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.
Assuming that CX,Y is the copula function of X and Y with marginal distribution functions FX(x) and FY(y) , in this work we study the selection distribution Z=d(X|Y∈T) . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.
We study oscillatory properties of solutions of the Emden-Fowler type differential equation $$u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,$$ where $0<\lambda <1$, $p\in L_{\rm loc }(\Bbb R_+;\Bbb R)$, $\sigma \in C(\Bbb R_+;\Bbb R_+)$ and $\sigma (t)\ge t$ for $t\in \Bbb R_+$. \endgraf Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. \endgraf Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).
For the equation y (n) + |y| k sgn y = 0, k > 1, n = 3, 4, existence of oscillatory solutions y = (x ∗ − x) −α h(log(x ∗ − x)), α = n ⁄ k − 1 , x < x∗ , is proved, where x ∗ is an arbitrary point and h is a periodic non-constant function on R. The result on existence of such solutions with a positive periodic non-constant function h on R is formulated for the equation y (n) = |y| k sgn y, k > 1, n = 12, 13, 14.
Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated.