Results 31 to 40 of about 1,199 (184)
Extension of Stein’s lemma derived by using an integration by differentiation technique
Examples and Counterexamples, 2022 We extend Stein’s lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein’s lemma, with the first being a rigorous proof by mathematical induction.
Konstantinos Mamis
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Multiindex Multivariable Hermite Polynomials [PDF]
Mathematical and Computational Applications, 2002 In the present paper multiindex multivariable Hermite polynomials in terms of series and generating function are defined. Their basic properties, differential and pure recurrence relations, differential equations, generating function relations and expansions have been established. Few deductions are also obtained.
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Hermite polynomials and Fibonacci oscillators [PDF]
Journal of Mathematical Physics, 2019 We compute the (q1, q2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1, q2)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states.
Andre A. Marinho, Francisco A. Brito
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Bivariate Poly-analytic Hermite Polynomials [PDF]
Results in Mathematics, 2020 A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical Hilbert space on the two-complex space with respect to the Gaussian measure.
Allal Ghanmi, Khalil Lamsaf
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Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver
International Journal for Numerical Methods in Fluids, EarlyView.A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
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Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials
Applied Mathematics in Science and EngineeringThis article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
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International Journal for Numerical Methods in Fluids, EarlyView.The immersed boundary method (IBM) was coupled with the moment representation lattice Boltzmann method (MR‐LBM), reducing bandwidth requirements compared to population‐based LBM formulations. A systematic assessment of IBM parameters was conducted to quantify their effect on computational performance.
Marco A. Ferrari +2 more
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Wildlife Biology, EarlyView.We compared population trends for rock ptarmigan Lagopus muta densities (2003‒2019) derived from walked transects and driven road transects in Mosfellsheiði and Slétta in southwest and northeast Iceland, respectively. The walked transects were laid out according to a random rule.
Matteo Ferrarini, Ólafur K. Nielsen
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Journal of Applied Crystallography, EarlyView.LamelODF is a MATLAB‐based toolbox aimed at simplifying the automated extraction of orientation distribution functions from 2D X‐ray diffraction data of lamellar minerals in transmission mode. It accommodates both laboratory and synchrotron data formats, providing an integrated pipeline from raw data to spatially resolved textural maps, enabling robust
Baptiste Dazas +5 more
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Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials
Open MathematicsThis study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-partial differential equations and investigate numerical aspects associated with these polynomials.
Wani Shahid Ahmad +2 more
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