Search results for "Mathematica"
showing 10 items of 7971 documents
Isotropic-nematic interface in suspensions of hard rods: Mean-field properties and capillary waves
2006
We present a study of the isotropic-nematic interface in a system of hard spherocylinders. First we compare results from Monte Carlo simulations and Onsager density functional theory for the interfacial profiles of the orientational order parameter and the density. Those interfacial properties that are not affected by capillary waves are in good agreement, despite the fact that Onsager theory overestimates the coexistence densities. Then we show results of a Monte Carlo study of the capillary waves of the interface. In agreement with recent theoretical investigations (Eur.Phys.J. E {\bf 18} 407 (2005)) we find a strongly anistropic capillary wave spectrum. For the wave-numbers accessed in o…
An integrated approach based on uniform quantization for the evaluation of complexity of short-term heart period variability: Application to 24 h Hol…
2007
We propose an integrated approach based on uniform quantization over a small number of levels for the evaluation and characterization of complexity of a process. This approach integrates information-domain analysis based on entropy rate, local nonlinear prediction, and pattern classification based on symbolic analysis. Normalized and non-normalized indexes quantifying complexity over short data sequences (â¼300 samples) are derived. This approach provides a rule for deciding the optimal length of the patterns that may be worth considering and some suggestions about possible strategies to group patterns into a smaller number of families. The approach is applied to 24 h Holter recordings of …
Indefinite integrals involving complete elliptic integrals of the third kind
2017
ABSTRACTA method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete …
A Lagrangian method for deriving new indefinite integrals of special functions
2015
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral is derived which involves an arbitrary function, and therefore yields an infinite number of indefinite integrals for any special function which obeys such a differential equation. Techniques are presented to obtain the more interesting integrals generated by such an approach, and many integrals, both previously known and completely new are derived using the method. Sample results are given for Bessel functions, Airy functions, Legendre functions and hype…
Fourier series for elliptic integrals and some generalizations via hypergeometric series
2008
Fourier series are derived for generalizations of the three canonical Legendre incomplete elliptic integrals using a hypergeometric series approach. The Fourier series for the incomplete Epstein–Hubbell integrals are obtained as special cases of the generalization of the Legendre integrals of the first and second kinds. The Fourier series for the integrals of the first and second kinds, and those for the Epstein–Hubbell integrals, were obtained recently using a different approach, but the series obtained for the generalization of the incomplete integral of the third kind is new. All cases of the integral of the third kind are given, with the modulus and the parameter being complex variables…
Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions
2017
Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the indep...
Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions
2017
ABSTRACTJacobian elliptic functions are used to obtain formulas for deriving indefinite integrals for the Jacobi Zeta function and Heuman's Lambda function. Only sample results are presented, mostly obtained from powers of the twelve Glaisher elliptic functions. However, this sample includes all such integrals in the literature, together with many new integrals. The method used is based on the differential equations obeyed by these functions when the independent variable is the argument u of elliptic function theory. The same method was used recently, in a companion paper, to derive similar integrals for the three canonical incomplete elliptic integrals.
Meta-analysis of the correlation between serum uric acid level and carotid intima-media thickness
2021
Objective Recently, increasing epidemiological evidence has shown that there is a correlation between serum uric acid level (SUA) and carotid intima-media thickness (CIMT). This paper explored the relationship between them through meta-analysis. Methods PubMed, Cochrane Library, EMBASE, Web of Science and Google Scholar were searched to obtain literature. The keywords used to retrieve the literature were carotid intima thickness, intima-media thickness, carotid atherosclerosis, carotid stenosis, carotid artery, uric acid, blood uric acid, and hyperuricaemia. The retrieval time was from the establishment of the database through July 2020. Stata15.0 and RevMan5.3 software were used for stati…
La carte, outil de diagnostic et de prospective pour les politiques scolaires
2006
ACL; International audience; Une étude de la localisation de nouveaux collèges dans le bassin de formation de Gap, en croissance démographique, montre que la carte constitue un robuste outil de diagnostic et de prospective pour les politiques scolaires. Tout d'abord, la carte, outil de recherche, mesure l'accessibilité des collèges et leurs aires de recrutement. Puis, vecteur de communication entre acteurs, elle "donne à voir", en le matérialisant, le territoire scolaire aux élus en charge des collèges, en modifiant leurs représentations de l'espace. Enfin, elle permet d'asseoir des scénarios.
Cartoon filter via adaptive abstraction
2016
We propose a non-parametric methodology to realize abstraction images.The redundant wavelet "a trous" algorithm is applied for details detection.An multi-scale circular median filter is used as a smoothing filter.The proposed algorithm is simple and fast on low-cost entry-level hardware. Abstraction in computer graphics defines a procedure that discriminates the essential information that is worth keeping. Usually details, that correspond to higher frequency components, allow to distinguish otherwise similar images. Vice versa, low frequencies are related to the main information, which are larger structures. Contours themselves may also be identified by high frequencies and separate each pi…