# Mathematics Commons™

## All Articles in Mathematics

17,858 full-text articles. Page 3 of 528.

Lai’S Conditions For Spanning And Dominating Closed Trails, 2019 Butler University

#### Lai’S Conditions For Spanning And Dominating Closed Trails, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu

##### Zhi-Hong Chen

No abstract provided.

2019 Marshall University

#### Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model.Pdf, Michael Otunuga

##### Olusegun Michael Otunuga

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to ...

Reverse Mathematics Of Matroids, 2019 Marshall University

#### Reverse Mathematics Of Matroids, Jeffry L. Hirst, Carl Mummert

##### Carl Mummert

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \Sigma^0_2 formulas.

Making Sense With Math: An Introduction To Math For People In College, 2019 Western Washington University

#### Making Sense With Math: An Introduction To Math For People In College, Roxane Elena Ronca

##### A Collection of Open Access Books and Monographs

Most math books for college students start out reviewing “rules” in an introductory chapter. The review usually goes like this: here are the “rules”, here are some examples of using those “rules” and here are 10 to 100 exercises where you will practice using those “rules” and then you’ll be tested on them.

The problem with that approach, even if it seems familiar and comfortable to you, is that people learn, in part, by connecting new ideas and perspectives to what they already understand, and correcting any previous misunderstandings. This process takes time and effort. Memorizing rules to quickly ...

Injury Severity Data For Front And Second Row Passengers In Frontal Crashes, 2019 Kettering University

#### Injury Severity Data For Front And Second Row Passengers In Frontal Crashes, Theresa Atkinson, Leszek Gawarecki, Massoud S. Tavakoli

##### Leszek Gawarecki

The data contained here were obtained from the National Highway Transportation Safety Administration׳s National Automotive Sampling System – Crashworthiness Data System (NASS-CDS) for the years 2008–2014. This publically available data set monitors motor vehicle crashes in the United States, using a stratified random sample frame, resulting in information on approximately 5000 crashes each year that can be utilized to create national estimates for crashes. The NASS-CDS data sets document vehicle, crash, and occupant factors. These data can be utilized to examine public health, law enforcement, roadway planning, and vehicle design issues. The data provided in this brief are a ...

Sharp Bounds For Decomposing Graphs Into Edges And Triangles, 2019 Iowa State University

#### Sharp Bounds For Decomposing Graphs Into Edges And Triangles, Adam Blumenthal, Bernard Lidicky, Oleg Pikhurko, Yanitsa Pehova, Florian Pfender, Jan Volec

##### Bernard Lidický

Let pi3(G) be the minimum of twice the number of edges plus three times the number of triangles over all edge-decompositions of G into copies of K2 and K3. We are interested in the value of pi3(n), the maximum of pi3(G) over graphs G with n vertices. This specific extremal function was first studied by Gyori and Tuza [Decompositions of graphs into complete subgraphs of given order, Studia Sci. Math. Hungar. 22 (1987), 315--320], who showed that pi3(n)<9n2/16.
In a recent advance on this problem, Kral, Lidicky, Martins and Pehova [arXiv:1710:08486] proved via flag ...

Fractional Strong Matching Preclusion For Two Variants Of Hypercubes, 2019 School of Computer, Qinghai Normal University

#### Fractional Strong Matching Preclusion For Two Variants Of Hypercubes, Huifen Ge, Tianlong Ma, Miaolin Wu, Yuzhi Xiao

##### Theory and Applications of Graphs

Let F be a subset of edges and vertices of a graph G. If G-F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each.

