Search results for "Formula"

A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions

2010

Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

Evaluation of nutritional parameters in infant formulas and powdered milk by Raman spectroscopy

2007

It has been made a critical evaluation of the application of near infrared Fourier transform-Raman spectroscopy for the simultaneous determination of the most important nutritional parameters such as energetic value, carbohydrate, protein and fat contents of infant formula and powdered milk samples based on the use of partial least squares (PLS) regression analysis. A highly heterogeneous population of 23 samples, covering a wide range of infant food formula and powdered milk, were obtained from the Spanish market. Raman spectra, obtained by excitation with a Nd:YAG laser at 1064 nm, show no disturbing fluorescence effects; therefore sample spectra can be recorded without any previous prepa…

Solution of a cauchy problem for an infinite chain of linear differential equations

2005

Defining the recurrence relations for orthogonal polynomials we have found an exact solution of a Cauchy problem for an infinite chain of linear differential equations with constant coefficients. These solutions have been found both for homogeneous and an inhomogeneous systems.

Regularity of solutions of cauchy problems with smooth cauchy data

1988

Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems

2002

AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.

Experimental Study of Central Baffle Flume

2019

In this paper, the hydraulics of a central baffle flume (CBF) were experimentally studied. Extensive experimental runs were carried out to highlight the effects of different geometrical parameters such as baffle length, contraction ratio, and the length of upstream and downstream guide walls. Two different approaches, i.e., the Π theorem of dimensional analysis coupled with the incomplete self-similarity theory and the energy balance equation, were applied to deduce the stage–discharge formula of a CBF characterized by different geometrical parameters. The stage–discharge relationship deduced by the dimensional analysis approach was more accurate than that obtained by the energy approach. F…

A remark on differentiable functions with partial derivatives in Lp

2004

AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

Path integral solution for non-linear system enforced by Poisson White Noise

2008

Abstract In this paper the response in terms of probability density function of non-linear systems under Poisson White Noise is considered. The problem is handled via path integral (PI) solution that may be considered as a step-by-step solution technique in terms of probability density function. First the extension of the PI to the case of Poisson White Noise is derived, then it is shown that at the limit when the time step becomes an infinitesimal quantity the Kolmogorov–Feller (K–F) equation is fully restored enforcing the validity of the approximations made in obtaining the conditional probability appearing in the Chapman Kolmogorov equation (starting point of the PI). Spectral counterpa…

Nuclear quantum effects in liquid water from path-integral simulations using anab initioforce-matching approach

2014

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterized by force-matching to density functional theory-based molecular dynamics simulations. The resulting effective potentials provide an inexpensive replacement for direct ab inito molecular dynamics simulations and allow efficient simulation of nuclear quantum effects. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals…

Semi-empirical Hartree-Fock calculations for KNbO 3 and KTaO 3

1997

As a first step in modeling the electronic structure of Perovskite-type ferroelectric mixed crystals K(Nb,Ta)O3, semiempirical calculations for pure KNbO3 and KTaO3 are performed with the intermediate neglect of the differential overlap (INDO) quantum chemical method. The calculations are mostly done for 40-atom supercells. The choice of the INDO parameters based on the comparison of results with ab initio and experimental data is discussed. INDO results for the equilibrium geometry and the (Gamma) -TO phonon frequencies are given. The results show that the accuracy of the INDO method is sufficient for reliably reproducing the energy differences on the order of 1 mRy (per formula unit) scal…