Mathematics Commons^™

Existence And Multiplicity For Positive Solutions Of A System Of First Order Differential Equations With Multipoint And Integral Boundary Conditions, Le Thi Phuong Ngoc, Nguyen Thanh Long

Turkish Journal of Mathematics

In this paper, we state and prove theorems related to the existence and multiplicity for positive solutions of a system of first order differential equations with multipoint and integral boundary conditions. The main tool is the fixed point theory. In order to illustrate the main results, we present some examples.

Biharmonic Pnmcv Submanifolds In Euclidean 5-Space, Rüya Şen, Nuretti̇n Cenk Turgay

Turkish Journal of Mathematics

In this article, we study 3-dimensional biconservative and biharmonic submanifolds of $\mathbb{E}^5$ with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into $\mathbb{E}^5$ can be determined intrinsically. Then, we complete the proof of Chen's biharmonic conjecture for PNMCV submanifolds of $\mathbb{E}^5$.

Duality Approach To The Regularity Problems For The Navier-Stokes Equations, Grigory Seregin

Turkish Journal of Mathematics

In this note, we describe a way to study local regularity of a weak solution to the Navier-Stokes equations, satisfying the simplest scale-invariant restriction, with the help of zooming and duality approach to the corresponding mild bounded ancient solution.

Three-Dimensional Homogeneous Contact Metric Manifold With Weakly $\Eta$-Einstein Structures, Sun Hyang Chun, Yunhee Euh

Turkish Journal of Mathematics

In this paper, we determine the geometric structures of 3-dimensional weakly $\eta$-Einstein almost contact metric manifolds and classify 3-dimensional weakly $\eta$-Einstein simply connected homogeneous contact metric manifolds based on Perrone's classification.

Asymptotic Behaviour Of Hyperbolic Partial Differential Equations, Shi-Zhuo Looi

Theses and Dissertations--Mathematics

We investigate the asymptotic behaviour of solutions to a range of linear and nonlinear hyperbolic equations on asymptotically flat spacetimes. We develop a comprehensive framework for the analysis of pointwise decay of linear and nonlinear wave equations on asymptotically flat manifolds of three space dimensions that are allowed to be time-varying or nonstationary, including quasilinear wave equations. The Minkowski space and time-varying perturbations thereof are included among these spacetimes. A result on scattering for a nonlinear wave equation with finite-energy solutions on nonstationary spacetimes is presented. This work was motivated in part by the investigation of more precise asymptotic behaviour …

An Inverse Problem Of Finding A Time-Dependent Coefficient In A Fractional Diffusion Equation, Durdimurod Durdiev, Dilshod Durdiev

Turkish Journal of Mathematics

This article is concerned with the study of unique solvability of an inverse coefficient problem of determining the coefficient at the lower term of a fractional diffusion equation. The direct problem is the initial-boundary problem for this equation with usual initial and homogeneous Dirichlet conditions. To determine the unknown coefficient, an overdetermination condition is given as the Neumann condition at the left end of the spatial interval. The theorems of existence and uniqueness of inverse problem solution are obtained. Furthermore, we propose a numerical algorithm based on a finite-difference scheme to accurately compute the inverse problem of simultaneously determining a …

Why Fractional Fuzzy, Mehran Mazandarani, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situation, control experts can only formulate their experience by using imprecise ("fuzzy") words from natural language. To incorporate this knowledge in automatic controllers, Lotfi Zadeh came up with a methodology that translate the informal expert statements into a precise control strategy. This methodology -- and its following modifications -- is known as fuzzy control. Fuzzy control often leads to a reasonable control -- and we can get an even better control results by tuning the resulting control strategy on the actual system. There are many parameters that can be changes during tuning, so tuning usually is rather …

From Mirrors To Wallpapers: A Virtual Math Circle Module On Symmetry, Nicole A. Sullivant, Christina L. Duron, Douglas T. Pfeffer

Journal of Math Circles

Symmetry is a natural property that children see in their everyday lives; it also has deep mathematical connections to areas like tiling and objects like wallpaper groups. The Tucson Math Circle (TMC) presents a 7-part module on symmetry that starts with reflective symmetry and culminates in the deconstruction of wallpapers into their ‘generating tiles’. This module utilizes a scaffolded, hands-on approach to cover old and new mathematical topics with various interactive activities; all activities are made available through free web-based platforms. In this paper, we provide lesson plans for the various activities used, and discuss their online implementation with Zoom, …

A Characterization Of Two-Dimensional Buchsbaum Matching Complexes, Bennet Goeckner, Fran Herr, Legrand Jones, Rowan Rowlands

Mathematics: Faculty Scholarship

The matching complex M (G) of a graph G is the set of all matchings in G. A

Buchsbaum simplicial complex is a generalization of both a homology manifold and

a Cohen–Macaulay complex. We give a complete characterization of the graphs G

for which M (G) is a two-dimensional Buchsbaum complex. As an intermediate step,

we determine which graphs have matching complexes that are themselves connected

graphs.

