Institute of Mathematics, Czech Academy of Sciences

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Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid
Institute of Mathematics, Czech Academy of Sciences - Tập 53 - Trang 131-142 - 2008
Andrei Irimia
The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field B due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics $$ \mathbb{E}_n^m $$ , which are... hiện toàn bộ
Book Reviews Amália Iványi: Hysteresis Models in Electromagnetic Computation. Akadémiai Kiadó, Budapest 1997; pp. 229
Institute of Mathematics, Czech Academy of Sciences - Tập 42 - Trang 398-398 - 1997
Daniel Mayer
Linearized Regression Model with Constraints of Type II
Institute of Mathematics, Czech Academy of Sciences - - 2003
Lubomír Kubáček
A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estima... hiện toàn bộ
Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations
Institute of Mathematics, Czech Academy of Sciences - Tập 67 - Trang 485-507 - 2021
Zujin Zhang, Chenxuan Tong
We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that $$\left| {{\omega ^r}(x,t)} \right| + \left| {{\omega ^z}(r,t)} \right| \leqslant {C \over {{r^{10}}}},\,\,\,\,\,0 < r \leqslant {1 \over 2}.$$ By employing the dimension reduction technique by Lei-Navas-Zhang, and analyzing ωr, ωz and ωθ/r on different hollo... hiện toàn bộ
Time-dependent electromagnetic waves in a cavity
Institute of Mathematics, Czech Academy of Sciences - - 2009
Bo Kjellmert, Thomas Strömberg
A Higher Order Pressure Segregation Scheme for the Time-Dependent Magnetohydrodynamics Equations
Institute of Mathematics, Czech Academy of Sciences - Tập 64 - Trang 531-556 - 2019
Yun-Bo Yang, Yao-Lin Jiang, Qiong-Xiang Kong
A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analy... hiện toàn bộ
An adaptive finite element method in reconstruction of coefficients in Maxwell’s equations from limited observations
Institute of Mathematics, Czech Academy of Sciences - Tập 61 - Trang 253-286 - 2016
Larisa Beilina, Samar Hosseinzadegan
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell’s system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of t... hiện toàn bộ
Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems
Institute of Mathematics, Czech Academy of Sciences - Tập 62 Số 1 - Trang 15-36 - 2017
Szekeres, Béla J., Izsák, Ferenc
Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on R2 and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the... hiện toàn bộ
Complete Solution of Tropical Vector Inequalities Using Matrix Sparsification
Institute of Mathematics, Czech Academy of Sciences - Tập 65 Số 6 - Trang 755-775 - 2020
Krivulin, Nikolai
We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices... hiện toàn bộ
An accurate active set newton algorithm for large scale bound constrained optimization
Institute of Mathematics, Czech Academy of Sciences - Tập 56 - Trang 297-314 - 2011
Li Sun, Guoping He, Yongli Wang, Changyin Zhou
A new algorithm for solving large scale bound constrained minimization problems is proposed. The algorithm is based on an accurate identification technique of the active set proposed by Facchinei, Fischer and Kanzow in 1998. A further division of the active set yields the global convergence of the new algorithm. In particular, the convergence rate is superlinear without requiring the strict comple... hiện toàn bộ
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