In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, degree L , M -fuzzy concavity is introduced and characterized as generalization id="M2"> -concave structure id="M3"> conca...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

We define a class of L-convex-concave subsets of RP n , where L is a projective sub-space of dimension l in RP n. These are sets whose sections by any (l+1)-dimensional space L ′ containing L are convex and concavely depend on L ′. We introduce an L-duality for these sets, and prove that the L-dual to an L-convex-concave set is an L *-convex-concave subset of (RP n) *. We discuss a version of A...

This paper is to characterize L-concavities and L-convexities via some derived forms of relations operators. Specifically, notions L-concave internal relation space hull are introduced. It proved that the category L-concave
 spaces isomorphic spaces. Also, L-convex enclosed

In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure compositions including distribution perimeter tilt, number summands, shape graph a typical composition. We present solutions to these applying Fristedt’s conditioning device on uniform measure.

An interferon-induced endoribonuclease, ribonuclease L (RNase L), is implicated in both the molecular mechanism of action of interferon and the fundamental control of RNA stability in mammalian cells. RNase L is catalytically active only after binding to an unusual activator molecule containing a 5'-phosphorylated 2',5'-linked oligoadenylate (2-5A), in the N-terminal half. Here, we report the c...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

Dijkstra’s algorithm is a well-known algorithm for the single-source shortest path problem in a directed graph with nonnegative edge length. We discuss Dijkstra’s algorithm from the viewpoint of discrete convex analysis, where the concept of discrete convexity called L-convexity plays a central role. We observe first that the dual of the linear programming (LP) formulation of the shortest path ...

This paper sheds a new light on submodular function minimization and maximization from the viewpoint of discrete convex analysis. L-convex functions and M-concave functions constitute subclasses of submodular functions on an integer interval. Whereas L-convex functions can be minimized efficiently on the basis of submodular (set) function minimization algorithms, M-concave functions are identif...