We consider modal logics of products of neighborhood frames and prove that for any pair L and L′ of logics from set {S4,D4,D,T} modal logic of products of Lneighborhood frames and L′-neighborhood frames is the fusion of L and L′.

In this paper, we investigate two L-neighborhood systems induced by an Lfuzzy topology in a complete residuated lattice L. We study the relationships among L-fuzzy topology, L-topologies and L-neighborhood systems. Finally, we give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54A05

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

Given a sequence (ak) = a0, a1, a2, . . . of real numbers, define a new sequence L(ak) = (bk) where bk = ak − ak−1ak+1. So (ak) is log-concave if and only if (bk) is a nonnegative sequence. Call (ak) infinitely log-concave if L(ak) is nonnegative for all i ≥ 1. Boros and Moll [3] conjectured that the rows of Pascal’s triangle are infinitely log-concave. Using a computer and a stronger version o...

the effective factors of forward speed, cylinder rotation, and clearance between a combine’s cylinder and concave on wheat kernel breakage and seed germination were studied in karaj area using a 955 model john dear combine. this study was conducted on three levels of adjustment for each of the variables, 1.2, 1.8 and 2.5 km/hr for forward speed, 800, 900, 1000 rpm for cylinder rotation as well ...

We propose a simple method of construction of new families of φ-divergences. This method called convex standardization is applicable to convex and concave functions ψ(t) twice continuously differentiable in a neighborhood of t = 1 with nonzero second derivative at the point t = 1. Using this method we introduce several extensions of the LeCam, power, χ and Matusita divergences. The extended fam...

We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional con...

We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional con...