Two-scale techniques are developed for sequences of maps {uk} ⊂ L(Ω; R ) satisfying a linear di erential constraint Auk = 0. These, together with Γconvergence arguments and using the unfolding operator, provide a homogenization result for energies of the type

In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic di¤erential equations in Hilbert spaces. Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [16], [17], we will prove a result of Datko type concerning the exponential dichotomy of stoch...

We propose a new method for evaluating the security of block ciphers against di erential cryptanalysis and propose new structures for block ciphers. To this end, we de ne the word-wise Markov (Feistel) cipher and random output-di erential (Feistel) cipher and clarify the relations among the di erential, the truncated di erential and the impossible di erential cryptanalyses of the random output-...

Abstract. We examine the linearization of the problem of reflection tomography with data taken to be either the scattering relation or travel time along reflected rays. We obtain coordinate invariant formulae for the Fréchet di↵erentials with respect to perturbations of the wavespeed and reflector locator for the relevant nonlinear maps. The di↵erential with respect to the wavespeed is a system...

We have developed algorithms to count singular values of a bidiagonalmatrix which are greater than a speci ed value This requires the transformation of the singular value problem to an equivalent symmetric eigenvalue problem The counting of sin gular values is paramount in the design of bisection and multisection type algorithms for computing singular values on serial and parallel machines The ...

We express the Chern-Schwartz-MacPherson class of a possibly singular variety in terms of the total Chern class of a bundle of di erential forms with logarithmic poles. As an application, we obtain a formula for the Chern-Schwartz-MacPherson class of a hypersurface of a nonsingular variety, in terms of the Chern-Mather class of a suitable sheaf. x

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

Metastable dynamics, which qualitatively refers to physical processes that involve an extremely slow approach to their nal equilibrium states, is often associated with singularly perturbed convection-di usion-reaction equations. A problem exhibits metastable behavior when the approach to equilibrium occurs on a time-scale of order O(eC" ), where C > 0 and " is the singular perturbation paramete...