Mathematics Commons^™

An Introduction To Differential Geometry Through Computation, Mark E. Fels

Mathematics and Statistics Faculty Presentations

No abstract provided.

Large Outgoing Solutions To Supercritical Wave Equations, Marius Beceanu, Sover Avy

Mathematics and Statistics Faculty Scholarship

We prove the existence of global solutions to the energy-supercritical wave equation in R^{3+1} u_{tt}-\Delta u + |u|^N u = 0, u(0) = u_0, u_t(0) = u_1, 4

Sexual Assault And The Doctrine Of Chances In The Courtroom, Ryan Wallentine

Research on Capitol Hill

Sexual assault can have devastating and long-lasting effects on victims, but many assailants get away with their crime without being prosecuted.

The doctrine of chances is a rule of evidence allowing evidences of past crimes, wrongs, or acts to show it is unlikely a defendant would be repeatedly and innocently involved in similar, suspicious circumstances.

Given that about 63.3% of assailants are repeat offenders, the doctrine of chances could effectively be used in sexual assault cases.

The main objective is to determine a precise probabilistic threshold for allowing the use of the doctrine of chances in sexual assault cases such …

An Introduction To Differential Geometry Through Computation, Mark E. Fels

Textbooks

The outline of the book is as follows. Chapter 1 reviews some basic facts about smooth functions from IRⁿ to IR^m, as well as the basic facts about vector spaces, basis, and algebras. Chapter 2 introduces tangent vectors and vector fields in IRⁿ using the standard two approaches with curves and derivations. Chapter 3 reviews linear transformations and their matrix representation so that in Chapter 4 the push-forward as an abstract linear transformation can be defined and its matrix representation as the Jacobian can be derived. As an application, the change of variable formula for vector …

Application Of Combinatorial Structures In Wireless Communication., Samiran Bag Dr.

Doctoral Theses

Wireless communication has a compelling need in today’s world. This need is driven by the sudden surge in the demand of ad-hoc networks like wireless sensor networks. These networks consist of many isolated devices called nodes that use the wireless medium for communication. There are three security notions attached to any wireless communication. These are data confidentiality, data integrity and data availability. Cryptographic protocols are required for achieving the first two notions which in turn require shared secret keys. The last notion viz. data availability mainly deals with protecting the data from ‘denial of service attack’.In this thesis, we apply …

Abstraction And Epistemic Economy, Marco Panza

MPP Published Research

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning …

On The Equivalence Of Probability Spaces, Daniel Alpay, Palle Jorgensen, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a general class of Gaussian processes W, indexed by a sigma-algebra F of a

general measure space (M,F, _), we give necessary and sufficient conditions for the validity

of a quadratic variation representation for such Gaussian processes, thus recovering _(A),

for A 2 F, as a quadratic variation of W over A. We further provide a harmonic analysis

representation for this general class of processes. We apply these two results to: (i) a computation

of generalized Ito-integrals; and (ii) a proof of an explicit, and measure-theoretic

equivalence formula, realizing an equivalence between the two approaches to Gaussian processes,

one …

Generalized Transmuted Family Of Distributions: Properties And Applications, Morad Alizadeh, Faton Merovci, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new …

Chimera States In A Hodgkin-Huxley Model Of Thermally Sensitive Neurons, Tera Glaze, Scott Lewis, Sonya Bahar

Physics Faculty Works

Chimera states occur when identically coupled groups of nonlinear oscillators exhibit radically different dynamics, with one group exhibiting synchronized oscillations and the other desynchronized behavior. This dynamical phenomenon has recently been studied in computational models and demonstrated experimentally in mechanical, optical, and chemical systems. The theoretical basis of these states is currently under active investigation. Chimera behavior is of particular relevance in the context of neural synchronization, given the phenomenon of unihemispheric sleep and the recent observation of asymmetric sleep in human patients with sleep apnea. The similarity of neural chimera states to neural “bump” states, which have been suggested …

Remembering Lynn Steen: A Steen-Numeracy Citation Index (2008-2015), H. L. Vacher

Numeracy

This editorial memorializes Lynn Arthur Steen (1941-2015) with a bibliographic resource that indexes all of his writings (papers, books, edited volumes, and papers contained therein) that are cited in papers in Numeracy. The citation index contains 67 cited works, each accompanied with a list of linked Numeracy papers that cite them. All told, there are 68 such citing papers (called sources); they cite the 67 cited works a total of 290 times and are listed alphabetically in a source index with links. The paired citation and source indexes provide a vehicle for easy browsing by which those familiar with …

