DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272020-05-26T09:09:12Z2020-05-26T09:09:12Zl-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficientsHamacher, PaulKim, Wansuhttp://hdl.handle.net/10203/2518972019-03-19T02:01:12ZTitle: l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
Authors: Hamacher, Paul; Kim, WansuChemotactic traveling waves with compact supportChoi, Sun-HoKim, Yong-Junghttp://hdl.handle.net/10203/2741292020-05-07T06:20:04Z2020-08-01T00:00:00ZTitle: Chemotactic traveling waves with compact support
Authors: Choi, Sun-Ho; Kim, Yong-Jung
Abstract: A logarithmic model type chemotaxis equation is introduced with porous medium diffusion and a population dependent consumption rate. The classical assumption that individual bacterium can sense the chemical gradient is not taken. Instead, the chemotactic term appears by assuming that the migration distance is inversely proportional to the amount of food if food is the reason for migration. The existence and uniqueness of a traveling wave solution of the model are obtained. In particular, solutions have interfaces that divide into constant and non-constant regions. In particular, the profile of the population distribution has compact support. Numerical simulations are provided and compared with analytic results.2020-08-01T00:00:00ZOn an optimal quadrature formula for approximation of Fourier integrals in the space L-2((1))Hayotov, Abdullo R.Jeon, SoominLee, Chang-Ockhttp://hdl.handle.net/10203/2735072020-03-26T02:20:10Z2020-07-01T00:00:00ZTitle: On an optimal quadrature formula for approximation of Fourier integrals in the space L-2((1))
Authors: Hayotov, Abdullo R.; Jeon, Soomin; Lee, Chang-Ock
Abstract: This paper deals with the construction of an optimal quadrature formula for approximation of Fourier integrals in the Sobolev space L-2((1)) [a, b] of non-periodic, complex valued functions which are square integrable with first order derivative. Here the quadrature sum consists of linear combination of the given function values in a uniform grid. The difference between the integral and the quadrature sum is estimated by the norm of the error functional. The optimal quadrature formula is obtained by minimizing the norm of the error functional with respect to coefficients. Analytic formulas for optimal coefficients can also be obtained using discrete analogue of the differential operator d(2)/dx(2). In addition, the convergence order of the optimal quadrature formula is studied. It is proved that the obtained formula is exact for all linear polynomials. Thus, it is shown that the convergence order of the optimal quadrature formula for functions of the space C-2[a, b] is O(h(2)). Moreover, several numerical resudlts are presented and the obtained optimal quadrature formula is applied to reconstruct the X-ray Computed Tomography image by approximating Fourier transforms.2020-07-01T00:00:00ZASYMMETRIC DISPERSAL AND EVOLUTIONAL SELECTION IN TWO-PATCH SYSTEMKim, Yong-JungSeo, HyowonYoon, Changwookhttp://hdl.handle.net/10203/2738542020-04-09T08:20:04Z2020-06-01T00:00:00ZTitle: ASYMMETRIC DISPERSAL AND EVOLUTIONAL SELECTION IN TWO-PATCH SYSTEM
Authors: Kim, Yong-Jung; Seo, Hyowon; Yoon, Changwook
Abstract: Biological organisms leave their habitat when the environment becomes harsh. The essence of a biological dispersal is not in the rate, but in the capability to adjust to the environmental changes. In nature, conditional asymmetric dispersal strategies appear due to the spatial and temporal heterogeneity in the environment. Authors show that such a dispersal strategy is evolutionary selected in the context two-patch problem of Lotka-Volterra competition model. They conclude that, if a conditional asymmetric dispersal strategy is taken, the dispersal is not necessarily disadvantageous even for the case that there is no temporal fluctuation of environment at all.2020-06-01T00:00:00Z