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...

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...

We address the enumeration of q-coloured planar maps counted by the number of edges and the number of monochromatic edges. We prove that the associated generating function is di erentially algebraic, that is, satis es a non-trivial polynomial di erential equation with respect to the edge variable. We give explicitly a di erential system that characterizes this series. We then prove a similar re...

Game theory is concerned with optimization problems involving several players with conicting interests. Di erential games are an interesting area inside this eld in which the problem is formulated by means of dynamical systems. In spite that the theoretical solution of di erential games is well known, faced with large-scale, complex systems, analytical or, even, numerical methods are not usuall...

This paper summarizes recent results on the number and characterization of di erential invariants of transformation groups Generalizations of theorems due to Ovsiannikov and to M Green are presented as well as a new approach to nding bounds on the number of independent di erential invariants Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables th...