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She works in the field of differential geometry. She examines the different metrics and geometric properties on cottangent bundles of differentiable manifolds. She's doing research using different tensor operators. | |
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Research team's study topics can be listed as ordered algebraic structures and their properties, fuzzy operators, orders obtained by fuzzy operators, the properties and applications of the orders. Also, they study on construction methods of fuzzy operators on different algebraic structures and relations between fuzzy operators. |
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Mathematical modeling of the accretive surface growth. The hard body accretions, such as seashells, horns, bones, teeth, etc. are not likely to be deformed. Thus, the shapes of hard bodies emerge in a mathematically elegant and self-similar global structures. Growth velocity vector defined by the help of a reference frame attached to an arbitrary generating curve is used for the mathematical modeling of this growth process. The evolution of a generating curve with the help of increasing growth rate constitutes the accretive growth process. We can describe such a model in different geometries by the help of kinematical tools and computer algorithms for modeling various biological beings in a realistic way. |
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The research group focusses on the implementation and improvement of numerical methods in fluid dynamics. The members of the group carry out researches on numerical solutions of heat and mass transfer of the fluid flow; error, convergence and stability analysis of finite difference method, finite element method and boundary element method; and computer programming for numerical methods. |
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Examination of geometric figures such as curves and surfaces in various geometries such as Euclidean, Non-Euclidean, Affine, Projective and so on. Research is carried out on the existence, uniqueness and equivalences of geometric figures such as curves and surfaces, through their invariants. For these purpose, invariant theory methods are used effectively. |
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Our research group works within the field of Applied Topology, encompassing disciplines such as persistent homology, computational geometry, proximity, digital topology, and topology of chaos. In our department, we might be considered a small group, with just my PhD student Fatih Ucan and my MSc student Sueda Inal. However, we collaborate with acclaimed researchers all over the globe. Our mentor is the esteemed Professor James Peters of the University of Manitoba, in charge of the ECE Computationally Intelligent Systems and Signals lab. |
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Investigation of geometric structure of numerical ranges and some characteristics of numerical Radius and Crawford numbers of some clases at linear bounded operations in Banach Spaces. |
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In this study, it is aimed to solve the problem of determining the similarities of polygons given in two-dimensional space by using invariants and to establish an algorithm that calculates these similarities effectively. . |
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Recently, our group works on mathematical modeling and numerical analysis of diverse phenomena of technological or medical interest including statistical mechanics, population dynamics. Our work includes modelling, as well as derivation and implementation of effective numerical methos to solve unjderlying problems. | |
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The main research areas of the research group are Sturm-Liouville theory, regular Sturm-Liouville problems, asymptotic estimates of eigenvalues and eigenfunctions when the potential function satisfies different conditions and the eigenvalue parameter is included in the boundary conditions, improved solution forms for Green's functions, Floquet theory and instability intervals. |
