In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...

We study oscillatory behavior of a class of second-order neutral di¤erential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional di¤erential inequalities. Our assumptions allow applications to di¤erential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results ...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

In this paper, an image denoising operator de ned by a non-linear partial di erential equation(PDE) is presented. Similar to the operators proposed by Perona, Malik and Catt e et al., it can remove noise, enhance step-like edges and keep the locality of the edges. Its extra ability is to keep thin edges. The criterion for stopping time is also investigated. The new operator is capable of removi...

We present an extension of the lambda-calculus with di erential constructions. We state and prove some basic results (con uence, strong normalization in the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of lambda-calculus.

We present an overview of intrinsic integration schemes for diierential equations evolving on manifolds, paying particular attention to homogeneous spaces. Various examples of applications are introduced , showing the generality of the methods. Finally we discuss abstract Runge{Kutta methods. We argue that homogeneous spaces are the natural structures for the study and the analysis of these met...

in this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. this method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . we investigate the existence and uniqueness of solutions. finally anumerical example is presented to illustrate the accuracy of the new technique.

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...

In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. Complanarts determine complanarity of solution vectors of systems of polynomial equations. Evaluation of complanart is reduced to evaluation of resultants. As in linear case, the pattern of eigenvectors de nes the pha...

Mycobacterium smegmatis contains three chaperonin (cpn60) genes homologous to the Escherichia coli groEL gene. One of these (cpn60.1) is required for biofilm formation, but is nonessential, whereas a second (cpn60.2) is essential. Mycobacterium smegmatis is unique among Mycobacteria in having a third chaperonin gene, cpn60.3. The cpn60.1 gene has a gene upstream (cpn10) that is homologous to th...