Let 5 be a set in an «-dimensional Euclidean space, E„. The following concept was used by Horn and Valentine [2] in their study of L sets, and it provides the basis of this investigation. Definition 1. A set VES is a set of visibility in S if, given any point p ES, there exists a point qEV such that the closed segment pqQS. Notation. Given a point xES, let Vix) denote a continuum1 of visibility...

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper, the relationships of induced L-convex spaces with L-hull operators, product spaces, and quotient are discussed. It is shown that structure exactly by convex structure. Moreover, sub-S1, sub- S2, S2 S3 separation axioms introduced in spaces. Some properties them investigated.

A game on a convex geometry is a real-valued function de®ned on the family L of the closed sets of a closure operator which satis®es the ®nite Minkowski±Krein±Milman property. If L is the Boolean algebra 2 N then we obtain a n-person cooperative game. We will introduce convex and quasi-convex games on convex geometries and we will study some properties of the core and the Weber set of these games.

This paper investigates the complexity of steepest descent algorithms for two classes of discrete convex functions, M-convex functions and L-convex functions. Simple tie-breaking rules yield complexity bounds that are polynomials in the dimension of the variables and the size of the effective domain. Combination of the present results with a standard scaling approach leads to an efficient algor...

Abstract In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $$L^p$$ Lp -spaces in mind as a typical application. We show that the basic results from linear $$C_0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML"><m...

Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish hydrodynamic limits while layers are present, and derive steady Navier-Stokes-Fourier system non-slip conditions. Our contribution focuses on novel weighted $W^{1,\infty}$ estimates for Milne problem geometric correction. Also, develop stronger remainder based an $L^{2m...