We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).
Applying the moment inequality of asymptotically almost negatively associated (AANA, in short) random variables which was obtained by Yuan and An (2009), some strong convergence results for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of Zhou et al. (2011), Sung (2011, 2012) to the case of AANA random variables, respectively.
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions.
We study the capitulation of 2-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields k = Q( √ 2pq, i), where i = √ −1 and p ≡ −q ≡ 1 (mod 4) are different primes. For each of the three quadratic extensions K/k inside the absolute genus field k (∗) of k, we determine a fundamental system of units and then compute the capitulation kernel of K/k. The generators of the groups Ams(k/F) and Am(k/F) are also determined from which we deduce that k (∗) is smaller than the relative genus field (k/Q(i))∗ . Then we prove that each strongly ambiguous class of k/Q(i) capitulates already in k (∗) , which gives an example generalizing a theorem of Furuya (1977).
The foliation of a Morse form $\omega$ on a closed manifold $M$ is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of $M$ and $\omega$. Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of $\mathop{\rm rk}\omega $ and ${\rm Sing} \omega $. The set of the ranks of all forms defining a given foliation without minimal components is described. It is shown that if $\omega$ has more centers than conic singularities then $b_1(M)=0$ and thus the foliation has no minimal components and homologically non-trivial compact leaves, its folitation graph being a tree.
Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation U in the unit interval with the neutral element e∈[0,1]. If operation U is continuous, then e=0 or e=1. So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element e∈(0,1), which is continuous in the open unit square may be given in [0,1)2 or (0,1]2 as an ordinal sum of a semigroup and a group. This group is isomorphic to the positive real numbers with multiplication. As a corollary we obtain the results of Hu, Li [7].
The probability p(s) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [0,1]. The function p is called a numerical event or multidimensional probability. When appropriately structured, sets P of numerical events form so-called algebras of S-probabilities. Their main feature is that they are orthomodular partially ordered sets of functions p with an inherent full set of states. A classical physical system can be characterized by the fact that the corresponding algebra P of S-probabilities is a Boolean lattice. We give necessary and sufficient conditions for systems of numerical events to be a lattice and characterize those systems which are Boolean. Assuming that only a finite number of measurements is available our focus is on finite algebras of S-probabilties.
Let K be a field and S = K[x1, ..., xm, y1,..., yn] be the standard bigraded polynomial ring over K. In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” S-modules with respect to Q = (y1, ..., yn). Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to Q in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to Q are considered., Leila Parsaei Majd, Ahad Rahimi., and Obsahuje seznam literatury
Let $G$ be a finite nonabelian group, ${\mathbb Z}G$ its associated integral group ring, and $\triangle (G)$ its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups $Q_{n}(G)=\triangle ^{n}(G)/\triangle ^{n+1}(G)$ is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.
Let $K = \mathbb {F}_q(T)$ be the rational function field over a finite field of $q$ elements. For any polynomial $f(T)\in \mathbb {F}_q[T]$ with positive degree, denote by $\Lambda _f$ the torsion points of the Carlitz module for the polynomial ring $\mathbb {F}_q[T]$. In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield $M$ of the cyclotomic function field $K(\Lambda _P)$ of degree $k$ over $\mathbb {F}_q(T)$, where $P\in \mathbb {F}_q[T]$ is an irreducible polynomial of positive degree and $k>1$ is a positive divisor of $q-1$. A formula for the analytic class number for the maximal real subfield $M^+$ of $M$ is also presented. Futhermore, a relative class number formula for ideal class group of $M$ will be given in terms of Artin $L$-function in this paper.