Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Some Properties of Rickart Modules(Ankara Üniversitesi, 2012) Üngör, Burcu; Kafkas, Gizem; Halıcıoğlu, Sait; Harmancı, AbdullahR birimli bir halka, M saº g R-mod¸l ve M nin endomorÖzma halkas¨ S = EndR(M) olsun. Her f 2 S iÁin rM(f) = eM olacak biÁimde e2 = e 2 S varsa (denk olarakKerf,Mmod¸l¸n¸nbirdirekttoplanan¨ise)MyeRickartmod¸lad¨verilmi?stir[8]. BuÁal¨?smadaRickartmod¸llerinˆzellikleriincelenmeyedevamedilmi?stir. M birRickart mod¸l olmak ¸zere, M nin S-kat¨ (s¨ras¨yla S-indirgenmi?s, S-simetrik, S-yar¨ deºgi?smeli, S-Armendariz)mod¸l olmas¨ iÁin gerek ve yeter ?sart¨n S nin kat¨ (s¨ras¨yla indirgenmi?s, simetrik, yar¨ deºgi?smeli, Armendariz) halka olduºgu gˆsterilmi?stir. M[x], S[x] halkas¨na gˆre Rickart mod¸l iken M nin de Rickart mod¸l oldugu,tersinin M nin S-Armendariz olmas¨ durumunda doºgru olduºgu ispatlanm¨?st¨r. Ayrıca bir M mod¸l¸n¸n Rickart ol- mas¨iÁingerekveyeter?sart¨nhersaºgmod¸l¸nM-temelprojektifolduºgueldeedilmi?stir.Article Citation - WoS: 4Relativistic Burgers and Nonlinear Schrödinger Equations(Pleiades Publishing, 2009) Pashaev, OktayWe construct relativistic complex Burgers-Schrodinger and nonlinear Schrodinger equations. In the nonrelativistic limit, they reduce to the standard Burgers and nonlinear Schrodinger equations and are integrable through all orders of relativistic corrections.Article Citation - WoS: 8Citation - Scopus: 7Time-Evolution of Squeezed Coherent States of a Generalized Quantum Parametric Oscillator(American Institute of Physics, 2019) Atılgan Büyükaşık, Şirin; Çayiç, ZehraTime evolution of squeezed coherent states for a quantum parametric oscillator with the most general self-adjoint quadratic Hamiltonian is found explicitly. For this, we use the unitary displacement and squeeze operators in coordinate representation and the evolution operator obtained by the Wei-Norman Lie algebraic approach. Then, we analyze squeezing properties of the wave packets according to the complex parameter of the squeeze operator and the time-variable parameters of the Hamiltonian. As an application, we construct all exactly solvable generalized quantum oscillator models classically corresponding to a driven simple harmonic oscillator. For each model, defined according to the frequency modification in position space, we describe explicitly the squeezing and displacement properties of the wave packets. This allows us to see the exact influence of all parameters and make a basic comparison between the different models.Article Locally Isomorphic Torsionless Modules Over Domains of Finite Character(World Scientific Publishing, 2019) Saylam, Başak Ay; Klingler, LeeIn a 2002 paper, P. Goeters and B. Olberding compare local, near, and stable isomorphisms of torsionless modules over h-local domains. In this paper, we compare these weaker forms of isomorphisms of torsionless modules over domains of finite character.Article Citation - WoS: 8Citation - Scopus: 8On the Structure of Modules Defined by Subinjectivity(World Scientific Publishing, 2019) Altınay, Ferhat; Büyükaşık, Engin; Durgun, YılmazThe aim of this paper is to present new results and generalize some results about indigent modules. The commutative rings whose simple modules are indigent or injective are fully determined. The rings whose cyclic right modules are indigent are shown to be semisimple Artinian. We give a complete characterization of indigent modules over commutative hereditary Noetherian rings. We show that a reduced module is indigent if and only if it is a Whitehead test module for injectivity over commutative hereditary noetherian rings. Furthermore, Dedekind domains are characterized by test modules for injectivity by subinjectivity.Article On the Number of Bound States of Semirelativistic Hamiltonian With Dirac Delta Potentials in One Dimension(National Research Council of Canada, 2018) Erman, FatihWe study the bound state problem for semirelativistic N attractive Dirac delta-potentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it.Article Rings and Modules Characterized by Opposites of Fp-Injectivity(Korean Mathematical Society, 2019) Büyükaşık, Engin; Kafkas Demirci, GizemLet R be a ring with unity. Given modules M-R and N-R, M-R is said to be absolutely N-R-pure if M circle times N -> L circle times N is a monomorphism for every extension L-R of M-R. For a module M-R, the subpurity domain of M-R is defined to be the collection of all modules N-R such that M-R is absolutely N-R-pure. Clearly M-R is absolutely F-R-pure for every flat module F-R, and that M-R is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, M-R is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. R-R is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is Priifer if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.Article Citation - WoS: 2Citation - Scopus: 2Integrally Closed Rings Which Are Prufer(Taylor and Francis Ltd., 2019) Ay Saylam, BaşakLet R be a commutative ring with zero divisors. It is well known that if R is integrally closed, then R is a Prufer domain if and only if there is an integer n > 1 such that, for all . We soften this result for commutative rings with zero divisors by proving that this integer n does not have to work for all a, b is an element of R.Article Citation - WoS: 2Citation - Scopus: 2Well Posedness Conditions for Planar Conewise Linear Systems(SAGE Publications Inc., 2019) Şahan, Gökhan; Eldem, VasfiIn this study, we give well-posedness conditions for planar conewise linear systems where the vector field is not necessarily continuous. It is further shown that, for a certain class of planar conewise linear systems, well posedness is independent of the conic partition of R-2. More specifically, the system is well posed for any conic partition of R-2.Article Citation - WoS: 11Citation - Scopus: 11Squeezing and Resonance in a Generalized Caldirola-Kanai Type Quantum Parametric Oscillator(American Institute of Physics, 2018) Atılgan Büyükaşık, ŞirinThe evolution operator of a Caldirola-Kanai type quantum parametric oscillator with a generalized quadratic Hamiltonian is obtained using the Wei-Norman Lie algebraic approach, and time evolution of the eigenstates of a harmonic oscillator and Glauber coherent states is found explicitly. Behavior of this oscillator is investigated under the influence of the external mixed term B(t)(qp+pq)/2, which affects the squeezing properties of the wave packets, and linear terms D0(t)q, E0(t)p responsible for their displacement in time. According to this, we construct all exact quantum models with different parameters B(t), for which the structure of the Caldirola-Kanai oscillator in position space is preserved. Then, for each model, we obtain explicit solutions and analyze the squeezing and displacement properties of the wave packets according to the frequency modification by B(t) and periodic forces in the corresponding classical equation of motion.