Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems,
2021
TÜBİTAK
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Turkish Journal of Mathematics
We propose and analyze a modified weak Galerkin finite element method (MWG-FEM) for solving singularly perturbed problems of convection-dominated type. The proposed method is constructed over piecewise polynomials of degree $k\geq1$ on interior of each element and piecewise constant on the boundary of each element. The present method is parameter-free and has less degrees of freedom compared to the classical weak Galerkin finite element method. The method is shown uniformly convergent for small perturbation parameters. An uniform convergence rate of $\mathcal {O}((N^{-1}\ln N)^k)$ in the energy-like norm is established on the piecewise uniform Shishkin mesh, where $N$ is the number …
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas,
2021
TÜBİTAK
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
Turkish Journal of Mathematics
In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.
Affine Ricci Solitons Associated To The Bott Connection On Three-Dimensionallorentzian Lie Groups,
2021
TÜBİTAK
Affine Ricci Solitons Associated To The Bott Connection On Three-Dimensionallorentzian Lie Groups, Tong Wu, Yong Wang
Turkish Journal of Mathematics
In this paper, we compute the Bott connection and their curvature on three-dimensional Lorentzian Lie groups with three different distributions, then we classify affine Ricci solitons associated to the Bott connection on the spaces under study.
A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers,
2021
TÜBİTAK
A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it. For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.
Quasi-Idempotent Ranks Of The Proper Ideals In Finite Symmetric Inverse Semigroups,
2021
TÜBİTAK
Quasi-Idempotent Ranks Of The Proper Ideals In Finite Symmetric Inverse Semigroups, Leyla Bugay
Turkish Journal of Mathematics
Let $I_{n}$ and $S_{n}$ be the symmetric inverse semigroup and the symmetric group on a finite chain $X_{n}=\{1,\ldots ,n \}$, respectively. Also, let $I_{n,r}= \{ \alpha \in I_{n}: im(\alpha) \leq r\}$ for $1\leq r\leq n-1$. For any $\alpha\in I_n$, if $\alpha\neq \alpha^2=\alpha^4$ then $\alpha$ is called a quasi-idempotent. In this paper, we show that the quasi-idempotent rank of $I_{n,r}$ (both as a semigroup and as an inverse semigroup) is $\binom{n}{2}$ if $r=2$, and $\binom{n}{r}+1$ if $r\geq 3$. The quasi-idempotent rank of $I_{n,1}$ is $n$ (as a semigroup) and $n-1$ (as an inverse semigroup).
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval,
2021
TÜBİTAK
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Turkish Journal of Mathematics
In the present paper, using the triangular $A-$statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on $\left[ 0,\infty \right)\times \left[ 0,\infty \right) $ with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.
Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials,
2021
TÜBİTAK
Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
The main purpose of this paper is to obtain computational identities and formulas for a certain class of combinatorial-type numbers and polynomials. By the aid of the generating function technique, we derive a recurrence relation and an infinite series involving the aforementioned class of combinatorial-type numbers. By applying the Riemann integral to the combinatorial-type polynomials with multivariables, we present some integral formulas for these polynomials, including the Bernoulli numbers of the second kind. By the implementation of the $p$-adic integral approach to the combinatorial-type polynomials with multivariables, we also obtain formulas for the Volkenborn integral and the fermionic $p$-adic integral …
Two-Weight Norm Inequalities For Some Fractional Type Operators Related To Schrödinger Operator On Weighted Morrey Spaces,
2021
TÜBİTAK
Two-Weight Norm Inequalities For Some Fractional Type Operators Related To Schrödinger Operator On Weighted Morrey Spaces, Wanyu Wu, Jiang Zhou
Turkish Journal of Mathematics
In this paper, we establish the two-weight norm inequalities for fractional maximal functions and fractional integral operators related to Schrödinger differential operator on weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
Computing Ribbon Obstructions For Colored Knots,
2021
Smith College
Computing Ribbon Obstructions For Colored Knots, Patricia Cahn, Alexandra Kjuchukova
Mathematics Sciences: Faculty Publications
Kjuchukova's p invariant gives a ribbon obstruction for Fox p-colored knots. The invariant is derived from dihedral branched covers of 4-manifolds, and can be used to calculate the signatures of these covers when singularities on the branching sets are present. In this note, we give an algorithm for evaluating p from a colored knot diagram, and compute a couple of examples.
Regularity For A Class Of Quasilinear Degenerate Parabolic Equations In The Heisenberg Group,
2021
Worcester Polytechnic Institute
Regularity For A Class Of Quasilinear Degenerate Parabolic Equations In The Heisenberg Group, Luca Capogna, Giovanna Citti, Nicola Garofalo
Mathematics Sciences: Faculty Publications
We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in [31] of the Hölder regularity of p-harmonic functions in the Heisenberg group Hn. Given a number p ≥ 2, in this paper we establish the C1 smoothness of weak solutions of a class of quasilinear PDE in Hn modeled on the equation.
