Mathematics Commons^™

On Spanning Sets And Generators Of Near-Vector Spaces, Karin-Therese Howell, Sogo Pierre Sanon

Turkish Journal of Mathematics

In this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.

General Dissipative Materials For Simple Histories, John Murrough Golden, G. Amendola, M. Fabrizio

Articles

A material with memory typically has a set of many free energy functionals associated with it, all members of which yield the same constitutive relations. An alternative interpretation of this set is explored in the present work. Explicit formulae are derived for the free energy and total dissipation of an arbitrary material in the cases of step function and sinusoidal/exponential histories. Expressions for the fraction of stored and dissipated energy are deduced. Also, various formulae are given for discrete spectrum materials. For materials with relaxation function containing one decaying exponential, the associated Day functional is the physical free energy. For …

Discriminants Of Polynomials In The Archimedean And Non-Archimedean Metrics, Vasili Bernick, Natalia Budarina, Hugh O'Donnell

Articles

An upper bound for the number of cubic polynomials which have small discriminant in terms of the Euclidean and p-adic metrics simultaneously is obtained.

A Geometric Generalizaion Of The Planar Gale-Nikaidô Theorem, Eduardo C. Balreira

Mathematics Faculty Research

The Gale-Nikaidô Theorem establishes global injectivity of maps defined over rectangular regions provided the Jacobian matrix is a P-matrix. We provide a purely geometric generalization of this result in the plane by showing that if the image of each edge of the rectangular domain is realized as a graph of a function over the appropriate axis, then the map is injective. We also show that the hypothesis that the Jacobian matrix is a P-matrix is simply one way to analytically check this geometric condition.

Categories Of Residuated Lattices, Daniel Wesley Fussner

Electronic Theses and Dissertations

We present dual variants of two algebraic constructions of certain classes of residuated lattices: The Galatos-Raftery construction of Sugihara monoids and their bounded expansions, and the Aguzzoli-Flaminio-Ugolini quadruples construction of srDL-algebras. Our dual presentation of these constructions is facilitated by both new algebraic results, and new duality-theoretic tools. On the algebraic front, we provide a complete description of implications among nontrivial distribution properties in the context of lattice-ordered structures equipped with a residuated binary operation. We also offer some new results about forbidden configurations in lattices endowed with an order-reversing involution. On the duality-theoretic front, we present new results on …

A Network Diffusion Ranking Family That Includes The Methods Of Markov, Massey, And Colley, Stephen Devlin, Thomas Treloar

Mathematics

We present a one parameter family of ratings and rankings that includes the Markov method, as well as the methods of Colley and Massey as particular cases. The rankings are based on a natural network diffusion process that unites the methodologies above in a common framework and brings strong intuition to how and why they differ. We also explore the behavior of the ranking family using both real and simulated data.

Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. I will restrict my attention to 4-dimensional spacetimes.

How To Make Tetrads, Charles G. Torre

How to... in 10 minutes or less

This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.

An Adjunction Formula For The Emerton-Jacquet Functor, John Bergdall, Przemyslaw Chojecki

Mathematics Faculty Research and Scholarship

The Emerton–Jacquet functor is a tool for studying locally analytic representations of p-adic Lie groups. It provides a way to access the theory of p-adic automorphic forms. Here we give an adjunction formula for the Emerton–Jacquet functor, relating it directly to locally analytic inductions, under a strict hypothesis that we call non-critical. We also further study the relationship to socles of principal series in the non-critical setting.

On A New Subclass Of Bi-Univalent Functions Defined By Using Salagean Operator, Bi̇lal Şeker

Turkish Journal of Mathematics

In this manuscript, by using the Salagean operator, new subclasses of bi-univalent functions in the open unit disk are defined. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found.

Generalized Metric $N$-Leibniz Algebras And Generalized Orthogonal Representation Of Metric Lie Algebras, Rong Tang, Lina Song

Turkish Journal of Mathematics

We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas). We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.

Harmonic Quadrangle In Isotropic Plane, Ema Jurkin, Marija Simic Horvath, Vladimir Volenec, Jelena Beban-Brkic

Turkish Journal of Mathematics

The concept of the harmonic quadrangle and the associated Brocard points are introduced and investigated in the isotropic plane by employing suitable analytic methods.

