In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

We prove an existence and uniqueness result for a Monge-Ampère type equation in the Cegrell class Eχ.

• M. Monge, Generation of the symmetric field by Newton polynomials in prime characteristic, published in Rocky Mountains Journal (2012). It was proved by Dvornicich-Zannier that the polynomials xa + ya, xb + yb, xc+yc generate the field of symmetric function in x, y over Q, when a,b,c have no common factor. We extend the result in prime characteristic p, under the additional hypothesis that a,...

This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction presented in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder. Résumé. Dans la présente note nous décrivons brièvement la construction introduite dans [7] à propo...

An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in R . This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory. As a further applicati...

We give examples of composition operators CΦ on H(D) showing that the condition ‖Φ‖∞ = 1 is not sufficient for their approximation numbers an(CΦ) to satisfy limn→∞[an(CΦ)] √ n = 1, contrary to the 1-dimensional case. We also give a situation where this implication holds. We make a link with the Monge-Ampère capacity of the image of Φ. Key-words : approximation numbers; Bergman space; bidisk; co...

The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control prblem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to th...