Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article The Application of a Finite Difference Method To a Dynamical Interface Problem(Acad. Publications, 2003) Tanoğlu, Gamze; Ağıroğlu, İzzet OnurA multiple-order-parameter model for Cu-Au system on a face cubic centered lattice was recently developed in the presence of anisotropy. In that model, three order parameters (non-conserved) and one concentration order parameter (conserved), which has been taken as a constant, were considered. Later on, the model has been extended, so that, concentration has been taken as a variable. It has been seen that two models were in a good agreement near critical temperature since the non-conserved order parameter behaves like a constant near critical temperature in both models.Conference Object Can Cpt Be Violated Through Extended Time Reversal?(World Scientific Publishing, 2001) Erdem, Recai; Ufuktepe, ÜnalWe consider the implications of the extension of time reversal through Wigner types and group extensions. We clarify its physical content and apply the results in a toy model. Finally we point out the possibility of violation of CPT in this framework.Conference Object On the Relativistic Supersymmetric Quantum Mechanics(Springer Verlag, 2002) Mir-Kasimov, Rufat M.; Kasım, Rıfat MirThe present paper is devoted to the one-dimensional relativistic supersymmetric quantum mechanics (RSUSYQM). A short formulation of RSUSYQM is given. We show that RSUSYQM is a q-deformed non-relativistic SUSYQM. Two simple examples are given.Conference Object Holomorphic Realization of Non-Commutative Space-Time and Gauge Invariance(IOP Publishing, 2003) Mir-Kasimov, Rufat M.The realization of the Poincare Lie algebra in terms of noncommutative differential calculus over the commutative algebra of functions is considered. The algebra of functions is defined on the spectrum of the unitary irreducible representations of the De Sitter group. Corresponding space-time carries the noncommutative geometry. Gauge invariance principle consistent with this noncommutative space is considered.Conference Object Derivative and Integration on Time Scale With Mathematica(Imperial College Press, 2003) Yantır, AhmetMathematical modelling of time dependent systems is always interesting for applied mathematicians. First continuous and then discrete mathematical models were built in the mathematical development from ancient to modem times. With the discovery of time scale, the problem of irregular systems was solved in the 1990s. In this paper we explain the derivative and integral of functions of time scales and the solution of some basic calculus problems using Mathematica.Conference Object Partial Differential Equations With Webmathematica(Imperial College Press, 2003) Ufuktepe, ÜnalThe growing popularity of the internet, and the increasing number of computers connected to it, make it an ideal framework for remote education. Many disciplines are rethinking their traditional philosophies and techniques to adapt to the new technologies. Web-based education is an effective framework for such learning, which simplifies theory understanding, encourages learning by discovery and experimentation and undoubtedly makes the learning process more pleasant. There is a need for adequate tools to help in the elaboration of courses that might make it possible to express all the possibilities offered by www teaching. webMathematica is a web-based technology developed by Wolfram Research that allows the generation of dynamic web content with Mathematica. With this technology, distance education students should be able to explore and experiment with mathematical concepts. In this paper we present a sample lecture for Partial Differential Equations in webMathematica for the distance learning environment.Conference Object Measure on Time Scales With Mathematica(Springer Verlag, 2006) Ufuktepe, Ünal; Yantır, AhmetIn this paper we study the Lebesgue Delta-measure on time scales. We refer to [3, 4] for the main notions and facts from the general measure and Lebesgue Delta integral theory. The objective of this paper is to show how the main concepts of Mathematica can be applied to fundamentals of Lebesgue Delta- and Lebesgue Delta- measure on an arbitrary time scale and also on a discrete time scale whose rule is given by the reader. As the time scale theory is investigated in two parts, by means of alpha and rho operators, we named the measures on time scales by the set function DMeasure and NMeasure respectively for arbitrary time scales.Conference Object Citation - Scopus: 1Hipokampüsün El ve Atlas Tabanlı Otomatik Bölütlenmesinin Hacimsel Olarak Karşılaştırılması(Institute of Electrical and Electronics Engineers Inc., 2009) Kutucu, Hakan; Eker, Çağdaş; Kitiş, Ömer; Gönül, Ali SaffetHigh-resolution Magnetic resonance imaging (MRI) is helpful in diagnosing diseases such as schizophrenia, alzheimer, dementia etc. Brain segmentation is an important preprocess in medical imaging applications. In this study we compare atlas based segmentation and manual segmentation of hippocampus for volumetric measures. A statistically difference was obtained between automatic and manual measurement. We conclude that contemporary techniques are not adequate to obtain sensitive data in some barin structures such as hippocampus core.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.Conference Object The Hirota Method for Reaction-Diffusion Equations With Three Distinct Roots(American Institute of Physics, 2004) Tanoğlu, Gamze; Pashaev, OktayThe Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reaction-diffusion equations of two types. The first equation has only nonlinear reaction part, while the second one has in addition the nonlinear transport term. For both cases, the reaction part has the form of the third order polynomial with three distinct roots. We found analytic one-soliton solutions and the relationships between three simple roots and the wave speed of the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is static.We show that the restriction on three distinct roots to obtain moving soliton is removed in the second case by, adding nonlinear transport term to the first equation.