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Articles 1021 - 1050 of 1334
Full-Text Articles in Mathematics
Examples Of Self-Dual Codes Over Some Sub-Hopf Algebras Of The Steenrod Algebra, Tane Vergi̇li̇, İsmet Karaca
Examples Of Self-Dual Codes Over Some Sub-Hopf Algebras Of The Steenrod Algebra, Tane Vergi̇li̇, İsmet Karaca
Turkish Journal of Mathematics
Codes over the finite sub-Hopf algebras $A(n)$ of the (mod 2) Steenrod algebra $\mathcal{A}$ were studied by Dougherty and Vergili. In this paper we study some Euclidean and Hermitian self-dual codes over $A(n)$ by considering Milnor basis elements.
The $T$-Successive Associated Stirling Numbers, $T$-Fibonacci--Stirling Numbers, And Unimodality, Hacene Belbachir, Assia-Fettouma Tebtoub
The $T$-Successive Associated Stirling Numbers, $T$-Fibonacci--Stirling Numbers, And Unimodality, Hacene Belbachir, Assia-Fettouma Tebtoub
Turkish Journal of Mathematics
Using a combinatorial approach, we introduce the \textit{$t$-successive associated Stirling numbers} and we give the recurrence relation and the generating function. We also establish the unimodality of sequence $\genfrac{\{}{\}}{0pt}{}{n-2k}{k}_{k}$ lying over a ray of the second kind's Stirling triangle. Some combinatorial identities are given.
On Tetravalent Normal Edge-Transitive Cayley Graphs On The Modular Group, Hesam Sharifi, Mohammad Reza Darafsheh
On Tetravalent Normal Edge-Transitive Cayley Graphs On The Modular Group, Hesam Sharifi, Mohammad Reza Darafsheh
Turkish Journal of Mathematics
A Cayley graph $\Gamma=Cay(G, S)$ on a group $G$ with respective toa subset $S\subseteq G$, $S=S^{-1}, 1\notın S$, is said to be normaledge-transitive if $N_{\mathbb{A}ut(\Gamma)}(\rho(G))$ is transitiveon edges of $\Gamma$, where $\rho(G)$ is a subgroup of $\mathbb{A}ut(\Gamma)$isomorphic to $G$. We determine all connected tetravalent normaledge-transitive Cayley graphs on the modular group of order $8n$in the case that every element of $S$ is of order $4n$.
Tetravalent Normal Edge-Transitive Cayley Graphs On A Certain Group Of Order $6n$, Mohammad Reza Darafsheh, Maysam Yaghoobian
Tetravalent Normal Edge-Transitive Cayley Graphs On A Certain Group Of Order $6n$, Mohammad Reza Darafsheh, Maysam Yaghoobian
Turkish Journal of Mathematics
Let $U_{6n}= \langle a,b a^{2n}=b^{3}=1,a^{-1}ba=b^{-1}\rangle $ be a groupof order 6n. In this paper tetravalent normal edge-transitive Cayleygraphs on $U_{6n}$ are considered. In this way several nonequivalent normaledge-transitive Cayley graphs on $U_{6n}$ are obtained whose automorphismgroups are given exactly.
Sufficient Conditions For The Compactifiability Of A Closed One-Form Foliation, Irina Gelbukh
Sufficient Conditions For The Compactifiability Of A Closed One-Form Foliation, Irina Gelbukh
Turkish Journal of Mathematics
We study the foliation defined by a closed $1$-form on a connected smooth closed orientable manifold.We call such a foliation compactifiable if all its leaves are closed in the complement of the singular set.In this paper, we give sufficient conditions for compactifiability of the foliation in homological terms.We also show that under these conditions, the foliation can be defined by closed $1$-forms with the ranks of their groups of periods in a certain range.In addition, we describe the structure of the group generated by the homology classes of all compact leaves of the foliation.
Optimality Conditions Via Weak Subdifferentials In Reflexive Banach Spaces, Sara Hassani, Musa Mammadov, Mina Jamshidi
Optimality Conditions Via Weak Subdifferentials In Reflexive Banach Spaces, Sara Hassani, Musa Mammadov, Mina Jamshidi
Turkish Journal of Mathematics
In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are investigated. It partly generalizes several related results obtained for finite dimensional spaces.
