Mathematics Commons^™

Increasing The Accuracy Of A Differential Solution Of A Differential Problem By The Method Of Concentrating A Sequence Of Networks, A Otarov

Karakalpak Scientific Journal

The method of increasing the accuracy of the difference solution of the differential problem based on the use of a thickened sequence of grids is presented in the article. The method is illustrated with the solution of a given boundary-value problem posed for an ordinary second-order differential equation.

Equivalent Constructions Of Cartan Pairs, Phung Thanh Tran

Math Theses

Feldman and Moore [4] introduce Cartan subalgebra of the von Neumann algebra M on a separable Hilbert space H from the natural subalgebra of M(R, sigma), the twisted algebra of matrices over the relation R on a Borel space (X, B, muy). They show that if M has a Cartan subalgebra A, then M is isomorphic to M(R, sigma) where A is the twisted algebra onto the diagonal subalgebra L^inf (X, muy). The relation R is unique to isomorphism and the orbit of the two-cohomology class on R in the torus T, which is the automorphism group of R, is …

Rossby Wave Breaking And Isentropic Stratosphere‐Troposphere Exchange During 1981–2015 In The Northern Hemisphere, Ping Jing, Swarnali Banerjee

Mathematics and Statistics: Faculty Publications and Other Works

To better understand the potential effects of climate change on atmospheric dynamics, this paper studies Rossby wave breaking and isentropic stratosphere‐troposphere exchange (STE) in the Northern Hemisphere between 320 and 380 K during 1981–2015 using the Modern‐Era Retrospective Analysis for Research and Application version 2 data. The isentropic STE is estimated using Contour Advection. Our results show that anticyclonic wave breaking events have become more frequent, especially in summer at higher isentropic surfaces, and cyclonic wave breaking events have become less frequent at 320 K. The anticyclonic wave breaking has shifted poleward in summer. The isentropic STE is found to …

Stranded Cellular Automaton And Weaving Products, Hao Yang

Mathematical Sciences Technical Reports (MSTR)

In order to analyze weaving products mathematically and find out valid weaving products, it is natural to relate them to Cellular Automaton. They are both generated based on specific rules and some initial conditions. Holden and Holden have created a Stranded Cellular Automaton that can represent common weaving and braiding products. Based on their previous findings, we were able to construct a Java program and analyze various aspects of the automaton they created. This paper will discuss the complexity of the Stranded Cellular Automaton, how to determine whether a weaving product holds together or not based on the automaton and …

A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Sooppy Nisar

Mathematics and Statistics Faculty Research & Creative Works

The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

A Symmetry-Based Explanation Of The Main Idea Behind Chubanov's Linear Programming Algorithm, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

Departmental Technical Reports (CS)

Many important real-life optimization problems can be described as optimizing a linear objective function under linear constraints -- i.e., as a linear programming problem. This problem is known to be not easy to solve. Reasonably natural algorithms -- such as iterative constraint satisfaction or simplex method -- often require exponential time. There exist efficient polynomial-time algorithms, but these algorithms are complicated and not very intuitive. Also, in contrast to many practical problems which can be computed faster by using parallel computers, linear programming has been proven to be the most difficult to parallelize. Recently, Sergei Chubanov proposed a modification of …

Marikina Flood Hazard Models Using Historical Data Of Water Level, Elvira P. De Lara-Tuprio, Evangeline P. Bautista, Reginaldo M. Marcelo, Ramil T. Bataller, Divino Angelo B. Esteban, Yvanne Paolo B. Yutuc

Mathematics Faculty Publications

In this paper, ten-year historical data of water levels recorded at Sto. Niño, Marikina station of MMDA-EFCOS were analysed and processed to determine the number of times per year (annual frequency) that critical levels of the Marikina River near the Sto. Niño station were reached and for how long (duration). Probability distributions for the annual frequency and duration were then fitted to the samples obtained. Monte Carlo simulation was applied in order to generate possible realizations of the random variables. Summary statistics were then obtained from the simulated values. Finally, backtesting using historical data of water levels after the period …

Semicontinuity Of Betweenness Functions, Paul Bankston, Aisling Mccluskey, Richard J. Smith

Mathematics, Statistics and Computer Science Faculty Research and Publications

A ternary relational structure〈X,[⋅,⋅,⋅]〉, interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior—within the hyperspace context—of the betweenness function {x,y}↦[x,y]. We investigate two broad scenarios: the first involves metric spaces and Menger's betweenness interpretation; the second deals with continua and the subcontinuum interpretation.

Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.