Lnl Polycategories And Doctrines Of Linear Logic, Michael Shulman

Mathematics: Faculty Scholarship

We define and study LNL polycategories, which abstract the judgmental structure of classical linear logic with exponentials. Many existing structures can be represented as LNL polycategories, including LNL adjunctions, linear exponential comonads, LNL multicategories, IL-indexed categories, linearly distributive categories with storage, commutative and strong monads, CBPV-structures, models of polarized calculi, Freyd-categories, and skew multicategories, as well as ordinary cartesian, symmetric, and planar multicategories and monoidal categories, symmetric polycategories, and linearly distributive and *-autonomous categories. To study such classes of structures uniformly, we define a notion of LNL doctrine, such that each of these classes of structures can be identified with …

Supplementary Material For The Article “Using Generative Ai For Literature Searches And Scholarly Writing: Is The Integrity Of The Scientific Discourse In Jeopardy?", Paul G. Schmidt, Amnon J. Meir

Mathematics Research

Supplementing our paper "Using Generative AI for Literature Searches and Scholarly Writing: Is the Integrity of the Scientific Discourse in Jeopardy?" [1], we furnish and analyze the evidence of AI-induced contamination of the scientific literature that we alluded to in Section 2 of the paper (Section 1 below). We also provide a comprehensive list of references, encompassing the titles in the bibliography of [1], the titles cited in [1], but not included in the bibliography, and the titles cited in Section 1 below, but not in [1]. Further, we summarize two specific conversations with ChatGPT, corroborating the observations in Section …

The Inequalities On Dual Numbers And Their Topological Structures, Buşra Aktaş, Olgun Durmaz, Hali̇t Gündoğan

Turkish Journal of Mathematics

Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings.

Metallic-Like Structures And Metallic-Like Maps, Adelina Manea

Turkish Journal of Mathematics

The metallic-like $(a,b)$-manifold is a manifold endowed with a polynomial structure of second degree which unifies the almost product, complex structures and includes metallic structures. We introduce the metallic-like maps between metallic-like $(a,b)$-manifolds and we give a criterion for the nonconstancy of these maps. We prove that an almost contact structure on a Riemannian manifold induces a metallic-like $(a,b)$-structure and we give an example of a nonconstant metallic-like endomorphism of a particular almost contact manifold.

Another Angle On Perspective, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Application Of Mixture Models For Doubly Inflated Count Data, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

In health and social science and other fields where count data analysis is important, zero-inflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero- and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation–maximization (EM) algorithm to obtain the parameter …

Generalized Sparse Bayesian Learning And Application To Image Reconstruction, Jan Glaubitz, Anne Gelb, Guohui Song

Mathematics & Statistics Faculty Publications

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the recovery is limited to a point estimate, it is impossible to quantify the uncertainty, which is often desirable. Due to these inherent limitations, a sparse Bayesian learning approach is sometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learning assumes that some linear transformation of the unknown is sparse. However, most of the methods developed are …

Ellipses, Leaves, And Solar Crescents, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Not Your Typical Tower Of Sauron: Solutions For Fermi Questions, September 2023, John Adam

Mathematics & Statistics Faculty Publications

The picture is of the tapering Chester Shot Tower, located in Chester, England. It was built in 1799 for the manufacture of lead shot for use in the Napoleonic Wars. Molten lead was poured through a sieve at the top of the tower, with the tiny droplets forming perfect spheres during the fall; these were then cooled in a vat of water at the base. This process was less labor-intensive than an earlier method using molds. It is the oldest of the three remaining shot towers in the UK. Using the parked van at the base, estimate (i) the height …

"Density" Of Light And Pi, John Adam

Mathematics & Statistics Faculty Publications

Question 1: What is the linear “density” of the spectral range on the ceiling? The crown molding is common for an older (circa 1925) house.

Question 2: The glass shown is a standard 16-oz. water glass engraved with many digits of pi. (The dimensions appear somewhat distorted because of the camera angle chosen to enhance the contrast of the numerals against the dark background.)

Shrub Sphericity, John Adam

Mathematics & Statistics Faculty Publications

Question 1: a. Show that α = 4.836, and hence find the sphericity index for (i) a cube and (ii) two identical "kissing" spheres, i.e., spheres in tangential contact. b. Estimate your sphericity index.

Question 2: Estimate χ for the yucca plant in the picture. It is about 1 m in diameter.

Quasisymmetric Functions Distinguishing Trees, Jean-Christophe Aval, Karimatou Djenabou, Peter R. W. Mcnamara

Faculty Journal Articles

A famous conjecture of Stanley states that his chromatic symmetric function distinguishes trees. As a quasisymmetric analogue, we conjecture that the chromatic quasisymmetric function of Shareshian and Wachs and of Ellzey distinguishes directed trees. This latter conjecture would be implied by an affirmative answer to a question of Hasebe and Tsujie about the P-partition enumerator distinguishing posets whose Hasse diagrams are trees. They proved the case of rooted trees and our results include a generalization of their result.