The Basic Competencies Of Biological Experimentation: Concept-Skill Statements, Nancy Pelaez, Trevor Anderson, Stephanie M. Gardner, Yue Yin, Joel K. Abraham, Edward Bartlett, Cara Gormally, Jeffrey P. Hill, Mildren Hoover, Carol Hurney, Tammy Long, Dina L. Newman, Karen Sirum, Michael Stevens

PIBERG Instructional Innovation Materials

This biological experimentation competencies map is a model created by members of the ACE-Bio Network of seven areas a competent biologist calls in when doing experimentation in biology. Each competency is represented by a summary word on a uniquely colored segment of the model. For presentation convenience, the seven major areas within experimentation in biology are mapped onto tables in a linear manner. However, this is not meant to convey a particular order that one must follow during experimentation. The areas are given equal weight and flexible order of their use throughout the process of experimentation. This work is meant …

Review: Transitivity And Bundle Shifts, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Atypical Visual And Somatosensory Adaptation In Schizophrenia-Spectrum Disorders, Gizely Andrade, John Butler, Gregory Peter, Sophie Molholm, John J. Foxe

Articles

Neurophysiological investigations in patients with schizophrenia consistently show early sensory processing deficits in the visual system. Importantly, comparable sensory deficits have also been established in healthy first-degree biological relatives of patients with schizophrenia and in first-episode drug-naive patients. The clear implication is that these measures are endophenotypic, related to the underlying genetic liability for schizophrenia. However, there is significant overlap between patient response distributions and those of healthy individuals without affected first-degree relatives. Here we sought to develop more sensitive measures of sensory dysfunction in this population, with an eye to establishing endophenotypic markers with better predictive capabilities. We used …

Records Of The Brooklyn College Mathematics Department, Brooklyn College

Finding Aids

This collection consists largely of handwritten grade books from Brooklyn College’s earliest years. Much of it also relates to the Math Department’s extracurricular activities such as contests. There are only two Subgroups in the collection: Notebooks: Records of Classes in Mathematics 1926 – 1976, and Department of Mathematics General Information.

Series 10, Ruth Dover

Series

Extra stuff to show more ways to work with series.

Large Initial Data Global Well-Posedness For A Supercritical Wave Equation, Marius Beceanu, Avy Soffer

Mathematics and Statistics Faculty Scholarship

We prove the existence of global solutions to the focusing energy-supercritical semilinear wave equation in R^{3+1} for arbitrary outgoing large initial data, after we modify the equation by projecting the nonlinearity on outgoing states.

Sampling And Interpolation On Some Nilpotent Lie Groups, Vignon Oussa

Mathematics Faculty Publications

No abstract provided.

Identifying An M-Ary Partition Identity Through An M-Ary Tree, Timothy B. Flower, Shannon R. Lockard

Mathematics Faculty Publications

The Calkin-Wilf tree is well-known as one way to enumerate the rationals, but also may be used to count hyperbinary partitions of an integer, h₂(n). We present an m-ary tree which is a generalization of the Calkin-Wilf tree and show how it may be used to count the hyper m-ary partitions of an integer, h_m(n). We then use properties of the m-ary tree to prove an identity relating values of h₂ to values of h_m, showing that one sequence is a subsequence of the other. Finally, …

Missouri Section Of The Mathematical Association Of America: Centennial History 1915-2015, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

"Compiling and writing the history of the Missouri MAA Section has been time-consuming, but it has mainly been rewarding and a wonderful learning experience. Both the Monthly and the MAA began with strong Midwestern and Missouri influences, something which our section can look back on with well-deserved pride. Missouri MAA members have consistently advanced collegiate mathematics, mathematics education, mathematics research and scholarship, and public appreciation for and understanding of mathematics in both Missouri and the nation. Looking to the future, the MAA and the Missouri Section can continue to be a great source of opportunities for leadership and service for …

Asymptotic Behavior Of Certain Integrodifferential Equations, Said R. Grace, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: (a(t)x'(t))' = e (t) + ∫ ^t_c (t - s)^{α - 1}k(t,s)ƒ(s,x(s))ds, c > 1, 0 < α < 1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.

Nonoscillation Criteria For Two-Dimensional Time-Scale Systems, Ozkan Ozturk, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional system of first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Qualitative Analysis On Differential, Fractional Differential, And Dynamic Equations And Related Topics, Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field.

