Search results for " function"
showing 10 items of 9395 documents
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.
Renal function and carotid atherosclerosis in adults with no known kidney disease
2017
Abstract Background and aims A high prevalence of atherosclerotic lesions characterizes patients with chronic kidney disease, though there is little data on the relationship between kidney function and atherosclerotic changes in the healthy population or in people with no known renal impairment. The aim of our study was to analyze, in a comprehensive general population with no known kidney disease, the relationship between renal function and subclinical carotid atherosclerotic damage. Methods and results A general real-life population of 611 participants (233 males and 378 females; age ≥18 years) with no known kidney failure was selected for the study. The glomerular filtration rate (GFR) w…
Renal haemodynamics and severity of carotid atherosclerosis in hypertensive patients with and without impaired renal function.
2014
Background and Aim. Renal resistance index (RRI), assessed by Duplex-Doppler sonography, has been classically considered as a mere expression of intrarenal vascular resistance. Recent studies, however, have showed that RRI is also influenced by upstream factors, especially arterial compliance, confirming its possible role as a marker of systemic vascular alterations. Several studies have shown that carotid intima-media thickness (cIMT) and carotid plaques (cP), assessed by ultrasonography, are documented markers of subclinical organ damage as well as expression of progressive atherosclerotic disease, and that they get worse with the progressive deterioration of renal function. The study was…
Consumer attitude toward using smart shopping carts: a comparative analysis of Italian and Croatian consumer attitudes
2016
This paper aims to explore consumer attitudes toward using smart shopping cart, considering country of origin, gender, age, and intentions to use smart shopping carts while purchasing. Moreover, it investigates the influence of extracted factors on consumers' attitudes toward using smart shopping carts and the users' levels of digital competence. The data was collected through survey questionnaires using a purposive sample of 313 Croatian and Italian respondents. To this end, we applied statistical methodologies such as binary logistic regression, factor analysis, and analysis of variance. We found that, compared with Croatians, Italian respondents have a more positive attitude toward using…
Multipotential Role of Growth Factor Mimetic Peptides for Osteochondral Tissue Engineering
2022
Articular cartilage is characterized by a poor self-healing capacity due to its aneural and avascular nature. Once injured, it undergoes a series of catabolic processes which lead to its progressive degeneration and the onset of a severe chronic disease called osteoarthritis (OA). In OA, important alterations of the morpho-functional organization occur in the cartilage extracellular matrix, involving all the nearby tissues, including the subchondral bone. Osteochondral engineering, based on a perfect combination of cells, biomaterials and biomolecules, is becoming increasingly successful for the regeneration of injured cartilage and underlying subchondral bone tissue. To this end, recently,…
Effects of Exercise on Patellar Cartilage in Women with Mild Knee Osteoarthritis
2015
AB Purpose: This study aims to investigate the effects of exercise on patellar cartilage using T2 relaxation time mapping of magnetic resonance imaging in postmenopausal women with mild patellofemoral joint osteoarthritis (OA). Methods: Eighty postmenopausal women (mean age, 58 (SD, 4.2) yr) with mild knee OA were randomized to either a supervised progressive impact exercise program three times a week for 12 months (n = 40) or a nonintervention control group (n = 40). Biochemical properties of cartilage were estimated using T2 relaxation time mapping, a parameter sensitive to collagen integrity, collagen orientation, and tissue hydration. Leg muscle strength and power, aerobic capacity, and…
New fitting scheme to obtain effective potential from Car-Parrinello molecular dynamics simulations: Application to silica
2008
A fitting scheme is proposed to obtain effective potentials from Car-Parrinello molecular dynamics (CPMD) simulations. It is used to parameterize a new pair potential for silica. MD simulations with this new potential are done to determine structural and dynamic properties and to compare these properties to those obtained from CPMD and a MD simulation using the so-called BKS potential. The new potential reproduces accurately the liquid structure generated by the CPMD trajectories, the experimental activation energies for the self-diffusion constants and the experimental density of amorphous silica. Also lattice parameters and elastic constants of alpha-quartz are well-reproduced, showing th…