Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 3Citation - Scopus: 3Reconstruction of Generalized Impedance Functions for 3d Acoustic Scattering(Academic Press Inc., 2019) Ivanyshyn Yaman, OlhaWe consider the inverse obstacle scattering problem of determining both of the surface impedance functions from far field measurements for a few incident plane waves at a fixed frequency. The reconstruction algorithm we propose is based on an iteratively regularized Newton-type method and nonlinear integral equations. The mathematical foundation of the method is presented and the feasibility is illustrated by numerical examples. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 12Citation - Scopus: 11Poor Modules With No Proper Poor Direct Summands(Academic Press Inc., 2018) Alizade, Rafail; Büyükaşık, Engin; López-Permouth, Sergio; Yang, LiuAs a mean to provide intrinsic characterizations of poor modules, the notion of a pauper module is introduced. A module is a pauper if it is poor and has no proper poor direct summand. We show that not all rings have pauper modules and explore conditions for their existence. In addition, we ponder the role of paupers in the characterization of poor modules over those rings that do have them by considering two possible types of ubiquity: one according to which every poor module contains a pauper direct summand and a second one according to which every poor module contains a pauper as a pure submodule. The second condition holds for the ring of integers and is just as significant as the first one for Noetherian rings since, in that context, modules having poor pure submodules must themselves be poor. It is shown that the existence of paupers is equivalent to the Noetherian condition for rings with no middle class. As indecomposable poor modules are pauper, we study rings with no indecomposable right middle class (i.e. the ring whose indecomposable right modules are pauper or injective). We show that semiartinian V-rings satisfy this property and also that a commutative Noetherian ring R has no indecomposable middle class if and only if R is the direct product of finitely many fields and at most one ring of composition length 2. Structure theorems are also provided for rings without indecomposable middle class when the rings are Artinian serial or right Artinian. Rings for which not having an indecomposable middle class suffices not to have a middle class include commutative Noetherian and Artinian serial rings. The structure of poor modules is completely determined over commutative hereditary Noetherian rings. Pauper Abelian groups with torsion-free rank one are fully characterized.Article Citation - WoS: 18Citation - Scopus: 19Well-Posedness for Nonlinear Schrödinger Equations With Boundary Forces in Low Dimensions by Strichartz Estimates(Academic Press Inc., 2015) Özsarı, TürkerIn this paper, we study the well-posedness of solutions for nonlinear Schrödinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of Dirichlet or Neumann force. We first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the Strichartz estimates on domains. Secondly, we obtain conditional uniqueness and local stability. Then, we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory. Regarding subquadratic sources, we appeal to classical methods and Trudinger's inequality to prove the uniqueness, which, combined with the existence of weak energy solutions, mass and energy inequalities, eventually implies the continuity of solutions in time.Article Citation - WoS: 1Citation - Scopus: 1Hereditary Rings With Countably Generated Cotorsion Envelope(Academic Press Inc., 2014) Guil Asensio, Pedro A.; Pusat, DilekLet R be a left hereditary ring. We show that if the left cotorsion envelope C(RR) of R is countably generated, then R is a semilocal ring. In particular, we deduce that C(RR) is finitely generated if and only if R is a semiperfect cotorsion ring. Our proof is based on set theoretical counting arguments. We also discuss some possible extensions of this result.Article Citation - WoS: 19Citation - Scopus: 19Rings and Modules Characterized by Opposites of Injectivity(Academic Press Inc., 2014) Alizade, Rafail; Büyükaşık, Engin; Er, NoyanIn a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-subinjective if every homomorphism N→M extends to some E(N)→M, where E(N) is the injective hull of N. Clearly, every module is subinjective relative to any injective module. Their work raises the following question: What is the structure of a ring over which every module is injective or subinjective relative only to the smallest possible family of modules, namely injectives? We show, using a dual opposite injectivity condition, that such a ring R is isomorphic to the direct product of a semisimple Artinian ring and an indecomposable ring which is (i) a hereditary Artinian serial ring with J2 = 0; or (ii) a QF-ring isomorphic to a matrix ring over a local ring. Each case is viable and, conversely, (i) is sufficient for the said property, and a partial converse is proved for a ring satisfying (ii). Using the above mentioned classification, it is also shown that such rings coincide with the fully saturated rings of Trlifaj except, possibly, when von Neumann regularity is assumed. Furthermore, rings and abelian groups which satisfy these opposite injectivity conditions are characterized.Article Citation - WoS: 15Citation - Scopus: 17A New Dynamical Model of Brainstorming: Linear, Nonlinear, Continuous (simultaneous) and Impulsive (sequential) Cases(Academic Press Inc., 2009) Coşkun, Hamit; Yılmaz, OğuzIn this paper, we extended the linear dynamical model of [Brown, V., Paulus, P. B. (1996). A simple dynamic model of social factors in group brainstorming. Small Group Research, 27, 91-114] on two accounts. First, we modelled the sequential type brainstorming using impulsive differential equations by treating each category as an impulse and tested its validity in the two experiments that investigated and demonstrated the beneficial effects of sequential priming and memory in individual brainstorming. Finally, we considered the nonlinear case of brainstorming in writing or brainwriting where dyads exchanged their ideas in a written format and that eliminated negative factors occurring in oral brainstorming (e.g., evaluation apprehension, free-riding, production blocking) and enhanced the upward performance matching, and conducted the second experiment in order to test its validity in this paradigm with the effects of sequential priming and memory. Comparisons showed good agreement between results of experiments and those of the mathematical model.