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Full-Text Articles in Physical Sciences and Mathematics

Coloring Complexes And Combinatorial Hopf Monoids, Jacob A. White Feb 2023

Coloring Complexes And Combinatorial Hopf Monoids, Jacob A. White

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the quasisymmetric function invariants associated to the combinatorial Hopf monoid. We show that the collection of all such coloring complexes forms a linearized combinatorial Hopf monoid, which is the terminal object in the category of combinatorial Hopf monoids with convex characters. We also study several examples of combinatorial Hopf monoids.

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Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, Atul Dixit, Ankush Goswami Feb 2023

Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, Atul Dixit, Ankush Goswami

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function p(n). Using a result of Shimura we also relate …

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Transcription And Translation Of Nicole Oresme: Quaestiones Super Geometricam Euclidis: Questio 2, Daniel E. Otero Jan 2023

Transcription And Translation Of Nicole Oresme: Quaestiones Super Geometricam Euclidis: Questio 2, Daniel E. Otero

2023, February 10-11 ORESME Reading Group Meeting

No abstract provided.

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Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", Jadon Wagstaff, Jesse Wheeler, Brennan Bean, Marc Maguire, Yan Sun Jan 2023

Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", Jadon Wagstaff, Jesse Wheeler, Brennan Bean, Marc Maguire, Yan Sun

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Recent amendments to design ground snow load requirements in ASCE 7-22 have reduced the size of case study regions by 91% from what they were in ASCE 7-16, primarily in western states. This reduction is made possible through the development of highly accurate regional generalized additive regression models (RGAMs), stitched together with a novel smoothing scheme implemented in the R software package remap, to produce the continental- scale maps of reliability-targeted design ground snow loads available in ASCE 7-22. This approach allows for better characterizations of the changing relationship between temperature, elevation, and ground snow loads across the Conterminous United …

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Counting Power Domination Sets In Complete M-Ary Trees, Hays Whitlatch, Katharine Shultis, Olivia Ramirez, Michele Ortiz, Sviatlana Kniahnitskaya Jan 2023

Counting Power Domination Sets In Complete M-Ary Trees, Hays Whitlatch, Katharine Shultis, Olivia Ramirez, Michele Ortiz, Sviatlana Kniahnitskaya

Theory and Applications of Graphs

Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count the number of power domination sets of size k in a labeled complete m-ary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time.

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Function Spaces Via Fractional Poisson Kernel On Carnot Groups And Applications, Ali Maalaoui, Andrea Pinamonti, Gareth Speight Jan 2023

Function Spaces Via Fractional Poisson Kernel On Carnot Groups And Applications, Ali Maalaoui, Andrea Pinamonti, Gareth Speight

Mathematics

We provide a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel and Poisson kernel. We apply our results to study commutators involving fractional powers of the sub-Laplacian. © 2022, The Hebrew University of Jerusalem.

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From Mirrors To Wallpapers: A Virtual Math Circle Module On Symmetry, Nicole A. Sullivant, Christina L. Duron, Douglas T. Pfeffer Jan 2023

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, …

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Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya Jan 2023

Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya

Theory and Applications of Graphs

A mixed graph is called \emph{second kind hermitian integral} (\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called \emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set $S$ for which a mixed circulant graph $\text{Circ}(\mathbb{Z}_n, S)$ is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, we express the eigenvalues and the HS-eigenvalues of unitary oriented circulant graphs in terms of generalized M$\ddot{\text{o}}$bius function.

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Spectral Sequences And Khovanov Homology, Zachary J. Winkeler Jan 2023

Spectral Sequences And Khovanov Homology, Zachary J. Winkeler

Dartmouth College Ph.D Dissertations

In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant MKh(L) for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the Asaeda-Pryzytycki-Sikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a Z^n-filtration on the Khovanov complex, and as a result we will get various spectral sequences relating MKh(L) to Kh(L), AKh(L), and APS(L). Our …

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Slices Of C_2, Klein-4, And Quaternionic Eilenberg-Mac Lane Spectra, Carissa Slone Jan 2023

Slices Of C_2, Klein-4, And Quaternionic Eilenberg-Mac Lane Spectra, Carissa Slone

Theses and Dissertations--Mathematics

We provide the slice (co)towers of \(\Si{V} H_{C_2}\ul M\) for a variety of \(C_2\)-representations \(V\) and \(C_2\)-Mackey functors \(\ul M\). We also determine a characterization of all 2-slices of equivariant spectra over the Klein four-group \(C_2\times C_2\). We then describe all slices of integral suspensions of the equivariant Eilenberg-MacLane spectrum \(H\ulZ\) for the constant Mackey functor over \(C_2\times C_2\). Additionally, we compute the slices and slice spectral sequence of integral suspensions of $H\ulZ$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors \(\mpi_{k\rho} H_{K_4}\ulZ\) and $\mpi_{k\rho} H_{Q_8}\ulZ$.

