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The curved spacetime Maxwell equations are applied to the anisotropically expanding Kasner metrics. Using the application of vector identities we derive 2$^\textrm{nd}$-order differential wave equations for the electromagnetic field…

General Relativity and Quantum Cosmology · Physics 2022-11-08 Brett Bochner

We obtain the viscous and diffusive fundamental solution for monochromatic internal waves in a uniformly stratified medium and for anisotropic Brinkman flow. These solutions take the form of single integrals with logarithmic singularities,…

Fluid Dynamics · Physics 2026-05-18 Saikumar Bheemarasetty , Stefan G. Llewellyn Smith

Asymptotic expansion of the wavelet transform for small values of the dilation parameter a is obtained using asymptotic expansion of the Mellin convolution technique ofWong. Asymptotic expansions of Morlet wavelet transform, Mexican hat…

Functional Analysis · Mathematics 2014-04-09 R S Pathak , Ashish Pathak

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…

Numerical Analysis · Mathematics 2021-06-15 Shantanu Shahane , Surya Pratap Vanka

We examine the sum of modified Bessel functions with argument depending quadratically on the summation index given by \[S_\nu(a)=\sum_{n\geq 1} (\frac{1}{2} an^2)^{-\nu} K_\nu(an^2)\qquad (|\arg\,a|<\pi/2)\] as the parameter $|a|\to 0$. It…

Classical Analysis and ODEs · Mathematics 2019-03-07 R. B. Paris

We present a useful function for describing the profiles of dark-matter haloes with a varying asymptotic inner slope -\alpha, ranging from a cusp to a core, where the profiles of density, mass-velocity and potential are simple analytic…

Astrophysics of Galaxies · Physics 2016-10-06 Avishai Dekel , Guy Ishai , Aaron A. Dutton , Andrea V. Maccio

We establish an expansion by Gamma-convergence of the Fisher information relative to the reference measure exp(-beta V), where V is a generic multiwell potential and beta goes to infinity. The expansion reveals a hierarchy of multiple…

Probability · Mathematics 2018-12-11 Giacomo Di Gesù , Mauro Mariani

Spiral waves are observed in many natural phenomena. They have been extensively represented by the mathematical FitzHugh-Nagumo (FHN) model [Barkley et al., Phys. Rev. A 42, 2489 (1990)] of excitable media. In incompressible fluid…

Plasma Physics · Physics 2018-04-03 Sandeep Kumar , Bhavesh Patel , Amita Das

The large $n$ behaviour of the hypergeometric polynomial $$\FFF{-n}{\sfrac12}{\sfrac12}{\sfrac12-n}{\sfrac12-n}{-1}$$ is considered by using integral representations of this polynomial. This ${}_3F_2$ polynomial is associated with the…

Classical Analysis and ODEs · Mathematics 2016-09-07 Nico M. Temme

Linear second order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two…

Classical Analysis and ODEs · Mathematics 2017-02-27 T. M. Dunster , A. Gil , J. Segura

We consider the asymptotic expansion of the functional series \[S_{\mu,\gamma}(a;\lambda)=\sum_{n=1}^\infty \frac{n^\gamma e^{-\lambda n^2/a^2}}{(n^2+a^2)^\mu}\] for real values of the parameters $\gamma$, $\lambda>0$ and $\mu\geq0$ as…

Classical Analysis and ODEs · Mathematics 2021-01-06 R B Paris

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis…

Numerical Analysis · Mathematics 2018-09-26 Sangwoo Kang , Marc Lambert , Won-Kwang Park

To obtain the waveform template of gravitational waves (GWs), substantial computational resources and exceedingly high precision are often required. In the previous study [JCAP 11 (2023) 070], we efficiently and accurately calculate GW…

General Relativity and Quantum Cosmology · Physics 2024-07-25 Changkai Chen , Jiliang Jing

This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping…

Numerical Analysis · Mathematics 2025-09-30 Xinyu Cheng , Zhaonan Luo , Sheng Wang

Let $F(x)= \sum_{\nu\in\NN^d} F_\nu x^\nu$ be a multivariate power series with complex coefficients that converges in a neighborhood of the origin. Assume $F=G/H$ for some functions $G$ and $H$ holomorphic in a neighborhood of the origin.…

Combinatorics · Mathematics 2012-08-07 Alexander Raichev , Mark C. Wilson

Asymptotic expansion of a variation with anticipative weights is derived by the theory of asymptotic expansion for Skorohod integrals having a mixed normal limit. The expansion formula is expressed with the quasi-torsion, quasi-tangent and…

Probability · Mathematics 2021-01-05 Nakahiro Yoshida

Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…

Classical Analysis and ODEs · Mathematics 2025-11-04 T. M. Dunster , Amparo Gil , Diego Ruiz-Antolin , Javier Segura

The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the singularity…

Quantum Physics · Physics 2013-05-29 Denis D. Sheka , Boris A. Ivanov , Franz G. Mertens

We have considered an expansion of solutions of the non-linear equations for both longitudinal and transverse waves in collisionless Maxwellian plasma in series of non-damping overtones of the field E(x,t) and electron velocity distribution…

Plasma Physics · Physics 2014-11-13 V. N. Soshnikov

We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…

Exactly Solvable and Integrable Systems · Physics 2024-07-08 A. M. Kamchatnov