Engaging English Learners In Purposeful Discourse In Elementary Mathematics,
2021
Walden University
Engaging English Learners In Purposeful Discourse In Elementary Mathematics, Karlyn E. Davis-Welton
Walden Dissertations and Doctoral Studies
Teachers are experiencing a change in practice, from teacher-centered to student-centered, which affects their work with English learners (ELs) in third through fifth grade mathematics classrooms. The implementation of student-centered discourse practices is essential to orchestrating productive mathematical discussions. However, the common practice is teacher-centered instruction where teacher talk is prevalent. Although the school district in this study provided professional development (PD) to address student-centered practices, PD for teaching ELs to interact in English in their mathematics classrooms remained to be addressed. The purpose of this study was to gain an understanding of teachers’ experiences with new discourse practices and …
Teacher Understanding Of Instructional Strategies In Elementary Mathematics,
2021
Walden University
Teacher Understanding Of Instructional Strategies In Elementary Mathematics, Erica Boatwright Glover
Walden Dissertations and Doctoral Studies
Synergizing Elementary School (pseudonym) consistently experiences low state-required mathematics test scores in grades 3 and 4 below district and state proficiency rates in mathematics. The purpose of this qualitative case study was to investigate what instructional practices used by Grade 3 and Grade 4 teachers are, aligned or not aligned, with research-based planning, standards-based instruction, attention to conditions of learning, and professional responsibilities of teachers to support students’ achievement in mathematics. This study's conceptual framework was grounded in Robert Marzano's model of teaching effectiveness called the focus teacher evaluation model. Data for this case study were gathered from semi-structured interviews …
Elliptical Fourier Analysis Of Crown Shape In Permanent Mandibular Molars From The Late Neolithic Cave Burials Of Belgium,
2021
Georgia State University
Elliptical Fourier Analysis Of Crown Shape In Permanent Mandibular Molars From The Late Neolithic Cave Burials Of Belgium, Frank L'Engle Williams, Juliet K. Brophy, Gregory J. Matthews
Mathematics and Statistics: Faculty Publications and Other Works
Prehistoric remains from caves and rockshelters are known from more than 250 sites situated along the Meuse River Basin of Belgium. Most of these osteological remnants date to the Late Neolithic period beginning after 4,500 years before present (BP), and five of these cave burials have been subject to intensive study, including Hastière Caverne M and Hastière Trou Garçon C from an earlier period of the Late Neolithic (4,345 ± 60 to 4,220 ± 45 years BP), Sclaigneaux and Bois Madame from the final/late Neolithic (4,155 ± 35 to 3,910 ± 40 years BP) and Maurenne Caverne de la Cave …
An Enumeration Of Nested Networks,
2021
The University of Akron
An Enumeration Of Nested Networks, Nathan Cornelius
Williams Honors College, Honors Research Projects
Nested networks have several applications in phylogenetics and electrical circuit theory. In many cases, there may exist more than one distinct network which correctly models a given data set. This proposes a combinatorial problem to determine all possible network solutions. In this paper, we partially solve this problem by developing exponential generating functions which enumerate all 1-nested and 2-nested unicyclic networks. We also describe our procedure to directly count all 1-nested and 2-nested networks and provide all 1-nested networks with 7, 8, and 9 terminal nodes.
Obstructive Wiring Patterns To Circular Planarity In Electrical Networks,
2021
The University of Akron
Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo
Williams Honors College, Honors Research Projects
In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …
Bipartite, Size, And Online Ramsey Numbers Of Some Cycles And Paths,
2021
Montclair State University
Bipartite, Size, And Online Ramsey Numbers Of Some Cycles And Paths, Eliyahu Schudrich
Theses, Dissertations and Culminating Projects
The basic premise of Ramsey Theory states that in a sufficiently large system, complete disorder is impossible. One instance from the world of graph theory says that given two fixed graphs F and H, there exists a finitely large graph G such that any red/blue edge coloring of the edges of G will produce a red copy of F or a blue copy of H. Much research has been conducted in recent decades on quantifying exactly how large G must be if we consider different classes of graphs for F and H. In this thesis, we explore several Ramsey- type …
Transitioning To An Active Learning Environment For Calculus At The University Of Florida,
2021
Embry-Riddle Aeronautical University
Transitioning To An Active Learning Environment For Calculus At The University Of Florida, Darryl Chamberlain, Amy Grady, Scott Keeran, Kevin Knudson, Ian Manly, Melissa Shabazz, Corey Stone
Publications
In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.
Zn Orbifolds Of Vertex Operator Algebras,
2021
University of Denver
Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill
Electronic Theses and Dissertations
Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra VG is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by VG if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, VG will also be strongly finitely generated. This is an analogue …
Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves,
2021
The University of Texas Rio Grande Valley
Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves, Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef A. Sifuentes, Erwin Suazo
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form n = 6k for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on …
Geometric Morphometric Analyses Define Riverine And Lacustrine Species Flocks Of Himalayan Snowtrout (Cyprinidae: Schizothorax) In Nepal,
2021
University of Arkansas, Fayetteville
Geometric Morphometric Analyses Define Riverine And Lacustrine Species Flocks Of Himalayan Snowtrout (Cyprinidae: Schizothorax) In Nepal, Binod Regmi, Marlis R. Douglas, David R. Edds, Michael E. Douglas
Biological Sciences Faculty Publications and Presentations
Freshwater fishes in the river and lake systems in the Himalayas and Tibetan Plateau are morphologically diverged but the evolutionary relationship of putative subspecies separated in these freshwater systems has not been explored. Snowtrout (Schizothorax spp.) are minnows (Cyprinidae) broadly distributed in Asia. Body shapes of 3 Lake Rara (northwest Nepal) endemics (S. macrophthalmus, S. nepalensis, S. raraensis) and 2 widely distributed riverine species (S. progastus, S. richardsonii) across 3 drainages in Nepal (i.e. Karnali, Gandaki, and Koshi Rivers) were studied using geometric morphometry. Data were derived from museum voucher specimens/tissues collected …