$\Ast$-Semiclean Rings, Shefali Gupta, Dinesh Udar

Turkish Journal of Mathematics

A ring $R$ is called semiclean if every element of $R$ can be expressed as sum of a periodic element and a unit. In this paper, we introduce a new class of ring, which is the $\ast$-version of the semiclean ring, i.e. the $\ast$-semiclean ring. A $\ast$-ring is $\ast$-semiclean if each element is a sum of a $\ast$-periodic element and a unit. The term $\ast$-semiclean is a stronger notion than semiclean. In this paper, many properties of $\ast$-semiclean rings are discussed. It is proved that if $p \in P(R)$ such that $pRp$ and $(1-p)R(1-p)$ are $\ast$-semiclean rings, then $R$ is …

Higher Spanier Groups, Johnny Aceti

West Chester University Master’s Theses

When non-trivial local structures are present in a topological space X, a common ap- proach to characterizing the isomorphism type of the n-th homotopy group πn(X, x0) is to consider the image of πn(X, x0) in the n-th ˇCech homotopy group ˇπn(X, x0) under the canonical homomorphism Ψn : πn(X, x0) → ˇπn(X, x0). The subgroup ker Ψn is the obstruc- tion to this tactic as it consists of precisely those elements of πn(X, x0), which cannont be detected by polyhedral approximations to X. In this paper we present a definition of higher dimensional analouges of Thick Spanier groups use …

An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …

Colorful Graph Associahedra, Satyan L. Devadoss, Mia Smith

Mathematics: Faculty Scholarship

Given a graph G, the graph associahedron is a simple convex polytope whose face poset is based on the connected subgraphs of G. With the additional assignment of a color palette, we define the colorful graph associahedron, show it to be a collection of simple abstract polytopes, and explore its properties.

Broadening Views Of Mathematical Creativity: Inclusion Of The Undergraduate Student Perspective, Emily Cilli-Turner, V. Rani Satyam, Miloš Savić, Gail Tang, Houssein El Turkey, Gulden Karakok

Mathematics: Faculty Scholarship

Numerous conceptions of creativity exist in the literature; yet these are commonly based on the perspectives of professional mathematicians. Including students’ perspectives in creativity is crucial not only for a more robust picture of what it means to be creative but also to combat damaging dominant narratives about who can be creative. We examined calculus students’ views of mathematical creativity, a group not often considered in the creativity literature, to broaden future considerations of creativity. Interviews with N=55 calculus students across various institutions were conducted. Results show six emergent wide-ranging themes of these students’ creativity views: actions and attitudes, application, …

Stochastic Optimization To Reduce Aircraft Taxi-In Time At Igia, New Delhi, Rajib Das, Saileswar Ghosh, Rajendra Desai, Pijus Kanti Bhuin, Stuti Agarwal

International Journal of Aviation, Aeronautics, and Aerospace

Since there is an uncertainty in the arrival times of flights, pre-scheduled allocation of runways and stands and the subsequent first-come-first-served treatment results in a sub-optimal allocation of runways and stands, this is the prime reason for the unusual delays in taxi-in times at IGIA, New Delhi.

We simulated the arrival pattern of aircraft and utilized stochastic optimization to arrive at the best runway-stands allocation for a day. Optimization is done using a GRG Non-Linear algorithm in the Frontline Systems Analytic Solver platform. We applied this model to eight representative scenarios of two different days. Our results show that without …

Bicategorical Traces And Cotraces, Justin Barhite

Theses and Dissertations--Mathematics

Familiar constructions like the trace of a matrix and the Euler characteristic of a closed smooth manifold are generalized by a notion of trace of an endomorphism of a dualizable object in a bicategory equipped with a piece of additional structure called a shadow functor. Another example of this bicategorical trace, in the form of maps between Hochschild homology of bimodules, appears in a 1987 paper by Joseph Lipman, alongside a more mysterious ”cotrace” map involving Hochschild cohomology. Putting this cotrace on the same category-theoretic footing as the trace has led us to propose a ”bicategorical cotrace” in a closed …

The Power Of Supercomputing Applied To Fractal Image Generation, Charlin Me Duff

Mathematics Senior Capstones

This project looks into how parallelism benefits the runtime of generating large fractal images. First, it explains what the Julia and Mandelbrot Sets are, who discovered them, and how they are calculated. Following that is an introduction to supercomputers, parallel computing, and Cal Poly Humboldt’s very own supercomputer. Once groundwork is laid, I explain my process of adapting a fractal image generation program from serial computing to different levels of parallelism. After that, is an analysis of the effects of levels of parallelism on the runtime of large fractal image generation. This paper concludes with a reflection on the project …

Eating Disorders And Autism: A Network Approach, Lillian C. King

Undergraduate Theses, Professional Papers, and Capstone Artifacts

This paper explores the overlap of ED and ASD symptoms, and evaluates the results of a study that used network analysis to investigate pathway and core ED and ASD comorbidity symptoms. Eating Disorders (EDs) and autism spectrum disorder (ASD) have several overlapping symptoms that may inform our understanding of both disorders. Increased knowledge of the overlap of EDs and ASD can improve the treatment of EDs in those with ASD.