In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh-Arnold-Robertson Pareto(III) (Yeh et al. [32]). We shall see that it is quite similar to the first order max-autoregressive ARMAX, but has a more robust parameter estimation procedure, being therefore more attractive for modeling purposes. Consistency and asymptotic normality of the presented estimators will also be stated.
We are concerned with the problem of differentiability of the derivatives of order m + 1 of solutions to the “nonlinear basic systems” of the type {\left( { - 1} \right)^m}\sum\limits_{\left| \alpha \right| = m} {{D^\alpha }{A^\alpha }\left( {{D^{\left( m \right)}}u} \right)} + \frac{{\partial u}}{{\partial t}} = 0\;in\;Q. We are able to show that {D^\alpha }u \in {L^2}\left( { - a,0,{H^\partial }\left( {B\left( \sigma \right),{\mathbb{R}^N}} \right)} \right),\;\left| \alpha \right| = m + 1, for \partial\in \left ( 0,1/2 \right )and this result suggests that more regularity is not expectable., Roberto Amato., and Obsahuje seznam literatury
We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality ax mod b ≤ x, with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers.
In this note we show that $B$-scrolls over null curves in a 3-dimensional Lorentzian space form $\bar{M}^3_1(c)$ are characterized as the only ruled surfaces with null rulings whose Gauss maps $G$ satisfy the condition $\Delta G=\Lambda G$, $\Lambda \:{X}(\bar{M})\rightarrow {X}(\bar{M})$ being a parallel endomorphism of ${X}(\bar{M})$.
This paper studies the uniqueness of meromorphic functions f n ∏ k i=1 (f (i) ) ni and g n ∏ k i=1 (g (i) ) ni that share two values, where n, nk, k ∈ N, ni ∈ N ∪ {0}, i = 1, 2, . . . , k − 1. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in $C^*$-algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel. Also, $2\times 2$ operator matrices are considered. As corollaries, we get some well-known results.
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior.
The article defines and explicates the concept of gold-plating, i.e. non-minimalistic transposition of EU directives. It describes its typical manifestations in legislative practice and elaborates when and why it should be avoided. It is submitted in the article that the Czech methodological transposition guidelines and RIA methodology insufficiently deal with the issue of gold-plating. Therefore, the article seeks to propose amendments to the relevant Czech methodology so as to limit the occurrence of unjustified gold-plating in Czech legislation.