On the gaps between -binomial coefficients
Florian Luca, Sylvester Manganye (2021)
Communications in Mathematics
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In this note, we estimate the distance between two -nomial coefficients , where and is an integer.
Florian Luca, Sylvester Manganye (2021)
Communications in Mathematics
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In this note, we estimate the distance between two -nomial coefficients , where and is an integer.
Laiyi Zhu, Xingjun Zhao (2022)
Czechoslovak Mathematical Journal
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Let be the space of all trigonometric polynomials of degree not greater than with complex coefficients. Arestov extended the result of Bernstein and others and proved that for and . We derive the multivariate version of the result of Golitschek and Lorentz for all trigonometric polynomials (with complex coeffcients) in variables of degree at most .
Nisar A. Rather, Suhail Gulzar, Aijaz A. Bhat (2022)
Archivum Mathematicum
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Let be a polynomial of degree at most which does not vanish in the disk , then for and , Boas and Rahman proved In this paper, we improve the above inequality for by involving some of the coefficients of the polynomial . Analogous result for the class of polynomials having no zero in is also given.
Lamberto Cattabriga, Luisa Zanghirati (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The surjectivity of the operator from the Gevrey space , , onto itself and its non-surjectivity from to is proved.
Ruyun Ma (2002)
Annales Polonici Mathematici
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Let α,β,γ,δ ≥ 0 and ϱ:= γβ + αγ + αδ > 0. Let ψ(t) = β + αt, ϕ(t) = γ + δ - γt, t ∈ [0,1]. We study the existence of positive solutions for the m-point boundary value problem ⎧u” + h(t)f(u) = 0, 0 < t < 1, ⎨ ⎩, where , (for i ∈ 1,…,m-2) are given constants satisfying , and . We show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and...
Indrajit Lahiri, Amit Sarkar (2016)
Mathematica Bohemica
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The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and...
De-Jun Feng (2016)
Journal of the European Mathematical Society
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For a real number and a positive integer , let . In this paper, we show that is dense in if and only if and is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].
Marian Genčev (2019)
Communications in Mathematics
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The scope of this note is a self-contained presentation of a mathematical method that enables us to give an absolute upper bound for the difference of the Gini coefficients where represents the vector of the gross wages and represents the vector of the corresponding super-gross wages that is used in the Czech Republic for calculating the net wage. Since (as of June 2019) , the study of the above difference seems to be somewhat inaccessible for many economists. However, our estimate...
Marcin Dudziński (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let: , where , , be a -dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf , and denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.
Lukas Braun (2019)
Communications in Mathematics
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We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the -Hilbert series is a Vandermonde-like determinant. We show that the -polynomial of the Grassmannian coincides with the -Narayana polynomial. A simplified formula for the -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the -Narayana numbers,...