In the year 1993, Gupta and Srivastava [3] introduced the integral modication of the well known Basakov operators by taking the weight functions of Szasz basis function, so called Baskakov-Szasz operators. To prove our one of the direct theorems, we use the technique of a mathematical tool which is the linear approximating method and is known as the Steklov means.
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The purpose of this paper is to present some theorems on existence and uniqueness of solution for nonautonomous second order Cauchy problem with a dumping operator and with dependent on t not densely defined operators.
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We study the porosity behavior of non-contractive mappings in a generalized metric space, a concept recently introduced in [1]. We also investigate partially the porosity position of a certain class of operators whose condition arises from [8].
Gogle VR są już szeroko stosowane w treningu umiejętności miękkich, a trójmiejski startup Flint Systems z powodzeniem udowodnił, że można je również wykorzystać w treningu umiejętności twardych. Porty, logistyka, offshore, wojsko, budownictwo, energetyka, edukacja – to tylko kilka sektorów, które mogą skorzystać na szkoleniu symulacyjnym VR.
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The paper is concerned with functional shifts and functional R-shifts for a right invertible operator D (cf. [30], [15]). Conditions for different kinds of invertibility of these functional shifts on a set of all D-monomials are established.
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By using the theory of extrapolation space X-1 associated with an operator A which is non densely defined in Banach space X, the existence and uniqueness of solutions of linear second order differential initial value problem (1) is proved.
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Operators preserving singularity and nonsingularity of matrices were studied in paper of P. Botta under the assumption that operators are linear. In the present paper the linearity of operators is not assumed: we only assume that operators are of the form T = (fi,j), wherei,j : K -> K and K is a field, i,j is an element of {1,2,...,n}. If n > 3, then in the matrix space Mn(K] operators preserving singularity and nonsingularity of matrices must be as in paper of P. Botta. If n < 2, operators may be nonlinear. In this case the forms of the operators are presented.
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Weak and strong convergence of resolvents of accretive operators have been studied in this paper under different iteration schemes. In particular for an accretive operator A, the inclusion 0 Ax has been solved. Applying this result, we have found the solution of equation x + Bx = f where B is a Lipschitzian accretive operator.
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There are investigated spaces v0,φ of sequences of bounded φ-variation. Spaces v0, φ are applied to the problem of weighted unconditional convergence of series. It is shown that (vo,φ,lφ* ), where lφ* means the Orlicz sequence space generated by the N-function φ*, is a pair of weighted unconditional convergence. There are also considered nonlinear convolution - type operators in v0,φ .
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In this paper we give an operatorial inequality which is applied to find estimations for the solutions of some integral and differential systems of inequalities.
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We consider some operations on affine planes which resemble the construction of a derived affine plane at a point of the Benz plane. We call them Benz-contractions (B-contractions) , distinguishing between chain contractions and generator contractions. We prove that the Pappos-Pascal configuration is the B-contraction of the affine plane of order 4 and we relate it to the Havlicek-Tietze configuration. We present a new (HT)o-configuration and research some problems of embeddability for (P-P), (H-T), and (HT)o. We propose a method of finding (n - 2) regular configurations on an arbitrary affine plane of order n. Among them are pairs of configurations with dual type and each such a pair can be completed with one point and n -f 1 lines to the initial plane. We prove that for an arbitrary n odd, the non-existence of the symmetric configuration ( n2-1/2, n+1/2) the non-existence of the projective plane of order n. On the basis of Gropp's article flOj, we solve some current problems concerning the existence of non-symmetric configurations with a natural index.
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Operators preserving the determinant of real matrices were studied in [1], [2] and [5] under assumption that the operator is linear. In this paper the linearity of the operators is not assumed: we only assume that the operators are of the form F = [fi,j], where functions fij : [...], we characterize these operators from [...] into itself preserving the determinant. An operator preserving the determinant of matrices must be linear as in [4]. The form of operator F is presented.
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In this note we explore commutativity up to a factor ab = alfa ba for Hermitian or normal elements of a complex Banach algebra. Our results generalize results obtained for bounded linear operators on Hilbert spaces.
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In the paper a topological presentation of Petri nets has been presented. The presentation is based on a closure operation defined for an arbitrary transitive and dense binary relation. Such relations lead to a natural definition of Petri nets as a special bitopological spaces. In the paper some elementare properties of such spaces-the counter parts of some properties of Petri nets-are described. The paper may be seen as a generalization of [3].
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In the present paper, the norm of the bounded linear operator nabla acting on the sequence space Lp has been found and the fine spectrum with respect to Goldberg's classification of the difference operator nabla over the sequence space Lp has been determined, where 1 < p < oo.
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We correct the mistake in the proof of Lemma 7 in our paper "Horizontal extension of connections into (2)-connections" published in Demonstratio Math. XXXVII (4) (2004).
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W artykule rozwiązano zagadnienie minimalizacji normy wahania napięcia rzeczywistego źródła energii elektrycznej, które zastępuje złożoną sieć zasilającą, uwzględniając również stany przejściowe. Stany te wywoływane są zmianami poboru mocy czynnej od strony odbiornika i kołysaniami sygnału napięcia źródłowego sieci. Użyto nowego aparatu matematycznego wynikłego z połączenia pojęcia ruchomej mocy czynnej i modulacji sygnałów harmonicznych.
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In the paper was solved the problem of minimizing the standard voltage fluctuations real source of electricity, which replaces a complex supply network, also taking into account transient states. These states are caused by changes in active power consumption from the receiver and signal rocking of voltage source network. It was used a new mathematical concepts resulting from the merger of moving active power and harmonic signals modulation.
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The purpose of this paper is to establish a strong convergence of an implicit iteration process to a common fixed point for a finite family of quasi-contractive operators. Our theorems give an armative response to a question raised by [Xu and Ori, Numer. Funct. Anal. Optim. 22 (2001) 767-773 ].
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