Mathematics Commons^™

On The Menger And Almost Menger Properties In Locales, Tilahun Bayih, Themba Dube, Oghenetega Ighedo

Mathematics, Physics, and Computer Science Faculty Articles and Research

The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober T_D-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered.

Sum Of Squares With Q-Series, Gosper’S Q- Trigonometry, An New Identities Via An Extended Bailey Transform, Zina Al Houchan

Theses

This report is concerned about q-series and some of their applications. Firstly, Jacobi’s q-series proof for Legendre’s theorem on sums of four squares will be presented. By way of comparison, the classical approach of this result will be also discussed. Secondly, Gosper’s q-trigonometry will be introduced using Jacobi’s theta functions and the theory of elliptic functions shall be employed to confirm one of Gosper’s conjectures. As an application, a proof for Fermat’s theorem on the sums of squares will be provided. Thirdly, an extended version of Bailey’s transform will be established and as a consequence, a variety of new q-series …

The Q-Gauss Product, Q-Trigonometry Via Landen-Like Identities, And Positive Alternating Q-Series, Sarah Abo Touk

Theses

The object of this report is q-series and their relationship with certain special functions. Firstly, Jackson’s q-analogue of the Euler gamma function is introduced and a q-analogue for a famous formula of Gauss on products of the gamma function will be presented. Secondly, Jacobi’s theta functions will be discussed in details and new Landenlike half argument formulas will be established. As an application, q-trigonometric formulas shall be derived and a new proof for a well-known q-series relation of Jacobi will be given. Thirdly, an extended Bailey transform will be presented and a variety of new q-series will be deduced as …

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Looking Back At Quantitative Reasoning, William Briggs

Numeracy

A teacher looks back on three decades of teaching, pondering, and writing about quantitative reasoning (QR) and shares a few lessons learned. The skills that we teach in QR courses are more important than ever in providing students with a sense of civic virtue: the ability to be engaged and informed citizens in an increasingly complex and quantitative world.

Food Security As A Factor Of Sustainable Development Of The Country, Timur Nurimbetov

Karakalpak Scientific Journal

The article examines the state of the food market and the trends in ensuring the country’s food security. The article also analyzes the regional characteristics of the agricultural products market in the Republic of Karakalpakstan. The saturation level of regional food markets has been studied. Scientific conclusions and practical recommendations on the supply of food to the population have been made.

Influence Of Laterial State Of Pair Impurity Complex On Recombination Processes In Semiconductors, L Yu Leyderman, R A. Ayukhanov, Abat Uteniyazov, E S. Esenbaeva, Sh X. Annayeva

Karakalpak Scientific Journal

The paper analyzes the question of the possible influence of the lateral state of a paired impurity complex on the recombination processes. It is shown that the lateral state of the paired impurity complex does not affect the recombination processes of nonequilibrium carriers - they go through that component of the impurity complex that exchanges carriers with both bands (in this particular case, through the component). The second component of the complex () can apparently play some role in the processes of carrier attachment.

Estimation Of Location Parameter Within Pre-Specified Error Bound With Second-Order Efficient Two-Stage Procedure, Bhargab Chattopadhyay, Swarnali Banerjee

Mathematics and Statistics: Faculty Publications and Other Works

This paper develops a general approach for constructing a confidence interval for a parameter of interest with a specified confidence coefficient and a specified width. This is done assuming known a positive lower bound for the unknown nuisance parameter and independence of suitable statistics. Under mild conditions, we develop a modified two-stage procedure which enjoys attractive optimality properties including a second-order efficiency property and asymptotic consistency property. We extend this work for finding a confidence interval for the location parameter of the inverse Gaussian distribution. As an illustration, we developed a modified mean absolute deviation-based procedure in the supplementary section …

Organization Of Compact Spinning Technology In Textile Clusters, Baxtiyar Aralbaevich Paluanov, Abdimalik Pirmatovich Pirmatov

Karakalpak Scientific Journal

The article proposes a system of continuous supply of raw cotton in continuous spinning technology and methods of maximizing the preservation of the natural properties of the fiber and obtaining high-quality yarn.