Elementary Set Theory, Richard P. Millspaugh

Open Educational Resources

This text is appropriate for a course that introduces undergraduates to proofs. The material includes elementary symbolic logic, logical arguments, basic set theory, functions and relations, the real number system, and an introduction to cardinality. The text is intended to be readable for sophomore and better freshmen majoring in mathematics.

The source files for the text can be found at https://github.com/RPMillspaugh/SetTheory

Use Of Standardized Patient Simulations To Assess Impact Of Motivational Interviewing Training On Social--Emotional Development, Suzanne M. Galal, Deepti Vyas, John Mayberry, Ed Rogan

College of the Pacific Faculty Articles

The objective of this study was to assess the impact of motivational interviewing (MI) training on students’ social–emotional development. Two simulations using standardized patients (SP) were conducted within a smoking cessation module. Students first completed a 4 h self-study module focused on smoking cessation tools and general counseling techniques. Faculty then administered a 15-item rubric focused on students’ self-assessment of their verbal/non-verbal communication, social–emotional competence and MI skills. Students then participated in a smoking cessation counseling session with an SP. SPs used the same rubric to assess student performance. Teaching assistants (TAs) observed and assessed the students using the same …

Tutte-Equivalent Matroids, Maria Margarita Rocha

Electronic Theses, Projects, and Dissertations

We begin by introducing matroids in the context of finite collections of vectors from a vector space over a specified field, where the notion of independence is linear independence. Then we will introduce the concept of a matroid invariant. Specifically, we will look at the Tutte polynomial, which is a well-defined two-variable invariant that can be used to determine differences and similarities between a collection of given matroids. The Tutte polynomial can tell us certain properties of a given matroid (such as the number of bases, independent sets, etc.) without the need to manually solve for them. Although the Tutte …

Cause And Consequence Of Aβ – Lipid Interactions In Alzheimer Disease Pathogenesis, Vijayaraghavan Rangachari, Dexter N. Dean, Pratip Rana, Ashuwin Vaidya, Preetam Ghosh

Department of Mathematics Faculty Scholarship and Creative Works

Self-templating propagation of protein aggregate conformations is increasingly becoming a significant factor in many neurological diseases. In Alzheimer disease (AD), intrinsically disordered amyloid-β (Aβ) peptides undergo aggregation that is sensitive to environmental conditions. High-molecular weight aggregates of Aβ that form insoluble fibrils are deposited as senile plaques in AD brains. However, low-molecular weight aggregates called soluble oligomers are known to be the primary toxic agents responsible for neuronal dysfunction. The aggregation process is highly stochastic involving both homotypic (Aβ-Aβ) and heterotypic (Aβ with interacting partners) interactions. Two of the important members of interacting partners are membrane lipids and surfactants, to …

Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, Bora Ferlengez

Dissertations, Theses, and Capstone Projects

In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures …

Linear Progress With Exponential Decay In Weakly Hyperbolic Groups, Matthew H. Sunderland

Dissertations, Theses, and Capstone Projects

A random walk w_n on a separable, geodesic hyperbolic metric space X converges to the boundary ∂X with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when (1) the step distribution has exponential tail and (2) the action on X is acylindrical. We extend exponential decay to the nonacylindrical case. We give an application to random Heegaard splittings.

The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

Dissertations, Theses, and Capstone Projects

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in …

Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag

Dissertations, Theses, and Capstone Projects

The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and represent these …

A Derivation Of Fluidic Maxwell-Proca Equations For Electrodynamics Of Superconductors & Its Implication To Chiral Cosmology Model, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

Mario Liu described a hydrodynamic Maxwell equations [3] and, also discussed potential implications of these new approaches to superconductors which were made after Tajmar’s paper [4]. In this paper, we present for the first time a derivation of fluidic Maxwell-Proca equations. The name of fluidic Maxwell-Proca is proposed because the equations were based on modifying Maxwell-Proca and Hirsch’s theory of electrodynamics of superconductor. It is hoped that this paper may stimulate further investigations and experiments in superconductor. It may be expected to have some impact to cosmology modeling too, for instance we consider a hypothetical argument that photon mass can …

Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, Trevor Pentzien, Bhanwar L. Puniya, Tomáš Helikar, Mihaela Teodora Matache

Mathematics Faculty Publications

A variety of biological networks can bemodeled as logical or Boolean networks. However, a simplification of the reality to binary states of the nodes does not ease the difficulty of analyzing the dynamics of large, complex networks, such as signal transduction networks, due to the exponential dependence of the state space on the number of nodes. This paper considers a recently introduced method for finding a fairly small subnetwork, representing a collection of nodes that determine the states of most other nodes with a reasonable level of entropy. The subnetwork contains the most determinative nodes that yield the highest information …