Acid And Base Stress And Transcriptomic Responses In Bacillus Subtilis., 2019 Kenyon College

#### Acid And Base Stress And Transcriptomic Responses In Bacillus Subtilis., Brian Jones, Jessica C. Wilks, Ryan D. Kitko, Sarah H. Cleeton, Grace E. Lee, Chinagozi S. Ugwu, Sandra S. Bondurant, Joan L. Slonczewski

##### Brian Jones

Acid and base environmental stress responses were investigated in Bacillus subtilis. B. subtilis AG174 cultures in buffered potassium-modified Luria broth were switched from pH 8.5 to pH 6.0 and recovered growth rapidly, whereas cultures switched from pH 6.0 to pH 8.5 showed a long lag time. Log-phase cultures at pH 6.0 survived 60 to 100% at pH 4.5, whereas cells grown at pH 7.0 survived <15%. Cells grown at pH 9.0 survived 40 to 100% at pH 10, whereas cells grown at pH 7.0 survived <5%. Thus, growth in a moderate acid or base induced adaptation to a more extreme acid or base, respectively. Expression indices from Affymetrix chip hybridization were obtained for 4,095 protein-encoding open reading frames of B. subtilis grown at external pH 6, pH 7, and pH 9. Growth at pH 6 upregulated acetoin production (alsDS), dehydrogenases (adhA, ald, fdhD, and gabD), and decarboxylases (psd and speA). Acid upregulated malate metabolism (maeN), metal export (czcDO and cadA), oxidative stress (catalase katA; OYE family namA), and the SigX extracytoplasmic stress regulon. Growth at pH 9 upregulated arginine catabolism (roc), which generates organic acids, glutamate synthase (gltAB), polyamine acetylation and transport (blt), the K(+)/H(+) antiporter (yhaTU), and cytochrome oxidoreductases (cyd, ctaACE, and qcrC). The SigH, SigL, and SigW regulons were upregulated at high pH. Overall, greater genetic adaptation was seen at pH 9 than at pH 6, which may explain the lag time required for growth shift to high pH. Low external pH favored dehydrogenases and decarboxylases that may consume acids and generate basic amines, whereas high external pH favored catabolism-generating acids.

2019 Marshall University

#### Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

##### Mathematics Faculty Research

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to ...

The Cone Of Z-Transformations On Lorentz Cone, 2019 University of Birmingham

#### The Cone Of Z-Transformations On Lorentz Cone, Sandor Zoltan Nemeth, Muddappa S. Gowda

##### Electronic Journal of Linear Algebra

In this paper, the structural properties of the cone of $\calz$-transformations on the Lorentz cone are described in terms of the semidefinite cone and copositive/completely positive cones induced by the Lorentz cone and its boundary. In particular, its dual is described as a slice of the semidefinite cone as well as a slice of the completely positive cone of the Lorentz cone. This provides an example of an instance where a conic linear program on a completely positive cone is reduced to a problem on the semidefinite cone.

9th Annual Postdoctoral Science Symposium, 2019 The Texas Medical Center Library

#### 9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association

##### MD Anderson Cancer Center Postdoctoral Association Annual Postdoctoral Science Symposium Abstracts

The mission of the Annual Postdoctoral Science Symposium (APSS) is to provide a platform for talented postdoctoral fellows throughout the Texas Medical Center to present their work to a wider audience. The MD Anderson Postdoctoral Association convened its inaugural Annual Postdoctoral Science Symposium (APSS) on August 4, 2011.

The APSS provides a professional venue for postdoctoral scientists to develop, clarify, and refine their research as a result of formal reviews and critiques of faculty and other postdoctoral scientists. Additionally, attendees discuss current research on a broad range of subjects while promoting academic interactions and enrichment and developing new collaborations.

On The Second Least Distance Eigenvalue Of A Graph, 2019 College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang 830046, P.R.China.

#### On The Second Least Distance Eigenvalue Of A Graph, Xueyi Huang, Qiongxiang Huang, Lu Lu

##### Lu Lu

Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\partial_1(G)\ge\partial_2(G)\ge\cdots\ge\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, the connected graphs with @n􀀀1(G) at least the smallest root of $x^3=3x^2-11x-6 = 0$ are determined. Additionally, some non-isomorphic distance cospectral graphs are given.

Reverse Mathematics And Uniformity In Proofs Without Excluded Middle, 2019 Marshall University

#### Reverse Mathematics And Uniformity In Proofs Without Excluded Middle, Jeffry L. Hirst, Carl Mummert

##### Carl Mummert

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a \Pi^1_2 sentence of a certain form is provable using E-HAω along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical ...

