O některých aplikacích Ljapunovovy theorie stability v elektrotechnice
O některých základních větách teorie lineárních elektrických obvodů
O rychlosti světla v prvcích lučebných
O středu optickém a hlavních bodech čoček. [I.]
O středu optickém a hlavních bodech čoček. [II.]
Oko redukované
On a 3D-Hypersingular Equation of a Problem for a Crack
MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.
On a certain two-sided symmetric condition in magnetic field analysis and computations
A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity...
On a Hypersingular Equation of a Problem, for a Crack in Elastic Media
Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.We give a procedure to reduce a hypersingular integral equation, arising in 2d diffraction problems on cracks in elastic media, to a Fredholm integral equation of the second kind, to which it is easier and more effectively to apply numerical methods than to the initial hypersingular equation.
On a potential problem with incident wave as a field source
On a quasi-variational inequality arising in semiconductor theory.
Some new mathematical results of existence and uniqueness of solutions are obtained for a class of quasi-variational inequalities modeling the free boundary problem for the determination of the depletion zone in reverse biased semiconductor diodes. The corresponding one (or two) obstacle implicit problems are solved by direct methods with weak regularity estimates for mixed boundary value elliptic problems of second order.
On acceleration methods for coupled nonlinear elliptic systems.
On an integral equation in the problem of the diffraction of a plane wave by a transparent circular cone.
On approximation of the Neumann problem by the penalty method
We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
On determining unknown functions in differential systems, with an application to biological reactors
In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...
On determining unknown functions in differential systems, with an application to biological reactors.
In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function φ. We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...
On discrete approximations for a class of linear functional differential equations
On evolution Galerkin methods for the Maxwell and the linearized Euler equations
The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present some numerical...
On geometry of fronts in wave propagations
We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
On highly oscillatory problems arising in electronic engineering
In this paper, we consider linear ordinary differential equations originating in electronic engineering, which exhibit exceedingly rapid oscillation. Moreover, the oscillation model is completely different from the familiar framework of asymptotic analysis of highly oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into asymptotic series, and this allows us to extend Filon-type approach to this setting. The outcome is a time-stepping method that guarantees ...