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EN
A new protocol using vectors of global timestamps for mutual exclusion in systems with Distributed Shared Memory (DSM) is described and some of its properties are proved.
3
Vectors in school mathematics
EN
Vectors have several meanings in the science. Mathematicians, physicists and other scientists make use of the notion of a vector. The notions they make use of are different in different subjects. Here we present different meanings of vectors and give some hints how to understand them in different subjects of science.
EN
Let: {Xi} be a sequence of r.v.'s, and: Mn := max (X1,..., Xn), mn := min (X1,..., Xn). Our goal is to prove the almost sure central limit theorem for the properly normalized vector {Mn,mn}, provided: 1) {Xi} is an i.i.d. sequence, 2) {Xi} is a certain standardized stationary Gaussian sequence.
EN
In the present paper, we consider the problem of reconstruction of the current state of the difference-differential system with commensurable delays. The results obtained are used for the reconstruction of the current states of linear retarded partial parabolic differential equation.
EN
A theoretical class of nonlinear systems is considered. An n-dimensional pipeline system is examined, as an example system, for investigating the effectiveness of a high-gain observer-based residual for detecting faults. Detailed conditions are given for the investigation of residual effectiveness, such as selection of operating points, control inputs, sensor faults, component faults, fault positions and observer eigenvalues. Then, for various values of n, defined fault types and defined fault positions, the observer-residual performance is noted and characteristics are derived and compared. Qualitative and quantitative evidence in graphical and table form shows, in several ways, how the performance and effectiveness of observer-based residuals change as n, and system complexity, increases.
EN
The paper concerns task and resource allocation in a complex of operations which may be considered as a part of the knowledge-based project management system. The brief overview of concepts and results concerning the allocation problem under uncertainty described by uncertain variables is presented. An application of two-level decomposition of the complex and the allocation taking into account uncertain and random parameters in the description of the operations are discussed. Two simple examples illustrate the approach presented.
EN
The feedback holdability problem for singular discrete-time linear systems is considered. Conditions are established for the existence of solutions to the following three problems for singular system (1) with regular pencil (E, A). Problem 1: find a gain matrix K such that the closed-loop trajectory is inside the nonnegative orthant R+n. Problem 2: find a gain matrix K such that the state vector xi of the closed-loop system xi = 0 for i greater than or equal k - 1, k = 1,...,n. Problem 3: find a gain matrix K such that ui = Kxi ∈ R+m and the trajectory of closed-loop system is inside R+n
EN
All symmetric polynomials of multiple variables, with the variables belonging to the fixed, final set, are the elements of the vector space of infinite dimension. The vector space contains numerous finite subspaces. These subspaces are subjected to a standard analysis. Set theory classifications and ordering relations indicate how to choose the basis. The investigation of transient matrices reveals sets of algebra identities. The unlimited set of these identities is particularly useful when it comes to engineering applications.
10
Six-dimensional Landau inequalities
PL
W pracy przedstawiono nowe pojęcia i wyniki dotyczące metodologii analizy zagadnień związanych z wartościami własnymi i wektorami i własnymi macierzy rzeczywistych o współczynnikach interwałowych postaci A = { A ; AC - A < A < A C + A } , gdzie A jest miarą niepewności . Przedstawione ujęcie jest prawdopodobnie najprostszym sposobem aproksymacji w modelowaniu drgań i ich własności w systemach o parametrach niepewnych.
EN
In the paper, we are concerned with interval - oriented methodology to mode l uncertaintie s o f eigenvalues , and eigenvectors of an nx n interva l rea l matrix A = { A ;AC - A< A< AC + A }, where A i s a measure of uncertainty. Presented methodology is probably the simples t way to model an d to approximate vibration properties of systems with uncertain parameters.
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