Physical Sciences and Mathematics Commons^™

Lifts Of Derivations To The Semitangent Bundle, Ari̇f A. Salimov, Ekrem Kadioğlu

Turkish Journal of Mathematics

The main purpose of this paper is to investigate the complete lifts of derivations for semitangent bundle and to discuss relations between these and lifts already known.

On Characterization Of Metric Completeness, Guo-Jing Jiang

Turkish Journal of Mathematics

We give seven necessary and sufficient conditions for a metric space to be complete.

On Generalized Higher Derivations, Atsushi Nakajima

Turkish Journal of Mathematics

We define the notion of generalized higher derivations and give some elementary relations between generalized higher derivations and higher derivations in the usual sense. We extend the result of an exact sequence of the set of all derivations $\text{Der}(A, M)$ and the set of all generalized derivations $g\text{Der}(A, M)$ given in [N1, Theorem 2.4]. Moreover, we discuss generalized higher Jordan derivations and Lie derivations.

Conjugacy Structure Type And Degree Structure Type In Finite P-Groups, Yadalah Marefat

Turkish Journal of Mathematics

Let $G$ be a finite $p-$group, and denote by $k(G)$ number of conjugacy classes in $G$. The aim of this paper is to introduce the conjugacy structure type and degree structure type for $p-$groups, and determine these parameters for $p-$groups of order $p^5$, and calculate $k(G)$ for them.

New And Old Types Of Homogeneity, Ali̇ Ahmad Fora

Turkish Journal of Mathematics

We introduce new types of homogeneity ; namely : locally homogeneity and closed homogeneity .Several results are included discussing some relations between these types and the old ones. Some characterization and decomposition theorems are obtained. Relevant examples and counterexamples are discussed throughout this paper.

A Borsuk-Ulak Theorem For Heisenberg Group Actions, Necdet Güner

Turkish Journal of Mathematics

Let $G=H_{2n+1}$ be a $(2n+1)$-dimensional Heisenberg Lie group acts on $M=C^m-\{0\}$ and $M^{'}=C^{m'}-\{0\}$ exponentially. By using Cohomological Index we proved the following theorem. If $f:M{\to}M^{'}$ is a $G$-equivariant map, then $m{\le}m'$.

On Conjugation In The Mod-P Steenrod Algebra, İsmet Karaca, İlkay Yaslan Karaca

Turkish Journal of Mathematics

In this paper we prove a formula involving the canonical anti-automorphism $\chi$ of the mod-$p$ Steenrod algebra.

The P-Stirling Numbers, Russel Merris

Turkish Journal of Mathematics

The purpose of this article is to introduce \( p \)-Stirling numbers of the first and second kinds.

Some Radius Problem For Certain Families Of Analytic Functions, Yaşar Polatoğlu, Meti̇n Bolcal

Turkish Journal of Mathematics

The aim of this paper is to give bounds of the radius of $\alpha $-convexity for certain families of analytic functions in the unit disc. The radius of $\alpha $-convexity is generalization of the radius of convexity and the radius of starlikeness, and introduced by S.S.Miller; P.T.Mocanu and M.O.Reade [3,4]

Constructible Circles On The Unit Sphere, Blaga Slavcheva Pauley

Theses Digitization Project

In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.

Solutions To The Chinese Postman Problem, Kenneth Peter Cramm

Theses Digitization Project

Considering the Chinese Postman Problem, in which a mailman must deliver mail to houses in a neighborhood. The mailman must cover each side of the street that has houses, at least once. The focus of this paper is our attempt to discover the optimal path, or the least number of times each street is walked. The integration of algorithms from graph theory and operations research form the method used to explain solutions to the Chinese Postman Problem.

Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun

Theses Digitization Project

No abstract provided.

The Proof Of Fermat's Last Theorem, Mohamad Trad

Theses Digitization Project

Fermat, Pierre de, is perhaps the most famous number theorist who ever lived. Fermat's Last Theorem states that the equation xn + yn = zn has no non-zero integer solutions for x, y and z when n>2.

