TR-Dizin

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14411/21

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Characterizations of the Commutators Involving Idempotents in Certain Subrings of $m_{2}(\\mathbb{z})$
(2023) Gümüşel, Günseli; Özdın, Tufan
In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]$ = $E_1E_2 − E_2E_1$ involving idempotents $E_1, E_2$ in certain subrings of $M_2(Z)$.
Citation - WoS: 16
Citation - Scopus: 20
Common Fixed Point Theorems in Cone Banach Spaces
(Hacettepe Univ, Fac Sci, 2011) Abdeljawad, Thabet; Karapinar, Erdal; Tas, Kenan; Mathematics
Recently, E. Karapinar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.
Citation - WoS: 4
Citation - Scopus: 5
Construction of a Complex Jacobi Matrix From Two-Spectra
(Hacettepe Univ, Fac Sci, 2011) Guseinov, Gusein Sh; Mathematics
In this paper we study the inverse spectral problem for two-spectra of finite order complex Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by deleting the first column and the first row of the Jacobi matrix. An explicit procedure of reconstruction of the matrix from the two-spectra is given.
Citation - WoS: 1
Citation - Scopus: 2
A Convergent Two-Level Linear Scheme for the Generalized Rosenau–kdv–rlw Equation
(Tubitak Scientific & Technological Research Council Turkey, 2019) Aydın, Ayhan
A new convergent two-level finite difference scheme is proposed for the numerical solution of initial valueproblem of the generalized Rosenau–KdV–RLW equation. The new scheme is second-order, linear, conservative, andunconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solutionis studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence ofthe scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating thesolitary wave graph of the equation. Wave generation subject to initial Gaussian condition has been studied numerically.Different wave generations are observed depending on the dispersion coefficients and the nonlinear advection term.Numerical experiments indicate that the present scheme is conservative, efficient, and of high accuracy, and well simulatesthe solitary waves for a long time.
A COUPLED FIXED POINT RESULT IN PARTIALLY ORDERED PARTIAL METRIC SPACES THROUGH IMPLICIT FUNCTION
(2013) Özyurt, Selma Gülyaz; Karapınar, Erdal
In this manuscript, we discuss the existence of coupled fixed points inthe context of partially ordered metric spaces through implicit relationsfor mappings F : X× X -> X such that F has the mixed monotoneproperty. Our main theorem improves and extends various results inthe literature. We also state an example to illustrate our work
Citation - WoS: 6
Citation - Scopus: 6
Dynamic Reliability and Performance Evaluation of Multi-State Systems With Two Components
(Hacettepe Univ, Fac Sci, 2011) Eryilmaz, Serkan; Industrial Engineering
In this paper we study multi-state systems consisting of two components when the number of system states and the number of states of each component are the same, i.e. the systems under consideration are homogeneous multi-state systems. In particular we evaluate multi-state series and cold standby systems assuming that the degradation in their components follow a Markov process. The behaviour of systems with respect to degradation rates is also investigated in terms of stochastic ordering.
Citation - WoS: 6
Citation - Scopus: 6
Exact and Nonstandard Finite Difference Schemes for the Burgers Equation B(2, 2)
(Tubitak Scientific & Technological Research Council Turkey, 2021) Köroğlu, Canan; Aydın, Ayhan
In this paper, we consider the Burgers equation B(2, 2) . Exact and nonstandard finite difference schemes(NSFD) for the Burgers equation B(2, 2) are designed. First, two exact finite difference schemes for the Burgers equationB(2, 2) are proposed using traveling wave solution. Then, two NSFD schemes are represented for this equation. Thesetwo NSFD schemes are compared with a standard finite difference (SFD) scheme. Numerical results show that the NSFDschemes are accurate and efficient in the numerical simulation of the kink-wave solution of the B(2, 2) equation. We seethat although the SFD scheme yields numerical instability for large step sizes, NSFD schemes provide reliable results forlong time integration. Local truncation errors show that the NSFD schemes are consistent with the B(2, 2) equation.
An Exhaustive Computer Search for Finding New Curves With Many Points Among Fibre Products of Two Kummer Covers Over $\\bbb{f}_5$ and $\\bbb{f}_7$
(2013) Özbudak, Ferruh; Temür, Burcu Gülmez; Yayla, Oğuz
In this paper we make an exhaustive computer search for finding new curves with many points among fibre products of 2 Kummer covers of the projective line over F5 and F7 . At the end of the search, we have 12 records and 6 new entries for the current Table of Curves with Many Points. In particular, we observe that the fibre product $y^3_1$ = $\\frac {5(x+2)(x +5)} {x}$, $y^3_2$ $\\frac {3x^2(x +5)} {x + 3}$ over F7 has genus 7 with 36 rational points. As this coincides with the Ihara bound, we conclude that the maximum number N7 (7) of F7 -rational points among all curves of genus 7 is 36. Our exhaustive search has been possible because of the methods given in the recent work by Özbudak and Temür (2012) for determining the number of rational points of such curves.
An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse
(2010) Faydaoğlu, Şerife; Guseınov, Gusein Sh.
The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.
Fedja’s Proof of Deepti’s Inequality
(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet
The paper aims to present, in a systematic way, an elegant proof of Deepti’s inequality. Both the inequalityand various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none haveappeared in the literature thus far. In this work, suggestions pertaining to users ‘Deepti’ and ‘fedja’ are traced, whencethe title. The results or the paper are new, and the proof is divided into a series of statements, many of which are ofinterest in themselves.
