Search results for "Integra"

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 (∼300 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…

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.

Biological responses to individualized small titanium implants for the treatment of focal full-thickness knee cartilage defects in a sheep model.

2019

Abstract Background The present study aimed to evaluate the functional, radiological and histological outcome of a customized focal implant for the treatment of focal full-thickness cartilage defects in sheep. Methods The study used magnetic resonance imaging data as the basis for construction of the titanium implant using a three-dimensional printing technique. This was then placed on the medial condyle of the knee joint in eight sheep and left in place in vivo over a period of six months. Following euthanasia, the local biological response was analyzed using micro-computed tomography, light microscopy and histological evaluation (International Cartilage Repair Society (ICRS) score). The v…

Pervaporation membrane reactors

2013

Pervaporation is a peculiar membrane separation process which is now considered for the integration with some types of reactions in new promising and interesting applications. Indeed, pervaporation membrane reactors are suitable to some specific utilizations also in sustainable chemistry, which is an area currently characterized by a growing interest. The fundamentals of this type of membrane reactors are presented and the advantages and the difficulties in many applications are discussed and reviewed with particular attention to the opportunities for future developments.

INTEGRAL SOLUTIONS TO A CLASS OF NONLOCAL EVOLUTION EQUATIONS

2010

We study the existence of integral solutions to a class of nonlinear evolution equations of the form [Formula: see text] where A : D(A) ⊆ X → 2X is an m-accretive operator on a Banach space X, and f : [0, T] × X → X and [Formula: see text] are given functions. We obtain sufficient conditions for this problem to have a unique integral solution.

Regularity of solutions of cauchy problems with smooth cauchy data

1988

Existence results and asymptotic behavior for nonlocal abstract Cauchy problems

2008

AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.