Sneak-Out Principle On Time Scales, Martin Bohner, Samir H. Saker

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we show that the so-called "sneak-out principle" for discrete inequalities is valid also on a general time scale. In particular, we prove some new dynamic inequalities on time scales which as special cases contain discrete inequalities obtained by Bennett and Grosse-Erdmann. The main results also are used to formulate the corresponding continuous integral inequalities, and these are essentially new. The techniques employed in this paper are elementary and rely mainly on the time scales integration by parts rule, the time scales chain rule, the time scales Hölder inequality, and the time scales Minkowski inequality.

Oscillation Criteria For Fourth Order Nonlinear Positive Delay Differential Equations With A Middle Term, Said R. Grace, Elvan Akin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we establish some new criteria for the oscillation of fourth order nonlinear delay differential equations of the form (Equation presented) provided that the second order equation (Equation presented) is nonoscillatiory or oscillatory. This equation with g(t) = t is considered in [8] and some oscillation criteria for this equation via certain energy functions are established. Here, we continue the study on the oscillatory behavior of this equation via some inequalities.

On Algebraic Properties Of Veronese Bi-Type Ideals Arising From Graphs, Maurizio Imbesi, Monica La Barbiera

Turkish Journal of Mathematics

Some algebraic properties of the ideals of Veronese bi-type arising from graphs with loops are studied. More precisely, the property of these ideals to be bi-polymatroidal is discussed. Moreover, we are able to determine the structure of the ideals of vertex covers for such generalized graph ideals.

A Note On Reduction Numbers And Hilbert-Samuel Functions Of Ideals Over Cohen-Macaulay Rings, Amir Mafi, Dler Naderi

Turkish Journal of Mathematics

Let $(R,\fm)$ be a Cohen--Macaulay local ring of dimension $d\geq 2$ with infinite residue field and $I$ an $\fm$-primary ideal of $R$. Let $I$ be integrally closed and $J$ be a minimal reduction of $I$. In this paper, we show that the following are equivalent: $(i)$ $P_I(n)=H_I(n)$ for $n=1,2$; $(ii)$ $P_I(n)=H_I(n)$ for all $n\geq 1$; $(iii)$ $I^3=JI^2$. Moreover, if $\Dim R=3$, $n(I)\leq 1$ and $\grade gr_I(R)_+>0$, then the reduction number $r(I)$ is independent.

Sharp Bounds For The First Nonzero Steklov Eigenvalues For$F$-Laplacians, Guangyue Huang, Bingqing Ma

Turkish Journal of Mathematics

Let $M$ be an $n$-dimensional compact Riemannian manifold with a boundary. In this paper, we consider the Steklov first eigenvalue with respect to the $f$-divergence form: $$ e^{f}{\rm div}(e^{-f}A\nabla u)=0\ {\rm in}\ \ M, \ \ \ \ \ \langle A(\nabla u),\nu\rangle-\eta u=0 \ \ {\rm on}\ \partial M,$$ where $A$ is a smooth symmetric and positive definite endomorphism of $TM$, and the following three fourth order Steklov eigenvalue problems: $$ (\Delta_f)^2u=0\ \ {\rm in}\ M, \ \ \ \ \ u=\Delta_f u-q\frac{\partial u}{\partial \nu}=0\ \ {\rm on}\ \partial M; $$ $$ (\Delta_f)^2u=0\ {\rm in}\ \ M, \ \ \ …

A Remark On Singularity Of Homeomorphisms And Hausdorff Dimension, Chun Wei, Shengyou Wen

Turkish Journal of Mathematics

We prove that there is a homeomorphism of the unit interval onto itself that is so singular that it maps some set $E$ of $\dim_HE=0$ onto a set $F$ of $\dim_H[0,1]\setminus F=0$.

Idempotents Of The Green Algebras Of Finite Dimensionalpointed Rank One Hopf Algebras Of Nilpotent Type, Zhihua Wang

Turkish Journal of Mathematics

In this paper, we intend to study idempotents of the Green algebra (complexified Green ring) of any finite dimensional pointed rank one Hopf algebra of nilpotent type over the complex number field. We first determine all one dimensional representations of the quotient algebra of the Green algebra modulo its Jacobson radical. This gives rise to all primitive idempotents of the quotient algebra. Then we present explicitly primitive idempotents of the Green algebra by lifting the ones of the quotient algebra. Finally, as an example, we describe all primitive idempotents of the Green algebra of the Taft algebra $T_3$.

A New Aspect To Picard Operators With Simulation Functions, Murat Olgun, Tuğçe Alyildiz, Özge Bi̇çer

Turkish Journal of Mathematics

In the present paper, considering the simulation function, we give a new class of Picard operators on complete metric spaces. We also provide a nontrivial example that shows the aforementioned class properly contains some earlier such classes.