Mathematics Commons^™

Algorithms For Numerical Implementation Of The Shooting Method Of Solving Boundary Value Problems For Second Order Differential Equations, A Otarov

Karakalpak Scientific Journal

In the article algorithms of numerical realization of a shooting method decisions of marginal problems for nonlinear ordinary differential equations of the second order are under construction.

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.

A Survey On Network Security-Related Data Collection Technologies, Huaqing Lin, Zheng Yan, Yu Chen, Lifang Zhang

Faculty Publications, Information Systems & Technology

Security threats and economic loss caused by network attacks, intrusions, and vulnerabilities have motivated intensive studies on network security. Normally, data collected in a network system can reflect or can be used to detect security threats. We define these data as network security-related data. Studying and analyzing security-related data can help detect network attacks and intrusions, thus making it possible to further measure the security level of the whole network system. Obviously, the first step in detecting network attacks and intrusions is to collect security-related data. However, in the context of big data and 5G, there exist a number of …

Why Zipf's Law: A Symmetry-Based Explanation, Daniel Cervantes, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have probability distributions for which, for large values of the corresponding quantity x, the probability density has the form ρ(x) ~ x^−αfor some α > 0. While, in principle, we have laws corresponding to different α, most frequently, we encounter situations -- first described by Zipf for linguistics -- when α is close to 1. The fact that Zipf's has appeared frequently in many different situations seems to indicate that there must be some fundamental reason behind this law. In this paper, we provide a possible explanation.

How To Explain The Results Of The Richard Thaler's 1997 Financial Times Contest, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In 1997, by using a letter published in Financial Times, Richard H. Thaler, the 2017 Nobel Prize winner in Economics, performed the following experiment: he asked readers to submit numbers from 0 to 100, so that the person whose number is the closest to 2/3 of the average will be the winner. An intuitive answer is to submit 2/3 of the average (50), i.e., 33 1/3. A logical answer, as can be explained, is to submit 0. The actual winning submission was -- depending on how we count -- 12 or 13. In this paper, we propose a possible explanation …

Mathemagics, Arthur Benjamin

Dalrymple Lecture Series

Dr. Arthur Benjamin is the Smallwood Family Professor of Mathematics at Harvey Mudd College in Claremont, California. He is also a professional magician, and in his entertaining and fast-paced performance, Dr. Benjamin will demonstrate how to mentally add and multiply numbers faster than a calculator, how to figure out the day of the week of any date in history, and other amazing feats of mind.

Better Ate Than Never: Reducing Wasted Food, Mia Ye '19, Katie Lu '19, Kevin Mikos '19, Aryan Walia '19

Distinguished Student Work

Food waste in modern society is a problem which is quickly gaining traction. The Environmental Protection Agency (EPA) estimates that more food reaches landfills than any single material in the trash. This wastes food resources, while 42 million Americans are food-insecure and in need. In order to prevent food waste from reaching landfills and incinerators, we must scrutinize the sources of waste and take novel measures to make use of all edible food. In this paper, we examine three main problems using mathematical modeling.

First, we created a model to see if food waste could be used to feed the …

The Generalized Hypergeometric Difference Equation, Martin Bohner, Tom Cuchta

Mathematics Faculty Research

A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.

Design And Analysis Of Graph-Based Codes Using Algebraic Lifts And Decoding Networks, Allison Beemer

Department of Mathematics: Dissertations, Theses, and Student Research

Error-correcting codes seek to address the problem of transmitting information efficiently and reliably across noisy channels. Among the most competitive codes developed in the last 70 years are low-density parity-check (LDPC) codes, a class of codes whose structure may be represented by sparse bipartite graphs. In addition to having the potential to be capacity-approaching, LDPC codes offer the significant practical advantage of low-complexity graph-based decoding algorithms. Graphical substructures called trapping sets, absorbing sets, and stopping sets characterize failure of these algorithms at high signal-to-noise ratios. This dissertation focuses on code design for and analysis of iterative graph-based message-passing decoders. The …

Minimizing The Number Of Independent Sets In Triangle-Free Regular Graphs, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics Faculty Scholarship and Creative Works

Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin–Tetali, and Zhao) that the independence polynomial of a d-regular graph is maximized by disjoint copies of Kd,d. Their proof uses linear programming bounds on the distribution of a cleverly chosen random variable. In this paper, we use this method to give lower bounds on the independence polynomial of regular graphs. We also give a new bound on the number of independent sets in triangle-free cubic graphs.