Reverse Mathematics And Properties Of Finite Character, 2019 Marshall University

#### Reverse Mathematics And Properties Of Finite Character, Damir D. Dzhafarov, Carl Mummert

##### Carl Mummert

We study the reverse mathematics of the principle stating that,for every property of finite character, every set has a maximal subset satisfying the property. In the context of set theory, this variant of Tukey’s lemma is equivalent to the axiom of choice. We study its behavior in the context of second-order arithmetic, where it applies to sets of natural numbers only, and give a full characterization of its strength in terms of the quantifier structure of the formula defining the property. We then study the interaction between properties of finite character and finitary closure operators, and the interaction ...

Calculus I For Engineers (Ga Southern), 2019 Georgia Southern University

This Grants Collection for Calculus I for Engineers was created under a Round Eleven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Initial Proposal
• Final Report

The Multilinear Structure Of Relu Networks, 2019 Loyola Marymount University

#### The Multilinear Structure Of Relu Networks, Thomas Laurent

##### Thomas Laurent

We study the loss surface of neural networks equipped with a hinge loss criterion and ReLU or leaky ReLU nonlinearities. Any such network defines a piecewise multilinear form in parameter space. By appealing to harmonic analysis we show that all local minima of such network are non-differentiable, except for those minima that occur in a region of parameter space where the loss surface is perfectly flat. Non-differentiable minima are therefore not technicalities or pathologies; they are heart of the problem when investigating the loss of ReLU networks. As a consequence, we must employ techniques from nonsmooth analysis to study these ...

2019 Loyola Marymount University

#### Deep Linear Networks With Arbitrary Loss: All Local Minima Are Global, Thomas Laurent

##### Thomas Laurent

We consider deep linear networks with arbitrary convex differentiable loss. We provide a short and elementary proof of the fact that all local minima are global minima if the hidden layers are either 1) at least as wide as the input layer, or 2) at least as wide as the output layer. This result is the strongest possible in the following sense: If the loss is convex and Lipschitz but not differentiable then deep linear networks can have sub-optimal local minima.

Fake News And Stem, 2019 Colorado Technical University

#### Fake News And Stem, Vikki French

##### The Liminal: Interdisciplinary Journal of Technology in Education

Based on over ten years teaching mathematics, statistics and science in universities, communities colleges, and for-profit universities, I have witnessed how Fake News is part of these disciplines and how students can easily be misled into accepting pseudoscience. This is a report of my findings.

Modest Automorphisms Of Presburger Arithmetic, 2019 The Graduate Center, City University of New York

#### Modest Automorphisms Of Presburger Arithmetic, Simon Heller

##### All Dissertations, Theses, and Capstone Projects

It is interesting to consider whether a structure can be expanded by an automorphism so that one obtains a nice description of the expanded structure's first-order properties. In this dissertation, we study some such expansions of models of Presburger arithmetic. Building on some of the work of Harnik (1986) and Llewellyn-Jones (2001), in Chapter 2 we use a back-and-forth construction to obtain two automorphisms of sufficiently saturated models of Presburger arithmetic. These constructions are done first in the quotient of the Presburger structure by the integers (which is a divisible ordered abelian group with some added structure), and then ...

Zeta Functions Of Classical Groups And Class Two Nilpotent Groups, 2019 The Graduate Center, City University of New York

#### Zeta Functions Of Classical Groups And Class Two Nilpotent Groups, Fikreab Solomon Admasu

##### All Dissertations, Theses, and Capstone Projects

This thesis is concerned with zeta functions and generating series associated with two families of groups that are intimately connected with each other: classical groups and class two nilpotent groups. Indeed, the zeta functions of classical groups count some special subgroups in class two nilpotent groups.

In the first chapter, we provide new expressions for the zeta functions of symplectic groups and even orthogonal groups in terms of the cotype zeta function of the integer lattice. In his paper on universal $p$-adic zeta functions, J. Igusa computed explicit formulae for the zeta functions of classical algebraic groups. These zeta ...