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This paper considers a class of densities formed by taking the prod uct of nonnegative polynomials and normal densities. We investigate some relations of these densities with Hermite polylnomials. We construct a set of polynomials orthogonal with respect to the polynomial-normal density (PND ) . We invesigate the distribution of sums of independent random variables (r.v.) with PND. We construct a stochastic process such that the one-dimensional density of this process is PND.
Results of quantification procedures and properties of expectations series obtained for two data vintages are described. Volume index of production sold in manufacturing is defined for end-of-sample and real time data, and evaluated against expectations expressed in business tendency surveys. Empirical analysis confirms that while there are only minor differences in quantification results with respect to data vintage, properties of expectations time series obtained on their basis do diverge.
Let be a complex Hilbert space and B(H) denotes the algebra of all bounded linear operators acting on H. In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators (A, B) ∈ B(H) × B(H) satisfying: ∥ AX – XB − I∥ ≥ 1, for all X ∈ B(H). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.
How to determine the total non-active power of arbitrary periodical poly-phase loads or in other words: how to sum non-active powers resulting from non-sinusoidal and unbalanced voltages and currents? With algebraic summation or via aggregate power like the standards propose? In the time domain or with harmonic decomposition? What is the genuine meaning of non-active and apparent power? The reader may be amazed by questioning these problems which seem to be solved. Instead this article shows that the general solution is not that of the standards which define limiting cases but one that exists since a long time in the form of the geometric power concept of W. Quade that is commonly unkown today. The geometric method is compared to the concepts of aggregate power (Rechtleistung) and the algebraic summation of fictitious non-active powers. The consequences and meaning of the different concepts are analyzed.
Jak wyznaczyć całkowitą moc nieczynną dowolnych okresowych odbiorników wielofazowych, czyli inaczej: jak zsumować moce nieczynne wynikające z niesinusoidalnych i niezrównoważonych napięć i prądów? Z sumowaniem algebraicznym czy za pomocą sumarycznej mocy, jak proponują normy? W dziedzinie czasu czy z rozkładem harmonicznym? Jakie jest prawdziwe znaczenie nieaktywnej i pozornej mocy? Czytelnik może być zdumiony kwestionowaniem tych problemów, które wydają się być rozwiązane. Zamiast tego artykuł ten pokazuje, że generalnym rozwiązaniem nie jest rozwiązanie norm definiujących przypadki graniczne, ale takie, które istnieje od dawna w postaci koncepcji geometrycznej potęgi W. Quade, która jest dziś powszechnie nieznana. Metodę geometryczną porównuje się z pojęciami zagregowanej mocy (Rechtleistung) i algebraicznym sumowaniem fikcyjnych mocy nieczynnych. Analizowane są konsekwencje i znaczenie różnych pojęć.
Content available remote Tangency and orthogonality in metric spaces
We consider an abstract definition of tangency in metric spaces and study some of its properties. We introduce also a particular structure on metric spaces and define, with respect this structure, the notion of tangency and orthogonality. Some properties of continuous curves in such spaces are investigated.
Content available remote Romanovski polynomials in selected physics problems
We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.
W pracy przedstawiono analityczną metodę rozwiązania zagadnienia drgań swobodnych i wymuszonych belki Timoshenki. Założono, że belka jest wykonana z materiału lepko-sprężystego opisanego modelem reologicznym Voigta-Kelvina. W opracowanej metodzie użyto reguł operatorowych przedstawionych w pracy [2]. Istotą tej metody jest rozdzielenie zmiennych w przestrzeni zespolonej oraz własność ortogonalności zespolonych wektorów drgań własnych. Rozwiązania uzyskano w postaci uogólnionych szeregów Fouriera.
In this paper an analytical method of solving the free and forced vibration problems of Timoshenko beam is presented. It's assumed, that the beam is carried out from a viscoelastic material, which is descriebed by the rheology Voigt-Kelvin model. The besis of the elaborate method are the operator principles [2]. The essence of this method is separation of variables in the conjugate space and the property of orthogonality of complex eigenvector of free vibration. The solution in the generalize form of the Fourier's series is obtained.
Content available remote Relatively orthocomplemented skew nearlattices in Rickart rings
A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular. The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Rickart *-rings. The paper demonstrates that they can successfully be treated also in Rickart rings without involution.
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