Progenitors, Symmetric Presentations And Constructions, Diana Aguirre

Electronic Theses, Projects, and Dissertations

Abstract

In this project, we searched for new constructions and symmetric presentations of important groups, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. My target nonabelian simple groups included sporadic groups, linear groups, and alternating groups. In addition, we discovered finite groups as homomorphic images of progenitors and proved some of their isomorphism type and original symmetric presentations. In this thesis we found original symmeric presentations of M12, J1 and the simplectic groups S(4,4) and S(3,4) on various con- trol groups. Using the technique of double coset enumeration we constucted J2 as a …

Monomial Progenitors And Related Topics, Madai Obaid Alnominy

Electronic Theses, Projects, and Dissertations

The main objective of this project is to find the original symmetric presentations of some very important finite groups and to give our constructions of some of these groups. We have found the Mathieu sporadic group M₁₁, HS × D₅, where HS is the sporadic group Higman-Sim group, the projective special unitary group U(3; 5) and the projective special linear group L₂(149) as homomorphic images of the monomial progenitors 11*⁴ :_m (5 :4), 5*⁶ :_m S₅ and 149*² :_m D₃₇. We have also discovered 2 …

Progenitors, Symmetric Presentations, And Related Topics, Joana Viridiana Luna

Electronic Theses, Projects, and Dissertations

Abstract

A progenitor developed by Robert T. Curtis is a type of infinite groups formed by the semi-direct product of a free group m∗n and a transitive permutation group of degree n. To produce finite homomorphic images we had to add relations to the progenitor of the form 2∗n : N. In this thesis we have investigated several permutations progenitors and monomials, 2∗12 : S4, 2∗12 : S4 × 2, 2∗13 : (13 : 4), 2∗30 : ((2• : 3) : 5), 2∗13 :13,2∗13 :(13:2),2∗13 :(13:S3),53∗2 :m (13:4),7∗8 :m (32 :8),and 53∗4 :m (13 : 4). We have discovered that …

Partitioning The Effects Of Eco-Evolutionary Feedbacks On Community Stability, Swati Patel, Michael H. Cortez, Sebastian J. Schreiber

Mathematics and Statistics Faculty Publications

A fundamental challenge in ecology continues to be identifying mechanisms that stabilize community dynamics. By altering the interactions within a community, eco-evolutionary feedbacks may play a role in community stability. Indeed, recent empirical and theoretical studies demonstrate that these feedbacks can stabilize or destabilize communities and, moreover, that this sometimes depends on the relative rate of ecological to evolutionary processes. So far, theory on how eco-evolutionary feedbacks impact stability exists only for a few special cases. In our work, we develop a general theory for determining the effects of eco-evolutionary feedbacks on stability in communities with an arbitrary number of …

Indicators For Early Assessment Of Palliative Care In Lung Cancer Patients: A Population Study Using Linked Health Data, Maria Kelly, Katie M. O'Brien, Michael Lucey, Kerri Clough-Gorr, Ailish Hannigan

Department of Mathematics Publications

Analysing linked, routinely collected data may be useful to identify characteristics of patients with suspected lung cancer who could benefit from early assessment for palliative care. The aim of this study was to compare characteristics of newly diagnosed lung cancer patients dying within 30 days of diagnosis (short term survivors) with those surviving more than 30 days. To identify indicators for early palliative care assessment we distinguished between characteristics available at diagnosis (age, gender, smoking status, marital status, comorbid disease, admission type, tumour stage and histology) from those available post diagnosis. A second aim was to examine the association between …

The Integral Formula For First-Order Elliptic Systems With Constant Coefficients In An Unbounded Domain, F.R. Tursunov

Scientific Journal of Samarkand University

In this note we present a formula for the solutions of systems of first -order differential equations of elliptic type of a special class in an unbounded domain.

On The Some Generalizations And Improvements Of The Best Polynomial Approximations Of Functions Of Many Real Variables, A. Khatamov

Scientific Journal of Samarkand University

The paper is devoted to some generalizations and improvements of results obtained in the paper [1] of the best joint polynomial approximations in uniform and integral metrics on a given bounded closed convex domain of the functions of many real variables (FMRV) from the seminormalized Sobolev space with last derivative of integrable on nonempty intersections of each straight line with this domain.

Preserver Problems On Matrices, Zejun Huang

Mathematics Colloquium Series

Preserver problems on matrices concern the characterization of linear or nonlinear maps or operators on matrices that preserve properties of the space of matrices or leave certain functions, subsets, and relations invariant. In this talk, I will present some results on both linear and nonlinear preserver problems on matrices.

The S-Multiplicity Function Of 2x2-Determinantal Rings, Lance Edward Miller, William D. Taylor

Mathematical Sciences Faculty Research

This article generalizes joint work of the first author and I. Swanson to the s-multiplicity recently introduced by the second author. For k a field and X=[xi,j] a m×n-matrix of variables, we utilize Gröbner bases to give a closed form the length λ(k[X]/(I2(X)+m⌈sq⌉+m[q])) where s∈Z[p−1], q is a sufficiently large power of p, and m is the homogeneous maximal ideal of k[X]. This shows this length is always eventually a {\it polynomial} function of q for all s.

Examples Of Finite Free Complexes Of Small Rank And Small Homology, Srikanth B. Iyengar, Mark E. Walker

Department of Mathematics: Faculty Publications

In this paper we construct counterexamples to five related conjectures concerning the rank an homology of finite free complexes over commuatitive noetherian rings, and, in particular, over group algebras of elementary abelian groups.