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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this paper the tensor interpolation by polynomials of several variables is considered. The effective formulas for polynomial coefficients for arithmetical case were obtained.
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Journal of Applied Analysis
EN We give a new proof and discuss an extension of Jack’s lemma for polynomials.
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Autobusy : technika, eksploatacja, systemy transportowe
PL Jednym z najistotniejszych urządzeń wpływających na działalność i otoczenie człowieka jest silnik spalinowy, który niezmiennie stanowi podstawowe źródło napędu w transporcie drogowym. Do oceny właściwości silnika w całym zakresie wykonywanej pracy służą charakterystyki, czyli zależności parametrów r[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this paper the tensor interpolation by polynomials of several variables is considered.
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Journal of Mathematics and Applications
2014 Vol. 37 59--66
EN [...] In this paper besides X we also consider some of its subclasses: X(...) and Y (...) S consisting of functions in X with the second coeffcient fixed and univalent starlike functions respectively. According to the suggestion, in Abstract we add one more paragraph at the end of the section: For X[...]
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Pomiary Automatyka Kontrola
PL W referacie zaprezentowano wyniki porównania niepewności przewidywanych wartości funkcji znalezionych na podstawie aproksymacji wyników pomiaru zwykłymi algebraicznymi oraz ortogonalnymi wielomianami Czebyszewa. Przedstawione są wzory analityczne do obliczenia niepewności tych funkcji.
EN In the paper the comparison results of the uncertainty of the forecasted values of function, obtained as a result of the measurement result approximation by both usual algebraic and Chebyshev polynomials are presented. The obtained formulas for calculation uncertainty of these function are presented[...]
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Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics
EN In this paper, we introduce a new generalization of the Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems. An explicit representation and an expansion of the matrix exponential in a series of these matrix polynomials is obtained[...]
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Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics
EN Let R be a prime ring with extended centroid C and characteristic different from 2, d a nonzero derivation of R, f(x1,..., xn) a nonzero multilinear polynomial over C such that [d2(f(x1,... , xn)),d(f(x1,... ,xn))]k = 0 for all x1,... ,xn in some nonzero right ideal [...] of R, where k is a fixed po[...]
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Archives of Electrical Engineering
PL W artykule przedstawione zostały nowe wyniki odnoszące się do jawnych rozwiązań równań opisujących pół-dyskretne modele stosowane w badaniach stanów nieustalonych w liniach długich. Podstawę w zrealizowanych badaniach stanowi teoria nieliniowych równań różnicowych. Wykazane zostało, że stosunek tran[...]
EN The paper presents new results related to explicit solutions of semi-discrete models which appear in studies of transients in lossy long transmission lines. The theory of nonlinear difference equations has been applied. It is shown that the ratio of transversal and longitudinal state variables distr[...]
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Journal of Mathematics and Applications
2014 Vol. 37 67--84
EN The main purpose of this paper is to study the controllability of solutions of the differential equation [...] In fact, we study the growth and oscillation of higher order differential polynomial with meromorphic coefficients in the unit disc [...] generated by solutions of the above kth order diffe[...]
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Computer Assisted Mechanics and Engineering Sciences
EN The paper demonstrates a specific power series expansion technique used to obtain the approximate solution of the two-dimensional wave equation in some unusual cases. The solution for inhomogeneous wave equation, for more complicated shape geometry of the body, discrete boundary conditions and a mem[...]
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Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics
2004 Vol. 37, nr 2 475--483
EN The author presents a proof of the theorem on a necessary and suficient condition for the semiscalar equivalency of the polynomial matrices with the relatively prime elementary divisors in terms of the Δ, C transformations of certain way builded numerical matrices.
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Journal of Mathematics and Applications
2018 Vol. 41 171--180
EN In this paper, we present some interesting results concerning the location of zeros of Lacunary-type of polynomial in the complex plane. By relaxing the hypothesis and putting less restrictive conditions on the coefficients of the polynomial, our results generalize and refines some classical results[...]
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Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics
EN We consider polynomials P in additive functions g1,... , gm and present two approaches for a characterization of those generalized polynomials p, which may be represented as p = P o (g1,..., gm). Under rather general assumptions on the domains of the gi and of P, one of the approaches is based on ce[...]
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Machine Dynamics Problems
EN The paper presents a powerful algorithm useful to solve the problem of experimental data values finding don't occur within the registered experimental data set by using the one-dimensional polynomial interpolation procedure via a cubic spline method. Described free algorithm is presented in the form[...]
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Acta of Bioengineering and Biomechanics
2018 Vol. 20, nr 1 169--184
EN The aim of this study was to investigate the curve fitting and model selection problem of the torque–velocity relationship of elbow flexors and extensors in untrained females. The second goal was to determine the optimal models in different function classes and the best, among the optimal ones. Last[...]
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Journal of Mathematics and Applications
2018 Vol. 41 123--156
EN We prove that the holomorphic differential equation ϕ’’(ϕ+c) = γ(ϕ’)² (ϕ:C→C be a holomorphic function and (γ, c) ϵ C²) plays a classical role on many problems of real and complex convexity. The condition exactly γ ϵ [wzór] (independently of the constant c) is of great importance in this paper. On [...]
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Elastomery
PL Wiele problemów technologicznych pojawiających się w przemyśle gumowym można rozwiązać w lepszy niż dotychczas sposób stosując aproksymacyjne metody optymalizacji. W artykule podano ogólne informacje dotyczące tych metod oraz przedstawiono 3 przykłady ich praktycznego zastosowania do optymalizacji s[...]
EN Many of the technical problems that appear in rubber industry can be resolved in better way than in the past if the approximation methods are applied. In this paper the general descriptions of approximation methods and three case studies of their use are presented. The chosen case studies concentrat[...]
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