Search results for " continuity."
showing 10 items of 229 documents
Mean curvature flow of graphs in warped products
2012
Let M be a complete Riemannian manifold which either is compact or has a pole, and let φ be a positive smooth function on M . In the warped product M ×φ R, we study the flow by the mean curvature of a locally Lipschitz continuous graph on M and prove that the flow exists for all time and that the evolving hypersurface is C∞ for t > 0 and is a graph for all t. Moreover, under certain conditions, the flow has a well defined limit.
MR2524292 (2010f:26007): Kolyada, V. I.; Lind, M. On functions of bounded p-variation. J. Math. Anal. Appl. 356 (2009), no. 2, 582–604. (Reviewer: Lu…
2009
For p∈(1,+∞), let f∈Lp be a 1-periodic function on the real line, with the norm of f given by ∥f∥p=(∫10|f(x)|pdx)1/p. The Lp-modulus of continuity of f is defined by ω(f,δ)p=sup0≤h≤δ(∫10|f(x+h)−f(x)|pdx)1/p, 0≤δ≤1. A partition of period 1 (or simply a partition) is a set Π={x0,x1,…,xn} of points such that x0<x1<…<xn=x0+1. For a given partition Π={x0,x1,…,xn} let vp(f;Π)=(∑k=0n−1|f(xk+1)−f(xk)|p)1/p. The modulus of p-continuity of f is defined by ω1−1/p(f,δ)=sup∥Π∥≤δvp(f;Π), where the supremum is taken over all partitions Π such that ∥Π∥=maxk(xk+1−xk)≤δ. In this paper, improving a previous estimate given by A. P. Terehin [Mat. Zametki 2 (1967), 289--300; MR0223512 (36 #6560)], it is shown th…
On Generalizing Lipschitz Global Methods forMultiobjective Optimization
2015
Lipschitz global methods for single-objective optimization can represent the optimal solutions with desired accuracy. In this paper, we highlight some directions on how the Lipschitz global methods can be extended as faithfully as possible to multiobjective optimization problems. In particular, we present a multiobjective version of the Pijavskiǐ-Schubert algorithm.
A systematic review of animal models for experimental neuroma
2015
Summary Peripheral neuromas can result in an unbearable neuropathic pain and functional impairment. Their treatment is still challenging, and their optimal management is to be defined. Experimental research still plays a major role, but - although numerous neuroma models have been proposed on different animals - there is still no single model recognised as being the reference. Several models show advantages over the others in specific aspects of neuroma physiopathology, prevention or treatment, making it unlikely that a single model could be of reference. A reproducible and standardised model of peripheral neuroma would allow better comparison of results from different studies. We present a…
Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity
2011
In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.
Non-Lipschitz Homogeneous Volterra Integral Equations
2018
In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …
On Ekeland's variational principle in partial metric spaces
2015
In this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of parti al metric spaces. As consequences of our results, we obtain some fixed p oint theorems of Caristi and Clarke types.
Approximation properties of q-Kantorovich-Stancu operator
2015
In this paper we study some properties of Kantorovich-type generalizations of the q-Stancu operators. We obtain some approximation properties for these operators, estimating the rate of convergence by using the first and second modulus of continuity. Also, we investigate the statistical approximation properties of the q-Kantorovich-Stancu operators using the Korovkin-type statistical approximation theorem.
La vida cotidiana de los vecinos de Manila a través de sus testamentos e inventarios de bienes
2019
With the general objective indicated in its title, this work tries to highlight relevant aspects in the continuity of the Spanish domain in the Philippines, dependent on the maintenance of the Spanish capital. The inevitable selection of topics has lead the preferences of this work towards the residents collaboration to defend the city, the conversion of many of them into traders of exotic products and singular slaves owners, and their collaboration to an incredible miscegenation due to the ethnic variety. On the other hand, to follow the footsteps of the first generation of residents in Manila, at the end of the 16th century and during the 17th century, this work gives us some information …
Absolutely continuous functions in Rn
2005
Abstract For each 0 α 1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý's and Hencl's definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L n , differentiable almost everywhere and satisfies the formula on change of variables.