Mathématiques > Accueil > Avancées en Mathématiques Pures et Appliquées > Numéro
This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related to the Bernoulli polynomials. Denoting by $$${(B_n)}_{n \in \mathbb{N}}$$$ the sequence of the Bernoulli numbers and by $$${(B_n(X))}_{n \in \mathbb{N}}$$$ the sequence of the Bernoulli polynomials, we especially obtain that for any natural number $$$n$$$, the reciprocal polynomial of the polynomial $$$\big(B_n(X) - B_n\big)$$$ is integer-valued.
We generalize the well-known transforms such as short-time Fourier transform, wavelet transform and shearlet transform and refer it as Continuous Modulated Shearlet Transform. Important properties like Plancherel formula and inversion formula have been investigated. Uncertainty inequalities associated with this transform are presented.
In this paper, we study a discrete anisotropic Kirchho type problem using variational methods and critical point theory, and we discuss the existence of two solutions for the problem. A example is presented to demonstrate the application of our main results.
2020
Volume 20- 11
Numéro 1 (Mai 2020)2021
Volume 21- 12
Numéro 1 (Janvier 2021)2022
Volume 22- 13
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