A Note On Dynamics In Functional Spaces,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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,
2017
TÜBİTAK
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.
Minimizing Graph Of The Connected Graphs Whose Complements Are Bicyclic With Two Cycles,
2017
TÜBİTAK
Minimizing Graph Of The Connected Graphs Whose Complements Are Bicyclic With Two Cycles, Muhammad Javaid
Turkish Journal of Mathematics
In a certain class of graphs, a graph is called minimizing if the least eigenvalueof its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, we characterize the minimizinggraph among all the connected graphs that belong to a class of graphs whose complements are bicyclic with two cycles.
A Note On The Conjugacy Problem For Finite Sylow Subgroups Of Linear Pseudofinite Groups,
2017
TÜBİTAK
A Note On The Conjugacy Problem For Finite Sylow Subgroups Of Linear Pseudofinite Groups, Pinar Uğurlu Kowalski̇
Turkish Journal of Mathematics
We prove the conjugacy of Sylow $2$-subgroups in pseudofinite $\mathfrak{M}_c$ (in particular linear) groups under the assumption that there is at least one finite Sylow $2$-subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with nonconjugate finite Sylow $2$-subgroups, which was constructed by Platonov.
On The Extended Spectrum Of Some Quasinormal Operators,
2017
TÜBİTAK
On The Extended Spectrum Of Some Quasinormal Operators, Meltem Sertbaş, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this paper we consider some extended eigenvalue problems for some quasinormal operators. The spectrum of an algebra homomorphism defined by a compact normal operator is also investigated.
More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications,
2017
TÜBİTAK
More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications, Mario Krnic, Josip Pecaric, Mirna Rodic
Turkish Journal of Mathematics
In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive.The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means.
Some Notes On $Gqn$ Rings,
2017
TÜBİTAK
Some Notes On $Gqn$ Rings, Long Wang, Junchao Wei
Turkish Journal of Mathematics
A ring $R$ is called ageneralized quasinormal ring (abbreviated as $GQN$ ring) if $ea∈N(R)$ for each $e∈ E(R)$ and $a∈ N(R)$. The class of $GQN$ rings is a proper generalization of quasinormal rings and $NI$ rings. Many properties of quasinormal rings are extended to $GQN$ rings. For a$GQN$ ring $R$ and $a∈ R$, it is shown that:1) if $a$ is a regular element, then $a$ is a strongly regular element;2) if $a$ is an exchange element, then $a$ is clean;3) if $R$ is a semiperiodic ring with $J(R)\neq N(R)$, then $R$ is commutative;4) if $R$ is an $MVNR$, then $R$ …
A Novel Kind Of Akns Integrable Couplings And Their Hamiltonian Structures,
2017
TÜBİTAK
A Novel Kind Of Akns Integrable Couplings And Their Hamiltonian Structures, Yu-Juan Zhang, Wen-Xiu Ma, Ömer Ünsal
Turkish Journal of Mathematics
We present a novel hierarchy of AKNS integrable couplings based on a specific semidirect sum of Lie algebras associated with sl$(2)$. By applying the variational identity, we derive a bi-Hamiltonian structure of the resulting coupling systems, thereby showing their Liouville integrability.
Modules Satisfying Double Chain Condition On Nonfinitely Generated Submodules Have Krull Dimension,
2017
TÜBİTAK
Modules Satisfying Double Chain Condition On Nonfinitely Generated Submodules Have Krull Dimension, Maryam Davoudian
Turkish Journal of Mathematics
We prove the result in the title. We study submodules $N$ of a module $M$ such that whenever $\frac{M}{N}$ satisfies the double infinite chain condition so does $M$.Moreover, we observe that an $\alpha $-atomic module, where $\alpha\geq 2$ is an ordinal number, satisfies the previous chain if and only if it satisfies the descending chain condition on nonfinitely generated submodules.