Lie Groups And Euler-Bernoulli Beam Equation, Medeu Amangeldi

Theses and Dissertations

Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.

Hb-Pls: A Statistical Method For Identifying Biological Process Or Pathway Regulators By Integrating Huber Loss And Berhu Penalty With Partial Least Squares Regression, Wenping Deng, Kui Zhang, Cheng He, Sanzhen Liu, Hairong Wei

Michigan Tech Publications, Part 1

Gene expression data features high dimensionality, multicollinearity, and non-Gaussian distribution noise, posing hurdles for identification of true regulatory genes controlling a biological process or pathway. In this study, we integrated the Huber loss function and the Berhu penalty (HB) into partial least squares (PLS) framework to deal with the high dimension and multicollinearity property of gene expression data, and developed a new method called HB-PLS regression to model the relationships between regulatory genes and pathway genes. To solve the Huber-Berhu optimization problem, an accelerated proximal gradient descent algorithm with at least 10 times faster than the general convex optimization solver …

Towards Constructing Vertex Algebroids, Nicholas J. Klecki

Theses and Dissertations

The notion of vertex algebroids were introduced in the late 1990's as a crucial tool for the study of chiral differential operators and chiral de Rham complex. Vertex algebroids play vital role in the study of N-graded vertex algebra. Also, they have deep connection with representation theory of Leibniz algebras. However, the classification of irreducible modules of vertex algebroids is not completed.

The aim of this thesis is to investigate the possibility of using the simple Lie algebra G_2 and its irreducible modules to construct vertex A-algebroids B that contain G_2 as their Levi factor. Under very mild and natural …

Heterogeneous Bacterial Swarms With Mixed Lengths, Shlomit Peled, Shawn D. Ryan, Sebastian Heidenreich, Markus Baer, Gil Ariel, Avraham Be'er

Mathematics and Statistics Faculty Publications

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming …

Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert

Mathematics Faculty Publications

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating …

Entropic Dynamics Of Networks, Felipe Xavier Costa, Pedro Pessoa

Northeast Journal of Complex Systems (NEJCS)

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.

Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt

Northeast Journal of Complex Systems (NEJCS)

The presence of hierarchy in many real-world networks is not yet fully understood. We observe that complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarse-grain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are …

Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs

UNO Student Research and Creative Activity Fair

Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections.

In …

Embedding Factorizations, Anna Johnsen

Theses and Dissertations

Let $V$ be a set of $n$ vertices for some $n\in\mathbb{N}$ and let $E$ be a collection of $h$-subsets of $V$. Then $\mathscr G = (V,E)$ is an $h$-unifrom hypergraph and we refer to $V$ as its vertex set and to $E$ as its edge set. We say that $\mathscr G$ is complete and denote it by $K_n^h$ if every $h$-subset of $V$ is contained in $E$. If every edge in $E$ is repeated $\lambda$ times, we say $G$ is $\lambda$-fold. Specifically, $\lambda K_n^h$ is the complete $\lambda$-fold $n$-vertex $h$-uniform hypergraph with an edge set containing $\lambda$ copies of every …

The Conditional Strong Matching Preclusion Of Augmented Cubes, Mohamad Abdallah, Eddie Cheng

Theory & Applications of Graphs

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube AQ_n, which is a variation of the hypercube Q_n that possesses favorable properties.

Characterizing 2-Trees Relative To Chordal And Series-Parallel Graphs, Terry A. Mckee

Theory & Applications of Graphs

The 2-connected 2-tree graphs are defined as being constructible from a single 3-cycle by recursively appending new degree-2 vertices so as to form 3-cycles that have unique edges in common with the existing graph. Such 2-trees can be characterized both as the edge-minimal chordal graphs and also as the edge-maximal series-parallel graphs. These are also precisely the 2-connected graphs that are simultaneously chordal and series-parallel, where these latter two better-known types of graphs have themselves been both characterized and applied in numerous ways that are unmotivated by their interaction with 2-trees and with each other.

Toward providing such motivation, the …