Coloring Complexes And Combinatorial Hopf Monoids, 2023 The University of Texas Rio Grande Valley

#### 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.

Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, 2023 The University of Texas Rio Grande Valley

#### 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 …

Transcription And Translation Of Nicole Oresme: Quaestiones Super Geometricam Euclidis: Questio 2, 2023 Xavier University

#### 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.

Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", 2023 University of Utah

#### 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

*Browse all Datasets*

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 …

Counting Power Domination Sets In Complete M-Ary Trees, 2023 Gonzaga University

#### 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.

Function Spaces Via Fractional Poisson Kernel On Carnot Groups And Applications, 2023 Clark University

#### 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.

From Mirrors To Wallpapers: A Virtual Math Circle Module On Symmetry, 2023 Central New Mexico Community College

#### 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, …

Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, 2023 Indian Institute of Technology Guwahati

#### 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.

Spectral Sequences And Khovanov Homology, 2023 Dartmouth College

#### 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 …

Slices Of C_2, Klein-4, And Quaternionic Eilenberg-Mac Lane Spectra, 2023 University of Kentucky

#### 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 $\mpi_{k\rho} H_{Q_8}\ulZ$.

Conceptual Mathematics In Society, 2023 Northern Illinois University

#### 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 …

Bipolar Soft Ideal Rough Set With Applications In Covid-19, 2023 TÜBİTAK

#### 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 …

Pell-Lucas Collocation Method For Solving A Class Of Second Order Nonlinear Differential Equations With Variable Delays, 2023 TÜBİTAK

#### 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 …

An Invariant Of Regular Isotopy For Disoriented Links, 2023 TÜBİTAK

#### 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.

A New Approach To Matrix Isomorphisms Of Complex Clifford Algebras Via Cantor Set, 2023 TÜBİTAK

#### 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.

Forming Coupled Dispersionless Equations Of Families Of Bertrand Curves, 2023 TÜBİTAK

#### 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.

#### 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.

Some Fractional Dirac Systems, 2023 TÜBİTAK

#### 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.

On The Properties Of Solutions For Nonautonomous Third-Order Stochastic Differential Equation With A Constant Delay, 2023 TÜBİTAK

#### 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.

#### 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.