution on this interval. The problem with this idea is that if we apply it to the …

Why The Graph Isomorphism Problem Is Easier Than Propositional Satisfiability: A Possible Qualitative Explanation, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

A recent result has shown that the graph isomorphism problem can be solved in quasi-polynomial time, while the general belief is that only exponential time algorithms are possible for propositional satisfiability. This is somewhat counter-intuitive, since for propositional satisfiability, we need to look for one of 2ⁿ options, while in graph isomorphism, we need to look for one of n! options, and n! is much larger than 2ⁿ. Our qualitative explanation for this counter-intuitive fact comes from the fact that, in general, a graph isomorphism problem has a unique solution -- in contrast to propositional satisfiability which, …

Decision Making Under Interval (And More General) Uncertainty: Monetary Vs. Utility Approaches, Vladik Kreinovich

Departmental Technical Reports (CS)

In many situations, e.g., in financial and economic decision making, the decision results either in a money gain (or loss) and/or in the gain of goods that can be exchanged for money or for other goods. In such situations, interval uncertainty means that we do not know the exact amount of money that we will get for each possible decision, we only know lower and upper bounds on this amount. In this case, a natural idea is to assign a fair price to different alternatives, and then to use these fair prices to select the best alternative. In the talk, …

Waning Influence Of History: Why?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the past, history played an important role in education: students learned history of science, history of mathematics, etc. In the last decades, the influence of history has waned. In this paper, we provide a natural explanation for this waning.