On The Convergence Of A Heuristic Parameter Choice Rule For Tikhonov Regularization, Mark Gockenbach, Elaheh Gorgin

Department of Mathematical Sciences Publications

Multiplicative regularization solves a linear inverse problem by minimizing the product of the norm of the data misfit and the norm of the solution. This technique is related to Tikhonov regularization with the parameter chosen to make the data misfit and regularization terms (of the Tikhonov objective function) equal. This suggests a heuristic parameter choice method, equivalent to the rule previously proposed by Reginska. Reginska's rule is well defined provided the data is sufficiently close to exact data and does not lie in the range of the operator. If a sufficiently large portion of the data error lies outside the …

Math Active Learning Lab: Math 92 Notebook, Michele Iiams, Gwennie Byron

Open Educational Resources

This course notebook has been designed for students of Math 92 (Algebra Prep II) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

• Topics in the Notebook are organized by weekly learning module.
• Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
• Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
• Completed Notebook is an invaluable tool when studying for exams.

Predicting Impacts Of Chemicals From Organisms To Ecosystem Service Delivery: A Case Study Of Endocrine Disruptor Effects On Trout, Valery E. Forbes, Steve Railsback, Chiara Accolla, Bjorn Birnir, Randall J.F. Bruins, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette I. Jager, Andrew Kanarek, Robert Pastorok, Richard Rebarber, Pernille Thorbek, Chris J. Salice

Department of Mathematics: Faculty Publications

We demonstrate how mechanistic modeling can be used to predict whether and how biological responses to chemicals at (sub)organismal levels in model species (i.e., what we typically measure) translate into impacts on ecosystem service delivery (i.e., what we care about). We consider a hypothetical case study of two species of trout, brown trout (Salmo trutta; BT) and greenback cutthroat trout (Oncorhynchus clarkii stomias; GCT). These hypothetical populations live in a high-altitude river system and are exposed to human-derived estrogen (17α‑ethinyl estradiol, EE2), which is the bioactive estrogen in many contraceptives. We use the individual based model in STREAM …

Genome-Wide Association Study For Variants That Modulate Relationships Between Cerebrospinal Fluid Amyloid-Beta 42, Tau, And P-Tau Levels, Taylor J. Maxwell, Chris Corcoran, Jorge L. Del-Aguila, John P. Budde, Yuetiva Deming, Carlos Cruchaga, Alison M. Goate, John S. K. Kauwe, Alzheimer's Disease Neuroimaging Initiative

Mathematics and Statistics Faculty Publications

Background: A relationship quantitative trait locus exists when the correlation between multiple traits varies by genotype for that locus. Relationship quantitative trait loci (rQTL) are often involved in gene-by-gene (G×G) interactions or gene-by-environmental interactions, making them a powerful tool for detecting G×G.

Methods: We performed genome-wide association studies to identify rQTL between tau and Aβ42 and ptau and Aβ42 with over 3000 individuals using age, gender, series, APOE ε2, APOE ε4, and two principal components for population structure as covariates. Each significant rQTL was separately screened for interactions with other loci for each trait in the rQTL model. Parametric bootstrapping …

Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that reviews …

When Does The Bombieri–Vinogradov Theorem Hold For A Given Multiplicative Function?, Andrew Granville, Xuancheng Shao

Mathematics Faculty Publications

Let f and g be 1-bounded multiplicative functions for which f ✻ g = 1_.=1. The Bombieri–Vinogradov theorem holds for both f and g if and only if the Siegel–Walfisz criterion holds for both f and g, and the Bombieri–Vinogradov theorem holds for f restricted to the primes.

Study On The Efficiency Of China’S Main River Ports Based On Dea Model, Yunwu Cao

World Maritime University Dissertations

No abstract provided.

Research On The Route Optimization Of Huzhou Port’S Outbound Container, Bo Zhang

World Maritime University Dissertations

No abstract provided.

Analysis Of Shanghai Aviation Hub Logistics Competitiveness, Tuo Chen

World Maritime University Dissertations

No abstract provided.

The Impact Of Wti And The Ordering Of Crude Tankers On Tanker Spot Freight Rate, Jiajia Xu

World Maritime University Dissertations

No abstract provided.

Horizontal Integration In The Port Industry In China Challenges And Outlook, Jiren Chen

World Maritime University Dissertations

No abstract provided.