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Asymptotics of the partition function of a random matrix model

Pavel M. Bleher, Alexander Its (2005)

Annales de l’institut Fourier

We prove a number of results concerning the large N asymptotics of the free energy of a random matrix model with a polynomial potential. Our approach is based on a deformation of potential and on the use of the underlying integrable structures of the matrix model. The main results include the existence of a full asymptotic expansion in even powers of N of the recurrence coefficients of the related orthogonal polynomials for a one-cut regular potential and the double scaling asymptotics of the free...

Box-spline histograms for multivariate density estimation

Karol Dziedziul, Piotr Paluszek (2010)

Applicationes Mathematicae

The uniform approach to calculation of MISE for histogram and density box-spline estimators gives us a possibility to obtain estimators of derivatives of densities and the asymptotic constant.

Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations

Sabine Roller, Thomas Schwartzkopff, Roland Fortenbach, Michael Dumbser, Claus-Dieter Munz (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other. They...

Calculation of low Mach number acoustics: a comparison of MPV, EIF and linearized Euler equations

Sabine Roller, Thomas Schwartzkopff, Roland Fortenbach, Michael Dumbser, Claus-Dieter Munz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other....

Cálculo rápido de las funciones de Bessel modificadas Kis(X) e Iis(X) y sus derivadas.

Lluís Closas Torrente, Juan Antonio Fernández Rubio (1987)

Stochastica

En este trabajo discutimos la resolución de la ecuación de Besseld2x/dx2 + (1/x)(dy/dx) - (1 - s2/x2)y = 0.Las funciones de Bessel modificadas Kv(x) e Iv(x) son las soluciones a la ecuación anterior cuando v = is. El valor de la función Kis(x) es real y el de la función Iis(x) es complejo, por ello definimos en su lugar una función real Mis(x). La función Iis(x) resultará ser una combinación de las funciones Kis(x) y Mis(x). Daremos algunos desarrollos en serie de Mis(x) y Kis(x) junto con sus derivadas...

Commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1994)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the functions x r e - λ x and x s e + μ x is evaluated for r , s = 0 , 1 , 2 , ... and all λ , μ . Further commutative neutrix convolution products are then deduced.

Complete monotonicity of the remainder in an asymptotic series related to the psi function

Zhen-Hang Yang, Jing-Feng Tian (2024)

Czechoslovak Mathematical Journal

Let p , q with p - q 0 , σ = 1 2 ( p + q - 1 ) and s = 1 2 ( 1 - p + q ) , and let 𝒟 m ( x ; p , q ) = 𝒟 0 ( x ; p , q ) + k = 1 m B 2 k ( s ) 2 k ( x + σ ) 2 k , where 𝒟 0 ( x ; p , q ) = ψ ( x + p ) + ψ ( x + q ) 2 - ln ( x + σ ) . We establish the asymptotic expansion 𝒟 0 ( x ; p , q ) - n = 1 B 2 n ( s ) 2 n ( x + σ ) 2 n as x , where B 2 n ( s ) stands for the Bernoulli polynomials. Further, we prove that the functions ( - 1 ) m 𝒟 m ( x ; p , q ) and ( - 1 ) m + 1 𝒟 m ( x ; p , q ) are completely monotonic in x on ( - σ , ) for every m 0 if and only if p - q [ 0 , 1 2 ] and p - q = 1 , respectively. This not only unifies the two known results but also yields some new results.

Desigualdades de Gorny-Cartan en espacios normados.

Piedad Guijarro Carranza (1988)

Stochastica

This work deals with the study of the bounds of the asymptotic expansions of complex functions in a normed space. Some inequalities are obtained similar to the Gorny-Cartan for the bounds of asymptotic expansions in an angle of the complex space.

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