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Conceptual Mathematics In Society, Ricela Feliciano-Semidei Jan 2023

Conceptual Mathematics In Society, Ricela Feliciano-Semidei

Books, Book Chapters, & Supplemental Materials

This textbook is a compilation of chapters with educational purposes for the course MATH 103 in Spring 2023. The first part (Chapters 1 and 2) includes logic and critical thinking. Understanding the thinking process and strategies for solving problems in an effective way will provide students with skills that will be required to succeed in all college math courses. The second part (Chapters 3 & 4) is an opportunity to develop numbers sense through strengthening conceptual understanding of fractions and algebraic thinking. This will help develop foundational mathematical knowledge for college mathematics courses. The third and fourth parts of this …

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Bipolar Soft Ideal Rough Set With Applications In Covid-19, Heba I. Mustafa Jan 2023

Bipolar Soft Ideal Rough Set With Applications In Covid-19, Heba I. Mustafa

Turkish Journal of Mathematics

Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft …

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Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim Jan 2023

Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, Şuayi̇p Yüzbaşi, Gamze Yildirim

Turkish Journal of Mathematics

In this study, the approximate solution of the nonlinear differential equation with variable delays is investigated by means of a collocation method based on the truncated Pell-Lucas series. In the first stage of the method, the assumed solution form (the truncated Pell-Lucas polynomial solution) is expressed in the matrix form of the standard bases. Next, the matrix forms of the necessary derivatives, the nonlinear terms, and the initial conditions are written. Then, with the help of the equally spaced collocation points and these matrix relations, the problem is reduced to a system of nonlinear algebraic equations. Finally, the obtained system …

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An Invariant Of Regular Isotopy For Disoriented Links, İsmet Altintaş, Hati̇ce Parlatici Jan 2023

An Invariant Of Regular Isotopy For Disoriented Links, İsmet Altintaş, Hati̇ce Parlatici

Turkish Journal of Mathematics

In this paper, we define a two-variable polynomial invariant of regular isotopy, $M_{K}$ for a disoriented link diagram $K$. By normalizing the polynomial $M_{K}$ using complete writhe, we obtain a polynomial invariant of ambient isotopy, $N_{K}$, for a disoriented link diagram $K$. The polynomial $N_{K}$ is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial $F$ to the disoriented links. Moreover, the polynomial $M_{K}$ is an expansion of the Kauffman polynomial $L$ to the disoriented links.

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A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, Derya Çeli̇k Jan 2023

A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, Derya Çeli̇k

Turkish Journal of Mathematics

We give a new way to obtain the standard isomorphisms of complex Clifford algebras, known as the tensor product of Pauli matrices, by representing the complex Clifford algebras on the space of complex valued functions defined over a finite subset of the Cantor set.

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Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, Kemal Eren Jan 2023

Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, Kemal Eren

Turkish Journal of Mathematics

In this study, we establish a link of the coupled dispersionless (CD) equations system with the motion of Bertrand curve pairs. Moreover, we find the Lax equations that provide the integrability of these equations. By taking an appropriate choice of variables we show the link of the short pulse (SP) equation with the motion of Bertrand curve pairs via the reciprocal (hodograph) transformation. Finally, we prove that the conserved quantity of the corresponding coupled dispersionless equations obtained from each of these curve pairs is constant.

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On A New Subclass Of Biunivalent Functions Associated With The $(P,Q)$-Lucas Polynomials And Bi-Bazilevic Type Functions Of Order $\Rho+I\Xi$, Hali̇t Orhan, İbrahi̇m Aktaş, Hava Arikan Jan 2023

On A New Subclass Of Biunivalent Functions Associated With The $(P,Q)$-Lucas Polynomials And Bi-Bazilevic Type Functions Of Order $\Rho+I\Xi$, Hali̇t Orhan, İbrahi̇m Aktaş, Hava Arikan

Turkish Journal of Mathematics

Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass of biunivalent functions. We obtained coefficient inequalities for functions belonging to the new subclass. In addition to these results, the upper bound for the Fekete-Szegö functional was obtained. Finally, for some special values of parameters, several corollaries were presented.