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Turkish Journal of Mathematics
Let $ (X,d,\preceq) $ be a partially ordered ultrametric space and $ f:X\to X $ a single valued mapping. We obtain sufficient conditions for the existence of a fixed point for the strongly contractive mapping $ f $. We also investigate the existence of a fixed point for strongly contractive mappings defined on partially ordered non-Archimedean normed spaces under the same conditions. Finally, we give some examples to discuss the assumptions of the theorems.
More Characterizations Of Dedekind Domains And V-Rings, Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
More Characterizations Of Dedekind Domains And V-Rings, Thuat Van Do, Hai Dinh Hoang, Samruam Baupradist
Turkish Journal of Mathematics
In this paper, cyclic $c-$injective modules are introduced and investigated. It is shown that a commutative Noetherian domain is Dedekind if and only if every simple module is cyclic $c-$injective. Finally, it is shown that injectivity, principal injectivity, mininjectivity, and simple injectivity are all equal to characterize right V-rings, right GV-rings, right pV-rings, and WV-rings.
Maximal Subsemigroups And Finiteness Conditions On Transformation Semigroups With Fixed Sets, Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Maximal Subsemigroups And Finiteness Conditions On Transformation Semigroups With Fixed Sets, Yanisa Chaiya, Preeyanuch Honyam, Jintana Sanwong
Turkish Journal of Mathematics
Let $Y$ be a fixed subset of a nonempty set $X$ and let $Fix(X,Y)$ be the set of all self maps on $X$ which fix all elements in $Y$. Then under the composition of maps, $Fix(X,Y)$ is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of $Fix\left(X,Y\right)$ and these maximal subsemigroups coincide with the maximal regular subsemigroups when $X\setminus Y$ is a finite set with $ X\setminus Y \geq 2$. We also give necessary and sufficient conditions for $Fix(X,Y)$ to be factorizable, unit-regular, and directly finite.
Dynamic Shum Inequalities, Ravi Agarwal, Martin Bohner, Donal O'Regan, Samir Saker
Dynamic Shum Inequalities, Ravi Agarwal, Martin Bohner, Donal O'Regan, Samir Saker
Turkish Journal of Mathematics
Recently, various forms and improvements of Opial dynamic inequalities have been given in the literature. In this paper, we give refinements of Opial inequalities on time scales that reduce in the continuous case to classical inequalities named after Beesack and Shum. These refinements are new in the important discrete case.
Correcting A Paper On The Randic And Geometric-Arithmetic Indices, Toufik Mansour, Mohammad Ali Rostami, Suresh Elumalai, Britto Antony Xavier
Correcting A Paper On The Randic And Geometric-Arithmetic Indices, Toufik Mansour, Mohammad Ali Rostami, Suresh Elumalai, Britto Antony Xavier
Turkish Journal of Mathematics
The Randic index $(R)$ and the geometric--arithmetic index $(GA)$ are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randic and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randic and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6.
Extensions Of Quasipolar Rings, Orhan Gürgün
Extensions Of Quasipolar Rings, Orhan Gürgün
Turkish Journal of Mathematics
An associative ring with identity is called quasipolar provided that for each $a\in R$ there exists an idempotent $p\in R$ such that $p\in comm^2(a)$, $a+p\in U(R)$ and $ap\in R^{qnil}$. In this article, we introduce the notion of quasipolar general rings (with or without identity). Some properties of quasipolar general rings are investigated. We prove that a general ring $I$ is quasipolar if and only if every element $a\in I$ can be written in the form $a=s+q$ where $s$ is strongly regular, $s\in comm^2(a)$, $q$ is quasinilpotent, and $sq=qs=0$. It is shown that every ideal of a quasipolar general ring is …
Sampling Theorem By Green's Function In A Space Ofvector-Functions, Hassan Atef Hassan
Sampling Theorem By Green's Function In A Space Ofvector-Functions, Hassan Atef Hassan
Turkish Journal of Mathematics
In this paper we give a sampling expansion for integral transforms whose kernels arise from Green's function of differential operators in a space of vector-functions. The differential operators are in a space of dimension $m$ and consist of systems of $m$ equations in $m$ unknowns. We assume the simplicity of the eigenvalues.
