Annual mean temperature of 50 well-distributed stations in India is analyzed for trend and climate jump. Four statistical tests are used to detect the Table-look-up test, which more appropriate than ‘t’ test time series data, has been applied first Sudden changes noticed by getting discontinuities or jump annual most stations. It was found that while northern received much earlier i.e. during d...

In this work, an eigenvalue problem for Dirac operators with discontinuities is investigated in the case when an eigenparameter appears not only in the differential equation but also in the boundary and jump conditions, polynomially. Mathematics Subject Classification: 34A55, 34B24, 34L05

We study local structure of time-optimal controls and trajectories for a 3dimensional control-affine system with a 2-dimensional control parameter with values in the disk. In particular, we give sufficient conditions, in terms of Lie bracket relations, for optimal controls to be smooth or to have only isolated jump discontinuities.

Crank-Nicolson is a popular method for solving parabolic equations because it is unconditionally stable and second order accurate. One drawback of CN is that it responds to jump discontinuities in the initial conditions with oscillations which are weakly damped and therefore may persist for a long time. We present a selection of methods to reduce the amplitude of these oscillations.

We consider a class of nonconvex functionals of the gradient in one dimension, which we regularize with a second order derivative term. After a proper rescaling, suggested by the associated dynamical problems, we show that the sequence {Fν} of regularized functionals Γ-converges, as ν → 0+, to a particular class of free-discontinuity functionals F , concentrated on SBV functions with finite ene...

Stochastic models for phenomena that can exhibit sudden changes involve the use of processes whose sample functions may have discontinuities. This report provides some tools for working with such processes. We develop a sample path formula for the cumulative jump height over a given time interval. From this formula an expression for the expected value of the cumulative jump random variable is d...

Discontinuities between distinct regions, described by different equation sets, cause difficulties for PDE/ODE solvers. We present a new algorithm that eliminates integrator discontinuities through regularizing discontinuities. First, the algorithm determines the optimum switch point between two functions spanning adjacent or overlapping domains. The optimum switch point is determined by search...

We consider the local convergence of hysteretic (relay) approximations to a diierential equation with discontinuous right hand side when the set of discontinuities consists of a jump across intersecting surfaces. We are particularly concerned with the anticipated behavior in settings for which the standard Filippov recipe is ambiguous. The approach represents work in progress.

In this paper we analyse local regularity of time-optimal controls and trajectories for an n -dimensional affine control system with a control parameter, taking values in a k -dimensional closed ball. In the case of k = n − 1 , we give sufficient conditions in terms of Lie bracket relations for all optimal controls to be smooth or to have only isolated jump discontinuities.

In this paper we analyse local regularity of time-optimal controls and trajectories for an n -dimensional affine control system with a control parameter, taking values in a k -dimensional closed ball. In the case of k = n − 1 , we give sufficient conditions in terms of Lie bracket relations for all optimal controls to be smooth or to have only isolated jump discontinuities.