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Some Fractional Dirac Systems, Yüksel Yalçinkaya Jan 2023

Some Fractional Dirac Systems, Yüksel Yalçinkaya

Turkish Journal of Mathematics

In this work, including $\alpha\epsilon(0,1)$; we examined the Dirac system in the frame which includes$\ \alpha$ order right and left Reimann-Liouville fractional integrals and derivatives with exponential kernels, and the Dirac system which includes $\alpha$ order right and left Caputo fractional integrals and derivatives with exponential kernels. Furthermore, we have given some definitions and properties for discrete exponential kernels and their associated fractional sums and fractional differences, and we have studied discrete fractional Dirac systems.

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On The Properties Of Solutions For Nonautonomous Third-Order Stochastic Differential Equation With A Constant Delay, Ayman Mohammed Mahmoud, Doaa Ali Mohamed Bakhit Jan 2023

On The Properties Of Solutions For Nonautonomous Third-Order Stochastic Differential Equation With A Constant Delay, Ayman Mohammed Mahmoud, Doaa Ali Mohamed Bakhit

Turkish Journal of Mathematics

In this work, complete Lyapunov functionals (LFs) are constructed and used for the established conditions on the nonlinear functions appearing in the main equation, to guarantee stochastically asymptotically stable (SAS), uniformly stochastically bounded (USB) and uniformly exponentially asymptotically stable (UEAS) in probability of solutions to the nonautonomous third-order stochastic differential equation (SDE) with a constant delay as \begin{align*} \begin{split} \dddot{x}(t)&+a(t)f(x(t),\dot{x}(t))\ddot{x}(t)+b(t)\phi(x(t))\dot{x}(t) +c(t)\psi(x(t-r))\\&+g(t,x)\dot{\omega}(t)=p(t,x(t),\dot{x}(t),\ddot{x}(t)). \end{split} \end{align*} In Section 4, we give two numerical examples as an application to illustrate the results.

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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 Jan 2023

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.

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Jackson-Type Theorem In The Weak $L_{1}$-Space, Rashid Aliev, Eldost Ismayilov Jan 2023

Jackson-Type Theorem In The Weak $L_{1}$-Space, Rashid Aliev, Eldost Ismayilov

Turkish Journal of Mathematics

The weak $L_{1}$-space meets in many areas of mathematics. For example, the conjugate functions of Lebesgue integrable functions belong to the weak $L_{1}$-space. The difficulty of working with the weak $L_{1}$-space is that the weak $L_{1}$-space is not a normed space. Moreover, infinitely differentiable (even continuous) functions are not dense in this space. Due to this, the theory of approximation was not produced in this space. In the present paper, we introduced the concept of the modulus of continuity of the functions from the weak $L_{1}$-space, studied its properties, found a criterion for convergence to zero of the modulus of …

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On The Distribution Of Adjacent Zeros Of Solutions To First-Order Neutral Differential Equations, Emad R. Attia, Ohoud N. Al-Masarer, Irena Jadlovska Jan 2023

On The Distribution Of Adjacent Zeros Of Solutions To First-Order Neutral Differential Equations, Emad R. Attia, Ohoud N. Al-Masarer, Irena Jadlovska

Turkish Journal of Mathematics

The purpose of this paper is to study the distribution of zeros of solutions to a first-order neutral differential equation of the form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' + q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for the distance between consecutive zeros of solutions, which improve upon many of the previously known ones. The results are formulated so that they can be generalized without much effort to equations for which the distribution of zeros problem is related to the study of …

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Novel Correlation Coefficients For Interval-Valued Fermatean Hesitant Fuzzy Sets With Pattern Recognition Application, İbrahi̇m Demi̇r Jan 2023

Novel Correlation Coefficients For Interval-Valued Fermatean Hesitant Fuzzy Sets With Pattern Recognition Application, İbrahi̇m Demi̇r

Turkish Journal of Mathematics

A combination of interval-valued Fermatean fuzzy sets with Fermatean hesitant fuzzy elements in the form of interval values is known as an interval-valued Fermatean hesitant fuzzy set. Since Fermatean hesitant fuzzy sets are effective instruments for representing more complex, ambiguous, and hazy information, interval-valued Fermatean hesitant fuzzy sets are expansions of these sets. This investigation will concentrate on four different types of correlation coefficients for Fermatean hesitant fuzzy sets and expand them to include correlation coefficients and weighted correlation coefficients for interval-valued Fermatean hesitant fuzzy sets. Finally, the numerical examples demonstrate the viability and usefulness of the suggested methodologies in …

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Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş Jan 2023

Geodesics And Isocline Distributions In Tangent Bundles Of Nonflat Lorentzian-Heisenberg Spaces, Murat Altunbaş

Turkish Journal of Mathematics

Let $(H_{3},g_{1})$ and $(H_{3},g_{2})$ be the Lorentzian-Heisenberg spaces with nonflat metrics $g_{1}$ and $g_{2},\ $and $(TH_{3},g_{1}^{s}),\ (TH_{3},g_{2}^{s})$ be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold $H_{3}.$We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold $H_{3}$. We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.

