We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision function, but also appears to play an important role exactly in the framework of possibility theory due to its sensitivity. Furthermore, the optimality of a decision function is easily verifiable.
Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy classes, and it is called $n$-decomposable in $G$ if it is a union of $n$ distinct $G$-conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5., Ruifang Chen, Xianhe Zhao., and Obsahuje bibliografické odkazy
The behavior of special classes of isometric foldings of the Riemannian sphere $S^2$ under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the {\it standard} spherical isometric folding $f_s$ defined by $f_s(x,y,z)=(x,y,|z|)$.
This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability are given in terms of the existence of positive definite solutions of LMIs.
In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than $c$ has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight $c$ which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of $\pi$-weight less than $\mathfrak p$ has a dense completely Hausdorff (and hence Urysohn) subspace. We show that there exists a Tychonoff space without dense normal subspaces and give other examples of spaces without “good” dense subsets.
Alice Jedličková (ed.) ; translation Melvyn Clarke, Martina Kurtyová ... [et al.]., Obsahuje seznam citovaných děl, and Obsahuje český text, částečně přeloženo
Let G be a connected graph of order n ≥ 3 and let c : E(G) → {1, 2, . . . , k} be a coloring of the edges of G (where adjacent edges may be colored the same). For each vertex v of G, the color code of v with respect to c is the k-tuple c(v) = (a1, a2, . . . , ak), where ai is the number of edges incident with v that are colored i (1 ≤ i ≤ k). The coloring c is detectable if distinct vertices have distinct color codes. The detection number det(G) of G is the minimum positive integer k for which G has a detectable k-coloring. We establish a formula for the detection number of a path in terms of its order. For each integer n ≥ 3, let Du(n) be the maximum detection number among all unicyclic graphs of order n and du(n) the minimum detection number among all unicyclic graphs of order n. The numbers Du(n) and du(n) are determined for all integers n > 3. Furthermore, it is shown that for integers k ≥ 2 and n ≥ 3, there exists a unicyclic graph G of order n having det(G) = k if and only if du(n) ≤ k ≤ Du(n).
In this contribution, we present the final outcome of the program initiated in [23], aimed at the determination of a periodic unit cell for plain weave composites with reinforcement imperfections. The emphasis is put on a realistic geometrical description of these material systems utilizing the information provided by in-situ two-dimensional micrographs. Complex geometry of an analyzed composite is approximated using a two-layer periodic unit cell allowing for a mutual shift as well as nesting of individual layers. The parameters of the idealized unit cell are derived via matching appropriate statistical descriptors related to the real material and the idealized geometrical model. Once the optimal geometry of the unit cell is determined, it can be converted to a CAD model and used ot generate the periodic finite element mesh applicable in the subsequent numerical treatment. The individual steps of this procedure are demonstrated in detail for a real world carbon-carbon composite system. and Obsahuje seznam literatury
The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume-finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume-finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.