전체 | 과거현황 (2017년 이전) | 논문

33

A FUNCTIONAL EQUATION ON HYPERPLANES PASSING THROUGH THE ORIGIN

Bae, Jae-Hyeong; Park, Won-Gil | Journal of the Chungcheong Mathematical Society (충청수학회지) 20/2 (2007)

32

A functional equation related to hyperplanes

Won-Gil Park and Jae-Hyeong Bae | Journal of applied mathematics & informatics 24/1 (2007)

31

Generic Initial Ideals of Artinian Ideals having Lefschetz Properties or the Strong Stanley Property

Jung Pil Park,Young Hyun Cho,Jea Man Ahn,Jea Man Ahn,Young Hyun Cho | Journal of Algebra 318/2 (2007)

30

Analysis and discretization of an optimal control problem for the forced Fisher equation

Sung-Dae Yang,Max Gunzburger,Wenxiang Zhu | Discrete and Continuous Dynamical Systems - Series B 8/3 (2007)

An optimal control problem for the forced Fisher equation is considered. The control is an artificially introduced genotype and the objective is to match, as well as possible, a specified gene frequency. The existence of a solution of the optimal control problem is proved and an optimality system is derived through the Lagrange multiplier technique. Numerical approximations of the optimality system are defined using finite element methods to effect spatial discretization and a backward Euler method for the time discretiza- tion. Convergence of semi-discrete in time approximations of the state system is proved and a gradient method for solving the nonlinear discrete systems is developed. The results of some preliminary computational experiments are provided.

29

Shooting methods for numerical solutions of exact controllability problems constrained by linear and semilinear 2-D wave equations

Yang,Sung-Dae | International Journal of Numerical Analysis 4/3 (2007)

28

Generic Initial Ideals of Arithmetically Cohen-Macaulay Projective Subschemes

Jung Pil Park,Hyang Mi Cho,Young Hyun Cho | Communications in Algebra 35/7 (2007)

27

Diffusion and Elastic Equations on Networks

Y.-S. CHUNG and S.-Y. CHUNG,J.-H. KIM | Publ. Res. Inst. Math. 43/3 (2007)

In this paper, we discuss discrete versions of the heat equations and the wave equations, which are called the ω-diffusion equations and the ω-elastic equations on graphs. After deriving some basic properties, we solve the ω-diffusion equations under (i) the condition that there is no boundary, (ii) the initial condition and (iii) the Dirichlet boundary condition. We also give some additional interesting properties on the ω-diffusion equations, such as the minimum and maximum principles, Huygens property and uniqueness via energy methods. Analogues of the ω-elastic equations on graphs are also discussed. Keywords: Discrete Laplacian, diffusion kernel, elastic kernel

26

Magnetotelluric inversion via reverse time migration algorithm of seismic data

Taeyoung Ha,Changsoo Shin | Journal of Computational Physics 225 (2007)

We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green’s function derived from a mixed finite element method proposed by Nédélec for Maxwell’s equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversion algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.

초록

We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green’s function derived from a mixed finite element method proposed by Nédélec for Maxwell’s equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversion algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.

초록

We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green’s function derived from a mixed finite element method proposed by Nédélec for Maxwell’s equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversion algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.