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NewU-Bernoulli, U-Euler and U-Genocchi polynomials and their matrices

In this paper, we introduce theU-Bernoulli,U-Euler, and U-Genocchi polynomials, their numbers, and their relationship with the Riemann zeta function. We also derive the Apostol-type generalizations to obtain some of their algebraic and differential properties. We introduce generalized U-Bernoulli,U-Euler and U-Genocchi polynomial Pascal-type matrix. We deduce some product formulas related to this matrix. Furthermore, we establish some explicit expressions for the U-Bernoulli, U-Euler, and U-G...

Impact of White Noise on the Exact Solutions of the Stochastic Riemann Wave Equation in Quantum Mechanics

In this article, the stochastic Riemann wave equation (SRWE) forced by white noise in the Itô sense is considered. The extended tanh function and mapping methods are applied to obtain new elliptic, rational, hyperbolic, and trigonometric stochastic solutions. Furthermore, we generalize some previous studies. The obtained solutions are important in explaining some exciting physical phenomena, since the SRWE is required for describing wave propagation. We plot numerous 3D and 2D graphical repre...

Approximate Symmetries and Conservation Laws for Mechanical Systems Described by Mixed Derivative Perturbed PDEs

This article focuses on developing and applying approximation techniques to derive conservation laws for the Timoshenko–Prescott mixed derivatives perturbed partial differential equations (PDEs). Central to our approach is employing approximate Noether-type symmetry operators linked to a conventional Lagrangian one. Within this framework, this paper highlights the creation of approximately conserved vectors for PDEs with mixed derivatives. A crucial observation is that the integration of thes...

Shape the EU future citizen. Environmental education on the European Green Deal

The Green SCENT project aims to educate European citizens to acquire green skills within the eight Focus Areas identified by the EU Green Deal Communication. The funded project involves 15 partners from 10 European countries. The very first outcome of the project is to build a competence framework for shaping the future environmental education of European citizens. The task specifically involved 13 researchers, organised into 8 teams (one for each focus area addressed by the Green Deal commun...

Timelike spherical curves according to equiform Bishop framein 3-dimensional Minkowski space

In this paper, we study the equiform Bishop formulae for the equiform timelike curves in3-dimensional Minkowski space where the equiform timelikespherical curves are defined accord-ing to the equiform Bishop frame. We establish a necessary and sufficient condition for an equiformtimelike curve to be an equiform timelike spherical curve. Furthermore, we give certain character-izations of equiform spherical curves in 3-dimensional Minkowski space, which are timelike withan equiform spacelike pr...

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