Search results for "Smooth"

Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

2006

Abstract It is shown that if the modulus Γ X of nearly uniform smoothness of a reflexive Banach space satisfies Γ X ′ ( 0 ) 1 , then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.

2-SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS

2008

AbstractIn this paper, some min–max theorems for even andC1functionals established by Ghoussoub are extended to the case of functionals that are the sum of a locally Lipschitz continuous, even term and a convex, proper, lower semi-continuous, even function. A class of non-smooth functionals admitting an unbounded sequence of critical values is also pointed out.

Polynomial Smoothing Splines

2014

Interpolating splines is a perfect tool for approximation of a continuous-time signal \(f(t)\) in the case when samples \(x[k]=f(k),\;k\in \mathbb {Z}\) are available. However, frequently, the samples are corrupted by random noise. In such case, the so-called smoothing splines provide better approximation. In this chapter we describe periodic smoothing splines in one and two dimensions. The SHA technique provides explicit expression of such splines and enables us to derive optimal values of the regularization parameters.

On approximation of a class of stochastic integrals and interpolation

2004

Given a diffusion Y = (Y_{t})_{t \in [0,T]} we give different equivalent conditions so that a stochastic integral has an L 2-approximation rate of n −η, {\rm \eta \in (0,1/2],} if one approximates by integrals over piece-wise constant integrands where equidistant time nets of cardinality n + 1 are used. In particular, we obtain assertions in terms of smoothness properties of g(Y T ) in the sense of Malliavin calculus. After optimizing over non-equidistant time-nets of cardinality n + 1 in case {\rm \eta > 0} , it turns out that one always obtains a rate of n^{ - 1/2}, which is optimal. This applies to all functions g obtained in an appropriate way by the real interpolation method between th…

A Mesh-free Particle Method for Transient Full-wave Simulation

2007

A mesh-free particle method is presented for electromagnetic (EM) transient simulation. The basic idea is to obtain numerical solutions for the partial differential equations describing the EM problem in time domain, by using a set of particles, considered as spatial interpolation points of the field variables, arbitrarily placed in the problem domain and by avoiding the use of a regular mesh. Irregular problems geometry with diffused non-homogeneous media can be modeled only with an initial set of arbitrarily distributed particles. The time dependence is accounted for with an explicit finite difference scheme. Moreover the particle discretization can be improved during the process time ste…

A coupled Finite Volume–Smoothed Particle Hydrodynamics method for incompressible flows

2016

Abstract An hybrid approach is proposed which allows to combine Finite Volume Method (FVM) and Smoothed Particle Hydrodynamics (SPH). The method is based on the partitioning of the computational domain into a portion discretized with a structured grid of hexahedral elements (the FVM-domain ) and a portion filled with Lagrangian particles (the SPH-domain ), separated by an interface made of triangular elements. A smooth transition between the solutions in the FVM and SPH regions is guaranteed by the introduction of a layer of grid cells in the SPH-domain and of a band of virtual particles in the FVM one (both neighboring the interface), on which the hydrodynamic variables are obtained throug…

Dissecting Abdominal Aortic Aneurysm Is Aggravated by Genetic Inactivation of LIGHT (TNFSF14)

2021

Abdominal aortic aneurysm (AAA), is a complex disorder characterized by vascular vessel wall remodeling. LIGHT (TNFSF14) is a proinflammatory cytokine associated with vascular disease. In the present study, the impact of genetic inactivation of Light was investigated in dissecting AAA induced by angiotensin II (AngII) in the Apolipoprotein E-deficient (Apoe−/−) mice. Studies in aortic human (ah) vascular smooth muscle cells (VSMC) to study potential translation to human pathology were also performed. AngII-treated Apoe−/−Light−/− mice displayed increased abdominal aorta maximum diameter and AAA severity compared with Apoe−/− mice. Notably, reduced smooth muscle α-actin+ area and Acta2 and C…

Effects of Some Directly-Acting Smooth Muscle Relaxant Drugs on Isolated Human Preparations of the Upper Urinary Tract

1985

It is generally assumed that drugs which induce relaxation of smooth muscles may be of clinical importance in some urological disorders; such drugs are indeed widely used, for example in the therapy of unstable bladders or to facilitate the passage of ureteral stones. Antispasmodic action may be classified in neurotropic and musculo-tropic action; the former acting on the autonomic nervous system and the latter directly on smooth muscle cells. Examples for the first type of action are anticholinergic drugs or alpha-adrenoceptor-antagonists, whereas papaverine is a classic drug with the second type of action.

Alterations of intestinal transit and fecal output in dystrophic mdx mice.

2009

Myogenic NOS and endogenous NO production are defective in colon from dystrophic (mdx) mice

2001

The aim of the present study was to evaluate whether alterations in the distribution and/or function of nitric oxide synthase (NOS) could be involved in the development of the spontaneous mechanical tone observed in colon from dystrophic (mdx) mice. By recording the intraluminal pressure of isolated colon from normal mice, we showed that Nω-nitro-L-arginine methyl ester (L-NAME) increased the tone, even in the presence of tetrodotoxin. The effect was prevented by L-arginine, nifedipine, or Ca2+-free solution. In colon from mdx mice, L-NAME was ineffective. Immunohistochemistry revealed that the presence and distribution of neuronal (nNOS), endothelial, and inducible NOS isoforms in smooth m…