This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these problems is proved. The solutions are constructed in an explicit form.
This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem of simultaneously minimizing a set of H∞ cost functions for a class of systems subject to bounded disturbances and/or parameter uncertainties. Numeric examples are reported to highlight the stabilizing action of the proposed control laws.
The sports sector has been fighting doping globally by harmonized rules in The World Anti-Doping Agency’s Code by strict liability. According to the Code it is each athlete’s personal duty to ensure that no prohibited substance enters his or her body. Athletes are responsible for any prohibited substance or its metabolites or markers found to be present in their samples. Accordingly, it is not necessary that intent, fault, negligence or knowing use on the athlete’s part be demonstrated in order to establish an antidoping violation. The article written for TLQ legal journal demonstrates how special regulation of doping is in the light of case of Jan Štěrba, bronze medalist of London 2012 Games. He was lucky that he escaped standard sanction of ineligibility and was punished only with reprimand for violation of Anti-Doping rules. The article at the same time presents additionally efforts of fight against doping by international cooperation among states by Council of Europe or UNESCO to enhance illustration how special doping regulation is. There is no doubt that this area of sports law will be still evolving due to many difficult and controversial aspects of it.
Let $A(G)$ be the adjacency matrix of $G$. The characteristic polynomial of the adjacency matrix $A$ is called the characteristic polynomial of the graph $G$ and is denoted by $\phi (G, \lambda)$ or simply $\phi (G)$. The spectrum of $G$ consists of the roots (together with their multiplicities) $\lambda _1(G)\geq \lambda _2(G)\geq \ldots \geq \lambda _n(G)$ of the equation $\phi (G, \lambda )=0$. The largest root $\lambda _1(G)$ is referred to as the spectral radius of $G$. A $\ddag $-shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by $G(l_1, l_2, \ldots , l_7)$ $(l_1\geq 0$, $l_i\geq 1$, $i=2,3,\ldots, 7)$ a $\ddag $-shape tree such that $G(l_1, l_2, \ldots , l_7)-u-v=P_{l_1}\cup P_{l_2}\cup \ldots \cup P_{l_7}$, where $u$ and $v$ are the vertices of degree 4. In this paper we prove that $3\sqrt {2}/{2}< \lambda _1(G(l_1, l_2, \ldots , l_7))< {5}/{2}$.
We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.
At the end of 2010 seven TM 71 extensometers, installed at or near the active faults in Slovenia, were in operation. Three of them are on the surface and four inside karst caves. The highest rates with stable sense of movements were observed on the Idrija fault. Average horizontal displacement rate was 0.24 mm/year. Short term rates were even greater and reached 0.54 mm/year. The Raša fault first experienced an uplift of the SW block of 0.16 mm/year, which was followed by a short-term down-slip of the same block at the rate of 0.37 mm/year. Later the sense of movement returned to uplift with a rate of 0.05 mm/year. The average horizontal displacement was 0.07 mm/year. The Kneža fault experienced very small average displacements (y=0.035 mm/year, z=0.03 mm/year and x=0.02 mm/year). Similar rates were observed in nearby Polog cave (y=0.015 mm/year, z=0.027 mm/year and x=0.016 mm/year), which is located close to the seismically active Ravne fault. For Kostanjevica cave, located near the Brežice fault, small average rates are characteristic (y=0.006 mm/year, z=0.017 mm/year and x=0.012 mm/year). In Postojna cave, located close to the Predjama fault, two monitoring sites are very stable with small tectonic movements, including general dextral horizontal movement of 0.05 mm from 2004 to 2010 (Postojna 1) and two significant short-term peaks of 0.08 mm (Postojna 1-y and Postojna 2-z)., Andrej Gosar, Stanka Šebela, Blahoslav Košťák and Josef Stemberk., and Obsahuje bibliografii
In this paper, the static output feedback stabilization (SOFS) of deterministic finite automata (DFA) via the semi-tensor product (STP) of matrices is investigated. Firstly, the matrix expression of Moore-type automata is presented by using STP. Here the concept of the set of output feedback feasible events (OFFE) is introduced and expressed in the vector form, and the stabilization of DFA is defined in the sense of static output feedback (SOF) control. Secondly, SOFS problem of DFA is investigated within the framework of STP, including single-equilibrium-based SOFS, multi-equilibrium-based SOFS, and further limit cycle-based SOFS. Then the necessary and sufficient conditions for the existence of the three types SOFS are proposed respectively. Meanwhile the efficient and systematic procedures based on the matrix theory to seek the corresponding SOF controller are provided for the three types SOFS problem. Finally, two examples are presented to illustrate the effectiveness of the proposed approach.