We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.
At the end of 2010 seven TM 71 extensometers, installed at or near the active faults in Slovenia, were in operation. Three of them are on the surface and four inside karst caves. The highest rates with stable sense of movements were observed on the Idrija fault. Average horizontal displacement rate was 0.24 mm/year. Short term rates were even greater and reached 0.54 mm/year. The Raša fault first experienced an uplift of the SW block of 0.16 mm/year, which was followed by a short-term down-slip of the same block at the rate of 0.37 mm/year. Later the sense of movement returned to uplift with a rate of 0.05 mm/year. The average horizontal displacement was 0.07 mm/year. The Kneža fault experienced very small average displacements (y=0.035 mm/year, z=0.03 mm/year and x=0.02 mm/year). Similar rates were observed in nearby Polog cave (y=0.015 mm/year, z=0.027 mm/year and x=0.016 mm/year), which is located close to the seismically active Ravne fault. For Kostanjevica cave, located near the Brežice fault, small average rates are characteristic (y=0.006 mm/year, z=0.017 mm/year and x=0.012 mm/year). In Postojna cave, located close to the Predjama fault, two monitoring sites are very stable with small tectonic movements, including general dextral horizontal movement of 0.05 mm from 2004 to 2010 (Postojna 1) and two significant short-term peaks of 0.08 mm (Postojna 1-y and Postojna 2-z)., Andrej Gosar, Stanka Šebela, Blahoslav Košťák and Josef Stemberk., and Obsahuje bibliografii
In this paper, the static output feedback stabilization (SOFS) of deterministic finite automata (DFA) via the semi-tensor product (STP) of matrices is investigated. Firstly, the matrix expression of Moore-type automata is presented by using STP. Here the concept of the set of output feedback feasible events (OFFE) is introduced and expressed in the vector form, and the stabilization of DFA is defined in the sense of static output feedback (SOF) control. Secondly, SOFS problem of DFA is investigated within the framework of STP, including single-equilibrium-based SOFS, multi-equilibrium-based SOFS, and further limit cycle-based SOFS. Then the necessary and sufficient conditions for the existence of the three types SOFS are proposed respectively. Meanwhile the efficient and systematic procedures based on the matrix theory to seek the corresponding SOF controller are provided for the three types SOFS problem. Finally, two examples are presented to illustrate the effectiveness of the proposed approach.
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].