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On The Band Functions And Bloch Functions, Oktay Veli̇ev Jan 2023

On The Band Functions And Bloch Functions, Oktay Veli̇ev

Turkish Journal of Mathematics

In this paper, we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients.

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Separation, Connectedness, And Disconnectedness, Mehmet Baran Jan 2023

Separation, Connectedness, And Disconnectedness, Mehmet Baran

Turkish Journal of Mathematics

The aim of this paper is to introduce the notions of hereditarily disconnected and totally disconnected objects in a topological category and examine the relationship as well as interrelationships between them. Moreover, we characterize each of $T_{2}$, connected, hereditarily disconnected, and totally disconnected objects in some topological categories and compare our results with the ones in the category of topological spaces.

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Approximation Results For The Moments Of Random Walk With Normally Distributed Interference Of Chance, Zülfi̇ye Hanali̇oğlu, Aynura Poladova, Tahi̇r Khani̇yev Jan 2023

Approximation Results For The Moments Of Random Walk With Normally Distributed Interference Of Chance, Zülfi̇ye Hanali̇oğlu, Aynura Poladova, Tahi̇r Khani̇yev

Turkish Journal of Mathematics

In this study, a random walk process $\left(X\left(t\right)\right)$ with normally distributed interference of chance is considered. In the literature, this process has been shown to be ergodic and the limit form of the ergodic distribution has been found. Here, unlike previous studies, the moments of the $X\left(t\right)$ process are investigated. Although studies investigating the moment problem for various stochastic processes (such as renewal-reward processes) exist in the literature, it has not been considered for random walk processes, as it requires the use of new mathematical tools. Therefore, in this study, firstly, the exact formulas for the first four moments of …

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Generalized Elliptical Quaternions With Some Applications, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r Jan 2023

Generalized Elliptical Quaternions With Some Applications, Harun Bariş Çolakoğlu, Mustafa Özdemi̇r

Turkish Journal of Mathematics

In this article, quaternions, which is a preferred and elegant method for expressing spherical rotations, are generalized with the help of generalized scalar product spaces, and elliptical rotations on any given ellipsoid are examined by them. To this end, firstly, we define the generalized elliptical scalar product space which accepts the given ellipsoid as a sphere and determines skew symmetric matrices, and the generalized vector product related to this scalar product space. Then we define the generalized elliptical quaternions by using these notions. Finally, elliptical rotations on any ellipsoid in the space are examined by using the unit generalized elliptical …

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The Class Of Demi Kb-Operators On Banach Lattices, Hedi Benkhaled, Aref Jeribi Jan 2023

The Class Of Demi Kb-Operators On Banach Lattices, Hedi Benkhaled, Aref Jeribi

Turkish Journal of Mathematics

In this paper, we introduce and study the new concept of demi KB-operators. Let $E$ be a Banach lattice. An operator $T: E\longrightarrow E$ is said to be a demi KB-operator if, for every positive increasing sequence $\{x_{n}\}$ in the closed unit ball $\mathcal{B}_{E}$ of $E$ such that $\{x_{n}-Tx_{n}\}$ is norm convergent to $x\in E$, there is a norm convergent subsequence of $\{x_{n}\}$. If the latter sequence has a weakly convergent subsequence then $T$ is called a weak demi KB-operator. We also investigate the relationship of these classes of operators with classical notions of operators, such as b-weakly demicompact operators …

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Inverse Nodal Problem For The Quadratic Pencil Of The Sturm$-$Liouville Equations With Parameter-Dependent Nonlocal Boundary Condition, Yaşar Çakmak, Baki̇ Keski̇n Jan 2023

Inverse Nodal Problem For The Quadratic Pencil Of The Sturm$-$Liouville Equations With Parameter-Dependent Nonlocal Boundary Condition, Yaşar Çakmak, Baki̇ Keski̇n

Turkish Journal of Mathematics

In this paper, we consider the inverse nodal problem for a quadratic pencil of the Sturm$-$Liouville equations with parameter-dependent Bitsadze$-$Samarskii type nonlocal boundary condition and we give an algorithm for the reconstruction of the potential functions by obtaining the asymptotics of the nodal points.

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