On A Family Of Saturated Numerical Semigroups With Multiplicity Four, Meral Süer, Sedat İlhan
On A Family Of Saturated Numerical Semigroups With Multiplicity Four, Meral Süer, Sedat İlhan
Turkish Journal of Mathematics
In this study, we will give some results on Arf numerical semigroups of multiplicity four generated by $\left\{ 4,k,k+1,k+2\right\} $ where $k$ is an integer not less than $5$ and $k\equiv 1(\mbox{mod } 4)$.
New Statistical Randomness Tests: 4-Bit Template Matching Tests, Fati̇h Sulak
New Statistical Randomness Tests: 4-Bit Template Matching Tests, Fati̇h Sulak
Turkish Journal of Mathematics
For cryptographic algorithms, secret keys should be generated randomly as the security of the system depends on the key and therefore generation of random sequences is vital. Randomness testing is done by means of statistical randomness tests. In this work, we show that the probabilities for the overlapping template matching test in the NIST test suite are only valid for a specific template and need to be recalculated for the other templates. We calculate the exact distribution for all 4-bit templates and propose new randomness tests, namely template matching tests. The new tests can be applied to any sequence of …
$\Mathcal{W}$-Gorenstein Objects In Triangulated Categories, Chaoling Huang, Kaituo Liu
$\Mathcal{W}$-Gorenstein Objects In Triangulated Categories, Chaoling Huang, Kaituo Liu
Turkish Journal of Mathematics
We fix a proper class of triangles $\xi$ in a triangulated category $\mathcal{C}$. Let $\mathcal{W}$ be a class of objects in $\mathcal{C}$ such that $\xi xt^i_\xi(W,\ W')=0$ for all $W, W'\in\mathcal{W}$ and all $i\geq 1$. In this paper, we introduce the notion of $\mathcal{W}$-Gorenstein objects and $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object in $\mathcal{C}$ and study the properties of $\mathcal{W}$-Gorenstein objects and characterize the finite $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object. Some applications are given.
Near Optimal Step Size And Momentum In Gradient Descent For Quadratic Functions, Engi̇n Taş, Memmedağa Memmedli̇
Near Optimal Step Size And Momentum In Gradient Descent For Quadratic Functions, Engi̇n Taş, Memmedağa Memmedli̇
Turkish Journal of Mathematics
Many problems in statistical estimation, classification, and regression can be cast as optimization problems. Gradient descent, which is one of the simplest and easy to implement multivariate optimization techniques, lies at the heart of many powerful classes of optimization methods. However, its major disadvantage is the slower rate of convergence with respect to the other more sophisticated algorithms. In order to improve the convergence speed of gradient descent, we simultaneously determine near-optimal scalar step size and momentum factor for gradient descent in a deterministic quadratic bowl from the largest and smallest eigenvalues of the Hessian. The resulting algorithm is demonstrated …
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
Turkish Journal of Mathematics
In this note, we study topologically transitive and hypercyclic composition operators on $C_p(X)$ or $C_k(X)$. We prove that if $G$ is a semigroup of continuous self maps of a countable metric space $X$ with the following properties: (1) every element of $G$ is one-to-one on $X$, (2) the action of $G$ is strongly run-away on $X$, then the action of $\hat{G}$ on $C_p(X)$ is topologically transitive and hypercyclic. If $G$ is the set of all one-to-one and continuous self maps of $\mathbb{R}\setminus \mathbb{Z}$, then the action of $\hat{G}$ on $C_k(\mathbb{R}\setminus \mathbb{Z})$ is hypercyclic. We also show that the action of …
Free Storage Basis Conversion Over Finite Fields, Ersan Akyildiz, Ndangang Yampa Harold, Ahmet Sinak
Free Storage Basis Conversion Over Finite Fields, Ersan Akyildiz, Ndangang Yampa Harold, Ahmet Sinak
Turkish Journal of Mathematics