Symmetry Algebras Of The Canonical Lie Group Geodesic Equations In Dimension Three, Ryad Ghanam, Gerard Thompson

VCUarts Qatar Faculty Research

For each of the two and three-dimensional indecomposable Lie algebras the geodesic equations of the associated canonical Lie group connection are given. In each case a basis for the associated Lie algebra of symmetries is constructed and the corresponding Lie brackets are written down.

An Incidence Approach To The Distinct Distances Problem, Bryce Mclaughlin

HMC Senior Theses

In 1946, Erdös posed the distinct distances problem, which asks for the minimum number of distinct distances that any set of n points in the real plane must realize. Erdös showed that any point set must realize at least &Omega(n^1/2) distances, but could only provide a construction which offered &Omega(n/&radic(log(n)))$ distances. He conjectured that the actual minimum number of distances was &Omega(n^1-&epsilon) for any &epsilon > 0, but that sublinear constructions were possible. This lower bound has been improved over the years, but Erdös' conjecture seemed to hold until in 2010 Larry Guth and Nets Hawk Katz …

On The Landscape Of Random Tropical Polynomials, Christopher Hoyt

HMC Senior Theses

Tropical polynomials are similar to classical polynomials, however addition and multiplication are replaced with tropical addition (minimums) and tropical multiplication (addition). Within this new construction, polynomials become piecewise linear curves with interesting behavior. All tropical polynomials are piecewise linear curves, and each linear component uniquely corresponds to a particular monomial. In addition, certain monomial in the tropical polynomial can be trivial due to the fact that tropical addition is the minimum operator. Therefore, it makes sense to consider a graph of connectivity of the monomials for any given tropical polynomial. We investigate tropical polynomials where all coefficients are chosen from …

On Matrix Rings With The Sip And The Ads, Fi̇gen Takil Mutlu

Turkish Journal of Mathematics

In this paper, matrix rings with the summand intersection property (SIP) and the absolute direct summand (ads) property (briefly, $SA$) are studied. A ring $R$ has the right SIP if the intersection of two direct summands of $R$ is also a direct summand. A right $R$-module $M$ has the ads property if for every decomposition $M=A\oplus B$ of $M$ and every complement $C$ of $A$ in $M$, we have $M=A\oplus C$. It is shown that the trivial extension of $R$ by $M$ has the SA if and only if $R$ has the SA, $M$ has the ads, and $(1-e)Me=0$ for …

The Great Escape, Caleb Kowalsk

Honors Program: Expanded Learning Clubs

No abstract provided.

Hilbert Bases, Descent Statistics, And Combinatorial Semigroup Algebras, Mccabe J. Olsen

Theses and Dissertations--Mathematics

The broad topic of this dissertation is the study of algebraic structure arising from polyhedral geometric objects. There are three distinct topics covered over three main chapters. However, each of these topics are further linked by a connection to the Eulerian polynomials.

Chapter 2 studies Euler-Mahonian identities arising from both the symmetric group and generalized permutation groups. Specifically, we study the algebraic structure of unit cube semigroup algebra using Gröbner basis methods to acquire these identities. Moreover, this serves as a bridge between previous methods involving polyhedral geometry and triangulations with descent bases methods arising in representation theory.

In Chapter …

Characterizing The Turbulent Structure Of The Cbl And The Entrainment, Wei Jia

Undergraduate Research Posters 2018

The convective boundary layer (CBL) is the lowest part of the atmosphere. The turbulent motions in the CBL are important for redistributing trace gases, particles, heat, and momentum between the surface and the free troposphere thus it is important that this process is properly represented in numerical models that attempts to simulate the atmosphere. This study is trying to characterize the water vapor structure in the quasi-stationary CBL, using statistical way to build the turbulent model and uses a high resolution model: Large Eddy Simulation (LES) to investigate the adequacy of the model. We found that the water vapor flux …

Investigating The Influence Of Cloud Size On Cumulus Cloud Entrainment, Theresa Lincheck

Undergraduate Research Posters 2018

Clouds play a crucial role in determining the weather on local and global scales, yet their complexity accounts for some of the largest uncertainties in weather forecasts and climate models. Environmental air mixing or being drawn into a current, called entrainment, is one source to blame for this complexity. When air entrains into a cloud evaporation of in-cloud condensates increase and temperatures in the cloud drop, reducing buoyancy. The overall effect of entrainment inhibits a cloud’s development, and usually results in the dissipation of a cloud. With the use of data generated from a high-resolution computer model known as Large …