Bounds For The Points Of Spectral Concentration Of Sturm-Liouville Problems, Daphne Gilbert, B.J. Harris

Articles

§1. Introduction. We consider the spectral function ρα(λ) associated with the Sturm–Liouville equation

with the boundary condition

[Introduction To] Mathematics Calculus Bc, John R. Hubbard, David R. Arterburn, Michael A. Perl

Bookshelf

This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests. Our review succinctly covers areas considered most relevant to this exam. Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you.

Jacobsthal Numbers And Alternating Sign Matrices, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

Let A(n) denote the number of n×n alternating sign matrices and J_m the m^thJacobsthal number. It is known that

A(n) = n-1 Õ l = 0 (3l+1)!(n+l)! .

The values of A(n) are in general highly composite. The goal of this paper is to prove that A(n) is odd if and only if n is a Jacobsthal number, thus showing that A(n) is odd infinitely often.

Mortar Estimates Independent Of Number Of Subdomains, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

The stability and error estimates for the mortar finite element method are well established. This work examines the dependence of constants in these estimates on shape and number of subdomains. By means of a Poincar´e inequality and some scaling arguments, these estimates are found not to deteriorate with increase in number of subdomains.

About Non-Spherically Symmetric Deformations Of An Incompressible Neo-Hookean Sphere, Marek Elźanowski

Mathematics and Statistics Faculty Publications and Presentations

A class of non-spherically symmetric deformations of a neo-Hookean incompressible elastic ball is considered. It is shown that the only possible solution, the cavitated radially symmetric solution and the deformation of radial inflation and polar stretching. These are the same solutions as found by Polignone-Warne and Warne [6] for a smaller class of deformations. This fact shows once again that the radial deformations are the only deformations, at least within the class considered, which may support a formation of a cavity in the center of an incompressible, isotropic, elastic sphere.

The Intersection Graph Conjecture For Loop Diagrams, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loop. We also compute the size of the subalgebra generated by these "loop diagrams."

Finite Type Link Concordance Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the linking numbers of the components.

Finite Type Link Homotopy Invariants Ii: Milnor's Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite type. Finally, we compare our approach to another approach for defining finite type invariants within linking classes.

Cyclic Dehn Surgery And The A-Polynomial, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

We present a necessary condition for Dehn surgery on a knot in double-struck S sign3 to be cyclic which is based on the A-polynomial of the knot. The condition involves a width of the Newton polygon of the A-polynomial, and provides a simple method of computing a list of possible cyclic surgery slopes. The width produces a list of at most three slopes for a hyperbolic knot which contains no closed essential surface in its complement (in agreement with the Cyclic Surgery Theorem). We conclude with an application to cyclic surgeries along non-boundary slopes of hyperbolic mutant knots.

On The Efficiency Of Finite Simple Semigroups, H. Ayik, C. M. Campbell, J. J. O'Connor, N. Ruskuc

Turkish Journal of Mathematics

Let $S$ be a finite simple semigroup, given as a Rees matrix semigroup $\mathcal{M}[G;I,\Lambda ;P]$ over a group $G$. We prove that the second homology of $S$ is $H_{2}(S)=H_{2}(G)\times {\mathbb Z}^{( I -1)( \Lambda -1)}$. It is known that for any finite presentation $\langle \: A\: \: R\: \rangle$ of $S$ we have $ R - A \geq \mbox{rank}(H_{2}(S))$; we say that $S$ is efficient if equality is attained for some presentation. Given a presentation $\langle \: A_{1}\: \: R_{1}\: \rangle$ for $G$, we find a presentation $\langle \: A\: \: R\: \rangle$ for $S$ such that $ R - …

On The Asymptotics Of Fourier Coefficients For The Potential In Hill's Equation, Haskiz Coşkun

Turkish Journal of Mathematics

We consider Hill's equation $y'' +(\lambda -q)y=0$ where $q\in L^{1}[0,\pi ].$ We show that if $l_{n}-$the length of the $n-th$ instability interval$-$ is of order $O(n^{-k})$ then the real Fourier coefficients $a_{n},b_{n}$ of $q$ are of the same order for$(k=1,2,3)$, which in turn implies that $q^{(k-2)}$, the $(k-2)th$ derivative of $q$, is absolutely continuous almost everywhere for $k=2,3.$

A Local Zero-Two Law And Some Applications, Radu Zaharopol

Turkish Journal of Mathematics

In the paper we obtain a local zero-two law for positive contractions of $L^1$-spaces, which we use in order to offer new proofs of a theorem of Orey concerning Markov chains, and of the strong asymptotic stability of certain Markov operators that have appeared in the study of the Tjon-Wu equation and in connection with the Hannsgen and Tyson model of the cell cycle.

