Abstract Modern methods of tracking and controlling complex systems are associated with the analysis shape statistical models sample arrays. Often values monitored parameters maintained only on a semi-infinite range values. In these cases, it is possible to use generalized beta exponential distribution first kind smooth statistics, that including such as Gompertz-Verhulst distributions special ...

Using the Bernstein theorem we give a simple proof of complete monotonicity three parameter generalized Mittag-Leffler function $E_{\alpha, \beta}^{\gamma}(-x)$ for $x \geq 0$ and suitably adjusted parameters $\alpha$, $\beta$ $\gamma$

The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...

Problem statement: When analyzing random variables it is useful to measure the degree of their monotone dependence or compare pairs of random variables with respect to their monotonicity. Existing coefficients measure general or linear dependence of random variables. Developing a measure of monotonicity is useful for practical applications as well as for general theory, since monotonicity is an...

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green [6]. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived as the expectation of this probability. These rules are characterized by the axioms efficiency, transl...

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...

The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability ...

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, we show that local monotonicity implies the pseudo-monotonicity. The main result is applied to various types of PDE such as reaction-diffusion...

B. S. MORDUKHOVICH and T. T. A. NGHIA Abstract. The paper introduces and characterizes new notions of Lipschitzian and Hölderian full stability of solutions to general parametric variational systems described via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces. These notions, postulated certain quantitative properties of single-valued localizati...