Representation of a field element plays a crucial role in the efficiency of field arithmetic. If an efficient representation of a field element in one basis exists, then field arithmetic in the hardware and/or software implementations becomes easy. Otherwise, a basis conversion to an efficient one is searched for easier arithmetic. However, this conversion often brings a storage problem for transition matrices associated with these bases. In this paper, we study this problem for conversion between normal and polynomial bases in the extension field $\mathbb{F}_{q^p}$ over $\mathbb{F}_q$ where $q=p^n$. We construct transition matrices that are of a special form. This …
Quasi-Metric Trees And $Q$-Hyperconvex Hulls, Zechariah Mushaandja, Olivier Olela Otafudu
Quasi-Metric Trees And $Q$-Hyperconvex Hulls, Zechariah Mushaandja, Olivier Olela Otafudu
Turkish Journal of Mathematics
The investigation of metric trees began with J. Tits in 1977. Recently we studied a more general notion of quasi-metric tree. In the current article we prove, among other facts, that the $q$-hyperconvex hull of a $q$-hyperconvex $T_0$-quasi-metric tree is itself a $T_0$-quasi-metric tree. This is achieved without using the four-point property, a geometric concept used by Aksoy and Maurizi to show that every complete metric tree is hyperconvex.
Lie Symmetry Analysis And Exact Solutions Of The Sawada-Kotera Equation, Youwei Zhang
Lie Symmetry Analysis And Exact Solutions Of The Sawada-Kotera Equation, Youwei Zhang
Turkish Journal of Mathematics
In the present paper, the Sawada-Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada-Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada-Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equation.
Dirac Systems With Regular And Singular Transmission Effects, Eki̇n Uğurlu
Dirac Systems With Regular And Singular Transmission Effects, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl's limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax-Phillips scattering function and Sz-Nagy-Foiaş characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.
A Mehrotra Predictor-Corrector Interior-Point Algorithm For Semidefinite Optimization, Mohammad Pirhaji, Maryam Zangiabadi, Hossein Mansouri
A Mehrotra Predictor-Corrector Interior-Point Algorithm For Semidefinite Optimization, Mohammad Pirhaji, Maryam Zangiabadi, Hossein Mansouri
Turkish Journal of Mathematics
This paper proposes a second-order Mehrotra-type predictor-corrector feasible interior-point algorithm for semidefinite optimization problems. In each iteration, the algorithm computes the Newton search directions through a new form of combination of the predictor and corrector directions. Using the Ai-Zhang wide neighborhood for linear complementarity problems, it is shown that the complexity bound of the algorithm is $O(\sqrt{n}\log \varepsilon^{-1})$ for the Nesterov-Todd search direction and $O({n}\log \varepsilon^{-1})$ for the Helmberg-Kojima-Monteiro search directions.
On The Attached Prime Ideals Of Localcohomology Modules Defined By A Pair Of Ideals, Zohreh Habibi, Maryam Jahangiri, Khadijeh Ahmadi Amoli
On The Attached Prime Ideals Of Localcohomology Modules Defined By A Pair Of Ideals, Zohreh Habibi, Maryam Jahangiri, Khadijeh Ahmadi Amoli
Turkish Journal of Mathematics
Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. For each $i\in N_0$ let $H^{i}_{I,J}(-)$ denote the $i$-th right derived functor of $\Gamma_{I,J}(-)$, where $\Gamma _{I,J}(M):=\{x \in M : I^{n}x\subseteq Jx \ \text {for} \ n\gg 1\}$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the concept of co-localization. Moreover, we illustrate the attached prime ideals of $H^{t}_{I,J}(M)$ on a nonlocal ring $R$, for $t= \dim M$ and $t= (I,J,M)$, where $(I,J,M)$ is the …
On Orthogonal Systems Of Shifts Of Scaling Function On Local Fields Of Positive Characteristic, Gleb Sergeevich Berdnikov, Iuliia Sergeevna Kruss, Sergey Fedorovich Lukomskii
On Orthogonal Systems Of Shifts Of Scaling Function On Local Fields Of Positive Characteristic, Gleb Sergeevich Berdnikov, Iuliia Sergeevna Kruss, Sergey Fedorovich Lukomskii
Turkish Journal of Mathematics
We present a new method for constructing an orthogonal step scaling function on local fields of positive characteristic, which generates multiresolution analysis.
Existence Of Unpredictable Solutions And Chaos, Marat Akhmet, Mehmet Onur Fen
Existence Of Unpredictable Solutions And Chaos, Marat Akhmet, Mehmet Onur Fen
Turkish Journal of Mathematics
Recently we introduced the concept of Poincaré chaos. In the present paper, by means of the Bebutov dynamical system, an unpredictable solution is considered as a generator of the chaos in a quasilinear system. The results can be easily extended to different types of differential equations. An example of an unpredictable function is provided. A proper irregular behavior in coupled Duffing equations is observed through simulations.
Exponent Of Local Ring Extensions Of Galois Rings And Digraphs Of The $K$Th Power Mapping, Ittiwat Tocharoenirattisai, Yotsanan Meemark
Exponent Of Local Ring Extensions Of Galois Rings And Digraphs Of The $K$Th Power Mapping, Ittiwat Tocharoenirattisai, Yotsanan Meemark
Turkish Journal of Mathematics
In this paper, we consider a local extension $R$ of the Galois ring of the form $GR(p^{n},d)[x]/(f(x)^{a})$, where $n,d$, and $a$ are positive integers; $p$ is a prime; and $f(x)$ is a monic polynomial in $GR(p^{n},d)[x]$ of degree $r$ such that the reduction $\overline{f}(x)$ in $\mathbb{F}_{p^{d}}[x]$ is irreducible. We establish the exponent of $R$ without complete determination of its unit group structure. We obtain better analysis of the iteration graphs $G^{(k)}(R)$ induced from the $k$th power mapping including the conditions on symmetric digraphs. In addition, we work on the digraph over a finite chain ring $R$. The structure of $G^{(k)}_{2}(R)$ …
Topological Entropies Of A Class Of Constrained Systems, Yanni Ma, Bingzhe Hou
Topological Entropies Of A Class Of Constrained Systems, Yanni Ma, Bingzhe Hou
Turkish Journal of Mathematics
In this paper, we consider a class of constrained systems named double upper bounds $(p,q)$-constrained systems ($(p,q)$-DUB systems in brief), which are one-dimensional subshifts of finite type. We determinate the topological entropies (Shannon capacities) $C(p,q)$ of all $(p,q)$-DUB systems and consequently order all $(p,q)$-DUB systems according to the size of topological entropies. In particular, $C(p, \infty)=C(p+1, p+1)$ are the only equalities possible among the topological entropies of $(p,q)$-DUB systems.
Koebe Sets For The Class Of Functions Convex In Two Directions, Leopold Koczan, Pawel Zaprawa
Koebe Sets For The Class Of Functions Convex In Two Directions, Leopold Koczan, Pawel Zaprawa
Turkish Journal of Mathematics
In this paper, we consider a class $K_\alpha$ of all functions $f$ univalent in the unit disk $\Delta$ that are normalized by $f(0)=f'(0)-1=0$ while the sets $f(\Delta)$ are convex in two symmetric directions: $e^{i\alpha\pi/2}$ and $e^{-i\alpha\pi/2}$, $\alpha\in[0,1]$. It means that the intersection of $f(\Delta)$ with each straight line having the direction $e^{i\alpha\pi/2}$ or $e^{-i\alpha\pi/2}$ is either a compact set or an empty set. We find the Koebe set for $K_\alpha$. Moreover, we perform the same operation for functions in $K_{\beta, \gamma}$, i.e. for functions that are convex in two fixed directions: $e^{i\beta\pi/2}$ and $e^{i\gamma\pi/2}$, $-1\leq \beta\leq\gamma \leq 1$.
Warped Product Spaces With Ricci Conditions, Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi
Warped Product Spaces With Ricci Conditions, Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi
Turkish Journal of Mathematics
In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.