Let L be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences (θ1, . . . , θn; x1, . . . , xn) in L can be reduced to solving the restriction of the system to the skeleton of L, plus solving the restrictions of the system to the intervals [x1, x¯¯1], . . . , [xn, x¯¯n].
The minimum orders of degree-continuous graphs with prescribed degree sets were investigated by Gimbel and Zhang, Czechoslovak Math. J. 51 (126) (2001), 163–171. The minimum orders were not completely determined in some cases. In this note, the exact values of the minimum orders for these cases are obtained by giving improved upper bounds.
We give a universal discrimination procedure for determining if a sample point drawn from an ergodic and stationary simple point process on the line with finite intensity comes from a homogeneous Poisson process with an unknown parameter. Presented with the sample on the interval [0,t] the discrimination procedure gt, which is a function of the finite subsets of [0,t], will almost surely eventually stabilize on either POISSON or NOTPOISSON with the first alternative occurring if and only if the process is indeed homogeneous Poisson. The procedure is based on a universal discrimination procedure for the independence of a discrete time series based on the observation of a sequence of outputs of this time series.
Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of $E$, thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in R m×n , min(m, n) ≤ 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
In this paper we present a result that relates merging of closed convex sets of discrete probability functions respectively by the squared Euclidean distance and the Kullback-Leibler divergence, using an inspiration from the Rényi entropy. While selecting the probability function with the highest Shannon entropy appears to be a convincingly justified way of representing a closed convex set of probability functions, the discussion on how to represent several closed convex sets of probability functions is still ongoing. The presented result provides a perspective on this discussion. Furthermore, for those who prefer the standard minimisation based on the squared Euclidean distance, it provides a connection to a probabilistic merging operator based on the Kullback-Leibler divergence, which is closely connected to the Shannon entropy.
Let G be a group. If every nontrivial subgroup of G has a proper supplement, then G is called an aS-group. We study some properties of aS-groups. For instance, it is shown that a nilpotent group G is an aS-group if and only if G is a subdirect product of cyclic groups of prime orders. We prove that if G is an aS-group which satisfies the descending chain condition on subgroups, then G is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an aS-group. Finally, it is shown that if G is an aS-group and |G| ≠ pq, p, where p and q are primes, then G has a triple factorization., Reza Nikandish, Babak Miraftab., and Obsahuje seznam literatury
Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.