We show that the jump set of the solution of the minimizing Total Variation ow decreases with time for any initial condition in BV (Ω)∩L (Ω). We prove that the size of the jump also decreases with time.

We study numerically a model for shear bands that is loosely based on anti-plane shearing of granular material. In the model, a shear band is idealized to a jump discontinuity in the solution to the dynamic PDE. We do not explicitly incorporate small scale eeects within the shear band into the model{rather at the shear band we impose a jump condition which includes a length parameter modeling t...

In this paper we describe a one-dimensional interface problem for the heat equation, with a nonlinear (quadratic) jump condition at the interface. We derive a numerical method for approximating solutions of this nonlinear problem and provide some results from numerical experiments. The novelty of this problem is precisely this nonlinear (quadratic) jump condition, and it arises in the study of ...

This paper treats the risk-averse optimal portfolio problem with consumption in continuous time with a stochastic-volatility, jump-diffusion (SVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SVJD model with double-uniform jumpamplitude distributions and time-varying market parameters for the optimal portfolio problem. Although unlimited borro...

Based on the multidimensional uncertain optimal control problem with jump, in this paper, a kind of special multidimensional uncertain optimal control problem: multidimensional uncertain linear-quadratic (LQ) optimal control problem with jump which has a quadratic objective function for a multidimensional uncertain linear control system with jump is studied. A necessary and sufficient condition...

The jump condition at a possibly non-material interface for geometricallynecessary dislocation density in field dislocation mechanics (FDM) and its averaged approximation, phenomenological mesoscopic FDM (PMFDM), is derived. In the context of grain boundaries, the condition implies a tensorial constraint on all five grain boundary parameters, slip transmission at the boundary, possible grain bo...

This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain discretization of a semi-Markovian jump linear system that preserves stability. Also we show a characterization for the exponential mean stability of continu...

CONTEXT Fatigue has been shown to disrupt dynamic stability in healthy volunteers. It is not known if wearing prophylactic ankle supports can improve dynamic stability in fatigued athletes. OBJECTIVE To determine the type of ankle brace that may be more effective at providing dynamic stability after a jump-landing task during normal and fatigued conditions. DESIGN Two separate repeated-meas...

The purpose of this study was to comparatively investigate the energy expenditure of jumping on sand and on a firm surface. Eight male university volleyball players were recruited in this study and performed 3 sets of 10 repetitive jumps on sand (the S condition), and also on a force platform (the F condition). The subjects jumped every two seconds during a set, and the interval between sets wa...