Applications Of The Tachibana Operator On Problems Of Lifts, Abdullah Mağden, Ekrem Kadioğlu, Ari̇f A. Salimov

Turkish Journal of Mathematics

The purpose of the present paper is to study, using the Tachibana operator, the complete lifts of affinor structures along a pure cross-section of the tensor bundle and to investigate their transfers. The results obtained are to some extent similar to results previously established for tangent (cotangent) bundles \lbrack 1\rbrack. However there are various important differences and it appears that the problem of lifting affinor structures to the tensor bundle on the pure cross-section presents difficulties which are not encountered in the case of the tangent (cotangent) bundle.

On Torsion-Free Barely Transitive Groups, Mahmut Kuzucuoğlu

Turkish Journal of Mathematics

B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter question negatively in a special case. Moreover we proved the following: Let $G$ be a simple barely transitive group, and $H$ be a stabilizer of a point. If for a non-identity element $x \in G$, $C_G (x)$ is infinite then, $C_G (x)$ cannot contain $H$.

Multipliers Between Orlicz Sequence Spaces, P. B. Djakov, M. S. Ramanuan

Turkish Journal of Mathematics

Let $M, N $ be Orlicz functions, and let $D(\ell_M , \ell_N ) $ be the space of all diagonal operators (that is multipliers) acting between the Orlicz sequence spaces $\ell_M$ and $\ell_N$. We prove that the space of multipliers $D(\ell_M , \ell_N )$ coincides with (and is isomorphic to) the Orlicz sequence space $ \ell_{M_N^{*}} ,$ where $ M_N^{*} $ is the Orlicz function defined by $M_N^{*}(\lambda ) = \sup \{ N(\lambda x) - M(x), \; x \in (0,1) \}$.

On The Metabelian Local Artin Map I: Galois Conjugation Law, Kazim İlhan İkeda

Turkish Journal of Mathematics

It is proved that, for a (henselian) local field $K$ and for a fixed Lubin-Tate splitting $\phi$ over $K$, the metabelian local Artin map (?, $K)_{\phi}: B(K, \phi) \tilde{\rightarrow} Gal (K^{(ab)^2} / K)$ satisfies the Galois conjugation law $$(\tilde{\sigma}^+(\alpha), \sigma (K))_{\tilde{\sigma}\phi\tilde{\sigma}^{-1}} = \tilde{\sigma} _{K^{(ab)^2}} (\alpha, K)_{\phi}\tilde{\sigma}^{-1} _{\tilde{\sigma}(K^{(ab)^2})}$$ for any $\alpha \in B(K, \phi)$, and for any embedding $\sigma : K \hookrightarrow K^{sep}$, where $\tilde{\sigma} \in$ Aut $(K^{sep}$) is a fixed extension to $K^{sep}$ of the embedding $\sigma : K \hookrightarrow K^{sep}$.

Representing Systems Of Exponentials And Projection On Initial Data In The Cauchy Problem, Yu. F. Korobeinik

Turkish Journal of Mathematics

The Cauchy problem for the equation \begin{equation} Mw\equiv \sum_{j=0}^m\sum_{s=0}^{l_j}a_{s,j}\frac{\partial^{s+j}w(z_1,z_2)}{\partial z_1^s\partial z_2^j}=0 \end{equation} \begin{equation} \frac{\partial^nw(z_1,z_2)}{\partial z_2^n}\mid_{z_{2}=0}=\varphi_n(z_1), n=0,1,\ldots , m-1 \end{equation} is investigated under the condition $l_j\leq l_m, j=0,1,\ldots,m-1$. It is shown that the operator of projection of solution of (1) on its initial data (2) in a definite situation has a linear continuous right inverse which can be determined effectively with the help of representing systems of exponentials in the space of initial data.