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Browsing by Author "Ufuktepe, Ünal"
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Analytic functions on time scales
Kapçak, Sinan (Izmir Institute of Technology, 2007)The concept of analyticity for complex functions on time scale complex plane was introduced by Bohner and Guseinov in 2005. They developed completely delta differentiability, delta analytic functions on products of two ... 
An application with webMathematica
Ufuktepe, Ünal (Springer, 2003)There 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 wellrecognized ... 
Applications of graph coloring
Ufuktepe, Ünal; Bacak, Gökşen (Springer, 2005)A graph G is a mathematical structure consisting of two sets V(G) (vertices of G) and E(G) (edges of G). Proper coloring of a graph is an assignment of colors either to the vertices of the graphs, or to the edges, in such ... 
Applications of Petri nets
Yılmaz, Buket (Izmir Institute of Technology, 2008)Petri nets are powerful formalism for modeling a wide range of dynamic systems and system behaviors. This thesis surveys the basic concept and application of Petri nets. The structure of Petri nets, their marking and ... 
Applying Mathematica and webMathematica to graph coloring
Ufuktepe, Ünal; Bacak, Gökşen (Elsevier, 200706)This paper analyzes some graph issues by using the symbolic program Mathematica and its version for the Web, webMathematica. In particular, we consider the problem of graph coloring: the assignment of colors to the ... 
Basic calculus on time scale with mathematica
Yantır, Ahmet; Ufuktepe, Ünal (Springer, 2003)Mathematical 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 ... 
Dynamical systems on time scales
Dündar, Veli (Izmir Institute of Technology, 2007)In this thesis, we have studied dynamical systems on time scales. Firstly, we give basic definitions and theorems about the time scales and dynamical systems. We present Floquet theory and stability criterion on periodic ... 
Ecalculus at IZTECH
Ufuktepe, Ünal; Ufuktepe, Günnur; Deniz, Aslı; Dündar, Veli (Springer, 2006)In today's new economy, characterized by industrial revolutions, globalization and information technology changes traditional classroom and teaching methods. Calculus is the basic course for the fresher at university. ... 
Edge coloring of a graph
Beşeri, Tina (Izmir Institute of Technology, 2004)The edge coloring problem is one of the fundamental problem on graphs which often appears in various scheduling problems like the le transfer problem on computer networks. In this thesis, we survey old and new results on ... 
Graph coloring with webMathematica
Ufuktepe, Ünal; Bacak, Gökşen; Beşeri Sevim, Tina (Springer, 2004)Coloring of a graph is an assignment of colors either to the edges of the graph G, or to vertices, or to maps in such a way that adjacent edges/vertices/maps are colored differently. We consider the problem of coloring ... 
Inequalities for buckling of a clamped plate
Ufuktepe, Ünal; Mchale, K. P. (TARU Publications, 2002)We study the eigenvalue problems for the buckling of a clamped plate. The previous upper bound on low eigenvalues due to Payne, Pólya, and Weinberger, and Rile and Yeh are reviewed. Using methods similar to those used in ... 
Inequalities for the vibrating clamped plate problem
Mchale, K. P.; Ufuktepe, Ünal (TÜBİTAK, 2001)We study the eigenvalues of the vibrating clamped plate problem. We have made improvements on the bounds of the ratios of the eigenvalues of the biharmonic operator (clamped plate) using the methods of Payne, Polya, and ... 
LebesgueStieltjes measure on time scales
Deniz, Aslı; Ufuktepe, Ünal (TÜBİTAK, 2009)The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed ... 
Mathematica applications on time scales
Yantır, Ahmet; Ufuktepe, Ünal (Springer, 2005)Stefan Hilger introduced the calculus on time scales in order to unify continuous and discrete analysis in 1988. The study of dynamic equations is an active area of research since time scales unifies both discrete and ... 
Measure theory on times scales
Deniz, Aslı (Izmir Institute of Technology, 2007)In this thesis, we have studied measure theory adapted to time scales. delta and nablameasures were first defined by Guseinov in 2003, then in a further study, the relationship between Lebesgue deltaintegral and Riemann ... 
Oscillation theory for second order differential equations and dynamic equations on time scales
Yantır, Ahmet (Izmir Institute of Technology, 2004)This thesis provides the oscillation criteria for second order linear differential equations and dynamic equations on time scales. We establish the comparison theorems and oscillation criteria for selfadjoint and nonself ... 
Probability theory applications on time scales
Kahraman, Sevcan (Izmir Institute of Technology, 2008)In this thesis we introduce probability theory adapted on time scales. In this study, we have modified some concepts of probability theory on time scales...Probability Function has been constructed on time scales. After ... 
Vertex coloring of a graph
Bacak, Gökşen (Izmir Institute of Technology, 2004)Vertex coloring is the following optimization problem; given a graph, how many colors are required to color its vertices in such a way that no two adjacent vertices receive the same color? The required number of colors is ...