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 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.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.Article Hirota Method for Solving Reaction-Diffusion Equations With Generalized Nonlinearity(World Academic Press, 2006) Tanoğlu, GamzeThe Hirota Method is applied to find an exact solitary wave solution to evolution equation with generalized nonlinearity. By introducing the power form of Hirota ansatz the bilinear representation for this equation is derived and the traveling wave solution is constructed by Hirota perturbation. We show that velocity of this solution is naturally fixed by truncating the Hirota’s perturbation expansion. So in our approach, this truncate on works similarly to the way Ablowitz and Zeppetella obtained an exact travelling wave solution of Fisher’s equation by finding the special wave speed for which the resulting ODE is of the Painleve type. In the special case the model admits N shock soliton solution and the reduction to Burgers’ equation.Article An Application With Webmathematica(Springer Verlag, 2003) Ufuktepe, ÜnalThere have been many technological dawns in the last 30 years, during which the desktop computer and the Internet have been developed. The importance of Internet in education, particularly using its Web is a well-recognized fact. A wealth of resources and techniques now exist which serve as a source both for exciting examples of new teaching practices, as well as easily accessible methods for adoption into various formats of teaching and learning. Internet technology allow teachers and students keep up with their minds. It let them try their ideas as soon as they come up with them. Generally, students appreciate the convenience, choice, and flexibility that an online courses offers. Instructional designers value the standardized framework and flexibility. WebMathematica is a web-based technology developed by Wolfram Research that allows the generation of dynamic web content with Mathematica. With this technology, the distance education students should be able to explore and experiment with the mathematical concepts. In this paper we will elucidate the pedagogical issues in the application of Hamiltonian systems in the webMathematica for the distance learning environment and the shape of the future "classroom" as well as relevant educational strategies towards improving mathematics education.Article Citation - WoS: 2Citation - Scopus: 1Basic Calculus on Time Scale With Mathematica(Springer Verlag, 2003) Yantır, Ahmet; Ufuktepe, ÜnalMathematical modeling of time dependent systems are always interesting for applied mathematicians. First continuous and then discrete mathematical modeling are built during the mathematical development from ancient to the modern times. By the discovery of the time scales, the problem of irregular controlling of time dependent systems is solved in 1990's. In this paper, we explain the derivative of functions on time scales and the solutions of some basic calculus problems by using Mathematica. © Springer-Verlag Berlin Heidelberg 2003.
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