Let $ 1\leq q <p < \infty $ and $1/r := 1/p \max (q/2, 1)$. We prove that ${\scr L}_{r,p}^{(c)}$, the ideal of operators of Geľfand type $l_{r,p}$, is contained in the ideal $\Pi _{p,q}$ of $(p,q)$-absolutely summing operators. For $q>2$ this generalizes a result of G. Bennett given for operators on a Hilbert space.
We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the Q-transform employed previously by Varshamov and Garakov (1969) as well as by Meyn (1990) for the synthesis of irreducible polynomials. While in the iterative procedure described by Kyuregyan the coefficients of the initial polynomial of the sequence have to satisfy certain hypotheses, in the present paper these conditions are removed. We construct infinite sequences of irreducible polynomials of nondecreasing degree starting from any irreducible polynomial., Simone Ugolini., and Obsahuje seznam literatury
We consider a random, uniformly elliptic coefficient field a on the lattice ℤd. The distribution ⟨.⟩of the coefficient field is assumed to be stationary. Delmotte and Deuschel showed that the gradient and second mixed derivative of the parabolic Green's function G(t,x,y) |2satisfy optimal annealed estimates which are L2 and L1, respectively, in probability, i.e., they obtained bounds on ⟨| ∇ x G (t,x,y)|2 ⟩1⁄2 and ⟨| ∇ x ∇y G(t,x,y)|⟩ .In particular, the elliptic Green's function G(x,y) satisfies optimal annealed bounds. In their recent work, the authors extended these elliptic bounds to higher moments, i.e., Lp in probability for all p<∞. In this note, we present a new argument that relies purely on elliptic theory to derive the elliptic estimates for ⟨| ∇ x G (x,y)|2 ⟩1⁄2 and ⟨| ∇ x ∇y G(x,y)|⟩.
In this paper we give an extension of $q$-Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of $q$-Chu-Vandermonde convolution formula and some other $q$-identities.
The aim of this paper is to introduce the Choquet integral representation of some information quantities in the possibility theory. A possibilistic T-independence concept is further analyzed with respect to its information-theoretic properties. The main result is then the introduction of a so called general ineasure of T-dependence. It is further proven that the general measure of T-dependence exhibits significant properties froin an information-theoretic point of view and can be conceived as an apt analogy of the well-known probabilistic inutual information.
The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function f. The relative controllability of the presented semilinear system is discussed. Rothe's fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time t>0 is presented. A numerical example is provided to illustrate the obtained theoretical results and a practical example is given to show a possible application of the study.
In this work we apply the method of a unique partition of a complex function f of complex variables into symmetrical functions to solving a certain type of functional equations.
In this paper, concepts and techniques of the system theory are used
to obtain state-space (Markovian) models of dynamic economic processes instead of the usual VARMA models. In this respect, the concept of stata is reviewed as are Hankel norm approximations and balanced realizations for stochastic models. We clarify some aspects of the balancing method for state space modelling of the observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We use a statě variance factorization algorithm, which does not require us to solve the algebraic Riccati equation. We relate the Aoki-Havenner method to the Arun-Kung method.