In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows to simplify the existing step-by-step algorithm-based solution. The paper presents explicit formulas to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The method is straight-forward and better suited for implementation in different computer algebra packages such as \textit{Mathematica} or \textit{Maple}.
States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which are the certain pastings of Boolean algebras the construction of a state-morphism is shown.
Statin-associated myopathy (SAM) represents a broad spectrum of disorders from insignificant myalgia to fatal rhabdomyolysis. Its frequency ranges from 1-5 % in clinical trials to 15-20 % in everyday clinical practice. To a large extent, these variations can be explained by the definition used. Thus, we propose a scoring system to classify statin-induced myopathy according to clinical and biochemical criteria as 1) possible, 2) probable or 3) definite. The etiology of this disorder remains poorly understood. Most probably, an underlying genetic cause is necessary for overt SAM to develop. Variants in a few gene groups that encode proteins involved in: i) statin metabolism and distribution (e.g. membrane transporters and enzymes; OATP1B1, ABCA1, MRP, CYP3A4), ii) coenzyme Q10 production (e.g. COQ10A and B), iii) energy metabolism of muscle tissue (e.g. PYGM, GAA, CPT2) and several others have been proposed as candidates which can predispose to SAM. Pharmacological properties of individual statin molecules (e.g. lipophilicity, excretion pathways) and patients´ characteristics influence the likelihood of SAM development. This review summarizes current data as well as our own results., M. Vrablik, L. Zlatohlavek, T. Stulc, V. Adamkova, M. Prusikova, L. Schwarzova, J. A. Hubacek, R. Ceska., and Obsahuje bibliografii
PATNET, the seismic network of the University of Patras, monitores regularly the seismic activity in the whole western Greece, using for a HYPO location a model, derived as an average representation for this broad area. One of the active regions of the western Greece is the Gulf of Corinth, which central part lies partially on the edge of the PATNET. Due to this and to the fact that the PATNET stations have mostly the vertical component only, the PATNET HYPO location of events in this region are often characterized by large standard errors in epicentres and especially in depths. Using a sequence of small earthquakes that occurred from February to May 2001 close to the city of Aigion, and was recorded by PATNET and as well by local Corinth rift laboratory (CRL) three-component network (CRLNET), we have derived for PATNET station and local model constants whose aplication improves the PATNET HYPO location of events in central part of Gulf of Corinth. These constants represent the main result useful for improvement of the future PATNET location in the given region., Jaromír Janský, Efthimios Sokos, Anna Serpetsidaki and Helene Lyon-Caen., and Obsahuje bibliografické odkazy
We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal. ∇-relation is partly studied by means of statisch pairs.
In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity of samples.
.In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept of causality between stochastic processes, which is based on Granger's definition of causality. Also, we provide applications of our results to solutions of some stochastic differential equations.
The present paper concerns the estimation of probability density functions using the particular parameterized class of distribution functions implemented by a single non-linear neuron, introduced in the previous contribution [12]. The estimation procedure is applied to the statistical characterization of sorne electrical and mechanical phenomena.
In this paper we study the set of statistical cluster points of sequences in $m$-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in $m$-dimensional spaces too. We also define a notion of $\Gamma $-statistical convergence. A sequence $x$ is $\Gamma $-statistically convergent to a set $C$ if $C$ is a minimal closed set such that for every $\epsilon > 0 $ the set $ \lbrace k\:\rho (C, x_k ) \ge \epsilon \rbrace $ has density zero. It is shown that every statistically bounded sequence is $\Gamma $-statistically convergent. Moreover if a sequence is $\Gamma $-statistically convergent then the limit set is a set of statistical cluster points.
In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We will discuss some questions related to the convergence of subseries of a given series.