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    Wyświetlanie 1-7 z 7
    Tytuł:
    Generalized derivations and generalized exponential monomials on hypergroups
    Autorzy:
    Fechner, Żywilla
    Gselmann, Eszter
    Székelyhidi, László
    Powiązania:
    https://bibliotekanauki.pl/articles/29519377.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    moment function
    moment sequence
    exponential monomial
    exponential polynomial
    derivation
    higher order derivation
    hypergroup
    Opis:
    In one of our former papers Endomorphisms of the measure algebra of commutative hypergroups we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with this, we are now looking for the connection between the generalized exponential polynomials of a commutative hypergroup and the higher order derivations of the corresponding measure algebra.
    Źródło:
    Opuscula Mathematica; 2023, 43, 4; 493-505
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On similarities between exponential polynomials and hermite polynomials
    Autorzy:
    Hetmaniok, E.
    Pleszczyński, M.
    Słota, D.
    Wituła, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/122357.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Stirling numbers
    Bell polynomials
    Hermite polynomials
    exponential polynomial
    generalized Hermite-Bell polynomials
    Dobinski’s formula
    Opis:
    The aim of this paper is to introduce and compare some fundamental analytical properties of the title polynomials. Many similarities between them are emphasized in the paper. Moreover, the authors present many isolated results, new proofs and identities.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 3; 93-104
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Conditions for asymptotic stability of first order scalar differential-difference equation with complex coefficients
    Autorzy:
    Kapica, Rafał
    Zawiski, Radosław
    Powiązania:
    https://bibliotekanauki.pl/articles/27314669.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    first order differential-difference equation with complex coefficients
    stability of differential-difference equation
    characteristic exponential polynomial of differential-difference equation
    retarded differential-difference equation
    DDE
    Opis:
    We investigate a scalar characteristic exponential polynomial with complex coefficients associated with a first order scalar differential-difference equation. Our analysis provides necessary and sufficient conditions for allocation of the roots in the complex open left half-plane what guarantees asymptotic stability of the differential-difference equation. The conditions are expressed explicitly in terms of complex coefficients of the characteristic exponential polynomial, what makes them easy to use in applications. We show examples including those for retarded PDEs in an abstract formulation.
    Źródło:
    Archives of Control Sciences; 2023, 33, 3; 607--629
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Entire functions of exponential type not vanishing in the half-plane \(\Im z > k\), where \(k > 0\)
    Autorzy:
    Hachani, Mohamed Amine
    Powiązania:
    https://bibliotekanauki.pl/articles/747061.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Inequalities
    entire functions of exponential type
    polynomial
    trigonometric polynomial
    Opis:
    Let \(P (z)\) be a polynomial of degree \(n\) having no zeros in \(|z| < k\), \(k \leq 1\), and let \(Q (z) := z^n \overline{P (1/{\overline {z}})}\). It was shown by Govil that if \(\max_{|z| = 1} |P^\prime (z)|\) and \(\max_{|z| = 1} |Q^\prime (z)|\) are attained at the same point of the unit circle \(|z| = 1\), then \[\max_{|z| = 1} |P'(z)| \leq \frac{n}{1 + k^n} \max_{|z| = 1} |P(z)|.\]The main result of the present article is a generalization of Govil's polynomial inequality to a class of entire functions of exponential type.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 1
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polynomial stability of evolution operators in Banach spaces
    Autorzy:
    Megan, M.
    Ceausu, T.
    Ramneantu, M. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/254941.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    evolution operator
    polynomial stability
    exponential stability
    Opis:
    The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
    Źródło:
    Opuscula Mathematica; 2011, 31, 2; 279-288
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Particle swarm optimization for solving a class of type-1 and type-2 fuzzy nonlinear equations
    Autorzy:
    Sadiqbatcha, S.
    Jafarzadeh, S.
    Ampatzidis, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/91663.pdf
    Data publikacji:
    2018
    Wydawca:
    Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
    Tematy:
    type-1 fuzzy sets
    type-2 fuzzy sets
    polynomial
    exponential equation
    particle swarm optimization (PSO)
    Opis:
    This paper proposes a modified particle swarm optimization (PSO) algorithm that can be used to solve a variety of fuzzy nonlinear equations, i.e. fuzzy polynomials and exponential equations. Fuzzy nonlinear equations are reduced to a number of interval nonlinear equations using alpha cuts. These equations are then sequentially solved using the proposed methodology. Finally, the membership functions of the fuzzy solutions are constructed using the interval results at each alpha cut. Unlike existing methods, the proposed algorithm does not impose any restriction on the fuzzy variables in the problem. It is designed to work for equations containing both positive and negative fuzzy sets and even for the cases when the support of the fuzzy sets extends across 0, which is a particularly problematic case.
    Źródło:
    Journal of Artificial Intelligence and Soft Computing Research; 2018, 8, 2; 103-110
    2083-2567
    2449-6499
    Pojawia się w:
    Journal of Artificial Intelligence and Soft Computing Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the exponential Orlicz norms of stopped Brownian motion
    Autorzy:
    Peškir, Goran
    Powiązania:
    https://bibliotekanauki.pl/articles/1288072.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Brownian motion (Wiener process)
    stopping time
    exponential Young function
    exponential Orlicz norm
    Doob's maximal inequality for martingales
    Burkholder-Gundy's inequality
    Davis' best constants
    Hermite polynomial
    continuous (local) martingale
    Ito's integral
    the quadratic variation process
    time change (of Brownian motion)
    Kahane-Khinchin's inequalities
    Opis:
    Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by $ψ_p(x) = exp(|x|^p)-1$ with 0 < p ≤ 2) of $max_{0≤t≤τ}|B_t|$ or $|B_τ|$ to be finite, where $B = (B_t)_{t≥0}$ is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that $∥max_{0≤t≤τ}|B_t|∥_{ψ_1} < ∞$ as soon as $E(τ^{k}) = O(C^{k}k^{k})$ for some constant C > 0 as k → ∞ (or equivalently $∥τ∥_{ψ_1} < ∞$). In particular, if τ ∼ Exp(λ) or $|N(0,σ^2)|$ then the last condition is satisfied, and we obtain $∥max_{0≤t≤τ}|B_t|∥_{ψ_1} ≤ K √{E(τ)}$ with some universal constant K > 0. Moreover, this inequality remains valid for any class of stopping times τ for B satisfying $E(τ^{k}) ≤ C(Eτ)^{k}k^{k}$ for all k ≥ 1 with some fixed constant C > 0. The method of proof relies upon Taylor expansion, Burkholder-Gundy's inequality, best constants in Doob's maximal inequality, Davis' best constants in the $L^p$-inequalities for stopped Brownian motion, and estimates of the smallest and largest positive zero of Hermite polynomials. The results extend to the case of any continuous local martingale (by applying the time change method of Dubins and Schwarz).
    Źródło:
    Studia Mathematica; 1995-1996, 117, 3; 253-273
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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