In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in Oberhuber \cite{Obe-2005-2,Obe-2005-1} which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry of the solution. Since it requires higher regularity of the solution, additional numerical viscosity is necessary in some cases. We also present theorem showing stability of the scheme together with the EOC and several results of the numerical experiments.
This paper presents a finite element for the analysis of beams strengthened by composite strips. The element is based on a mixed formulation of the mechanical model of the strengthened beam, the adhesive and the composite strip, working simultaneously. The solution allows us to study the influence of rhe adhesive layer on the behaviour of the strengthened beam.
The proposed element is verified with solutions of other analytical models or different finire element models and schemes. and Obsahuje seznam literatury
This paper presents a computational procedure for the design of an observer of a nonlinear system. Outputs can be delayed, however, this delay must be known and constant. The characteristic feature of the design procedure is computation of a solution of a partial differential equation. This equation is solved using the finite element method. Conditions under which existence of a solution is guaranteed are derived. These are formulated by means of theory of partial differential equations in L2-space. Three examples demonstrate viability of this approach and provide a comparison with the solution method based on expansions into Taylor polynomials.
Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups $G$ whose set of numbers of subgroups of possible orders $n(G)$ has exactly two elements. We show that if $G$ is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then $G$ has a normal Sylow subgroup of prime order and $G $ is solvable. Moreover, as an application we give a detailed description of non-nilpotent groups with $n(G)=\{1, q+1\}$ for some prime $q$. In particular, $G$ is supersolvable under this condition.
In this paper we investigate finite rank operators in the Jacobson radical $\mathcal R_{\mathcal N\otimes \mathcal M}$ of $\mathop {\mathrm Alg}(\mathcal N\otimes \mathcal M)$, where $\mathcal N$, $\mathcal M$ are nests. Based on the concrete characterizations of rank one operators in $\mathop {\mathrm Alg}(\mathcal N\otimes \mathcal M)$ and $\mathcal R_{\mathcal N\otimes \mathcal M}$, we obtain that each finite rank operator in $\mathcal R_{\mathcal N\otimes \mathcal M}$ can be written as a finite sum of rank one operators in $\mathcal R_{\mathcal N\otimes \mathcal M}$ and the weak closure of $\mathcal R_{\mathcal N\otimes \mathcal M}$ equals $\mathop {\mathrm Alg}({\mathcal N\otimes \mathcal M})$ if and only if at least one of $\mathcal N$, $\mathcal M$ is continuous.
Parameters of finite seismic source model were determined for a set of 36 selected events of the West Bohemia 2000 earthquakes swarm (Ml from 1.7 to 3.0) using stopping phases method. Two stopping phases are generated along the source border where the rupture process terminates and these phases form Hilbert transform pair, which is also the criterion for their identification. Circular and e liptical source models were considered and corresponding source parameters were calculated by inverting interpreted stopping phases delays. As generalization of circular to elliptical model was found to be statistically insignificant, only results related to the circular source including error estimates are presented. Our results are in a good agreement with previously published theoretical formula concerning source radius and magnitude and also fairly well confirm general theoretical assumption about constant stress drop. The determined stress drop ranges between 1 - 10 MPa with the typical value of 2.4 MPa., Petr Kolář and Bohuslav Růžek., and Obsahuje bibliografické odkazy
The study of paramedial groupoids (with emphasis on the structure of simple paramedial groupoids) was initiated in [1] and continued in [2], [3] and [5]. The aim of the present paper is to give a full description of finite simple zeropotent paramedial groupoids (i.e., of finite simple paramedial groupoids of type (II)—see [2]). A reader is referred to [1], [2], [3] and [7] for notation and various prerequisites.
This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only does quasinilpotent equivalence of two socle elements imply spectral equality, but also the trace, determinant and spectral multiplicities of the elements must agree. It is hence shown that quasinilpotent equivalence is established by a weaker formula (than that of the spectral semidistance). More generally, in the second part, we show that two elements possessing finite spectra are quasinilpotent equivalent if and only if they share the same set of Riesz projections. This is then used to obtain further characterizations in a number of general, as well as more specific situations. Thirdly, we show that the ideas in the preceding sections turn out to be useful in the case of $C^*$-algebras, but now for elements with infinite spectra; we give two results which may indicate a direction for further research.