Citation - Scopus: 2
Field Extensions Having the Unique Subfield Property, and G-Cogalois Extensions
(2002) Albu,T.
We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the unique subfield property, and prove that these extensions are precisely the simple G-Cogalois extensions with a cyclic Kneser group. © TÜBİTAK.
An Integrated Intuitionistic Fuzzy Multi Criteria Decision Making Method for Facility Location Selection
(2011) Boran, Fatih Emre
The facility location selection, which is one of the important activities in strategic planning for a wide range of private and public companies, is a multi-criteria decision making problem including both quantitative and qualitative criteria. Traditional methods for facility location selection can not be effectively handled because information can not be represented by precise information under many conditions. This paper proposes the integration of intuitionistic fuzzy preference relation aiming to obtain weights of criteria and intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method aiming to rank alternatives for dealing with imprecise information on selecting the most desirable facility location. To illustrate the application of the proposed method, a practical application is given.
Citation - WoS: 1
Citation - Scopus: 2
LS-14 Test Suite for Long Sequences
(Hacettepe Univ, Fac Sci, 2024) Akcengiz, Ziya; Aslan, Melis; Doğanaksoy, Ali; Sulak, Fatih; Uguz, Muhiddin
Random number sequences are used in many branches of science. Because of many techni- cal reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain pat- terns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical ap- proximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collec- tion for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we in- troduce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.
A Note on the Generalized Matsumoto Relation
(2017) Dalyan, Elif; Medetoğulları, Elif; Pamuk, Mehmetcik
We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.
Number fields and divisible groups via model theory
(Tubitak Scientific & Technological Research Council Turkey, 2021) CELIK, Sermin C. A. M.; GORAL, Haydar
In this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.
Number of Pseudo–anosov Elements in the Mapping Class Group of a Four–holed Sphere
(2010) Ozan, Ferihe Atalan; Korkmaz, Mustafa
We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.
On a Class of Permutation Trinomials Over Finite Fields
(Tubitak Scientific & Technological Research Council Turkey, 2024) Temür, Burcu Gülmez; Özkaya, Buket
In this paper, we study the permutation properties of the class of trinomials of the form f (x) = x4q+1 + λ1xq+4 + λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and suﬀicient conditions on λ1 and λ2 such that f (x) permutes Fq2 , where q is odd and q = 22k+1, k ∈
On Pairs of $ell$-Köthe Spaces
(2010) Karapınar, Erdal
Let $ell$ be a Banach sequence space with a monotone norm $parallel centerdot parallel_{ell}$, in which the canonical system ($e_i$) is a normalized unconditional basis. Let $a = (a_i), a_i rightarrow infty, lambda=(lambda_i)$ be sequences of positive numbers. We study the problem on isomorphic classification of pairs $F = biggl(K^{ell} biggl( exp biggl(-frac{1}{p}a_i biggr)biggr),K^{ell}biggl(exp biggl(-frac{1}{p}a_i + lambda_i biggr)biggr)biggr)$. For this purpose, we consider the sequence of so-called m-rectangle characteristics $mu^F_m$. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type $ell$-power series spaces. By using analytic scale and a modification of some invariants (modified compound invariants) it is proven that m-rectangular characteristics are invariant on the class of such pairs. Deriving the characteristic $tilde{beta}$ from the characteristic $beta$, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121–142, 1997).
Citation - WoS: 1
Citation - Scopus: 1
On Some Permutation Trinomials in Characteristic Three
(Hacettepe Univ, Fac Sci, 2025) Temür, Burcu Gülmez; Özkaya, Buket
In this paper, we determine the permutation properties of the polynomial x3 +xq+2 −x4q−1 over the finite field Fq2 in characteristic three. Moreover, we consider the trinomials of the form x4q−1 + x2q+1 ± x3. In particular, we first show that x3 + xq+2 − x4q−1 permutes Fq2 with q = 3m if and only if m is odd. This enables us to show that the suﬃcient condition in [34, Theorem 4] is also necessary. Next, we prove that x4q−1 + x2q+1 − x3 permutes Fq2 with q = 3m if and only if m ̸≡ 0 (mod 4). Consequently, we prove that the suﬃcient condition in [20, Theorem 3.2] is also necessary. Finally, we investigate the trinomial x4q−1 + x2q+1 + x3 and show that it is never a permutation polynomial of Fq2 in any characteristic. All the polynomials considered in this work are not quasi-multiplicative equivalent to any known class of permutation trinomials.
On Strongly Autinertial Groups
(Tubitak Scientific & Technological Research Council Turkey, 2018) Onur, Cansu Betin
A subgroup X of G is said to be inert under automorphisms (autinert) if |X : $X^\\alpha$ ∩ X| is finite for allα ∈ Aut(G) and it is called strongly autinert if | < X, $X^\\alpha$ >: X| is finite for all α ∈ Aut(G). A group is calledstrongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. Wecharacterize such groups for a finitely generated case. Namely, we prove that a finitely generated group G is stronglyautinertial if and only if one of the following hold:i) G is finite;ii) G = ⟨a⟩ ⋉ F where F is a finite subgroup of G and ⟨a⟩ is a torsion-free subgroup of G.Moreover, in the preliminary part, we give basic results on strongly autinert subgroups.

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