The theory of u0-positive operators with respect to a cone in a Banach space is applied to eigenvalue problems associated with the second order ∆-differential equation (often referred to as a differential equation on a measure chain) given by y(t) + λp(t)y(σ(t)) = 0, t ∈ [0, 1], satisfying the boundary conditions y(0) = 0 = y(σ2(1)). The existence of a smallest positive eigenvalue is proven and...

We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox [10], of the including topos....

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

Flexible polymers in dilute solution enhance the viscosity in slow flows. But in strong, rapidly varying, shear fields, they behave elastically. A turbulent cascade (from large to small scales) should thus be deeply modified when the elastic stresses become comparable to the Reynold's stress. A (tentative) scaling picture for these effects has been proposed by M. Tabor and the present author1):...

Let f : P n <mml:mo stret...

Choose random functions f1, f2, f3, . . . independently and uniformly from among the nn functions from [n] into [n]. For t > 1, let gt = ft ◦ ft−1 ◦ · · · ◦ f1 be the composition of the first t functions, and let T be the smallest t for which gt is constant(i.e. gt(i) = gt(j) for all i, j). The goal of this paper is to determine the asymptotic distribution of T . We prove that, for any positive...

Suppose G is a finite graph with vertex-set V (G) and edge-set E(G). An edge-magic total labelling on G is a one-to-one map λ from V (G)∪E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. Such a labelling is called strong if the smallest labels appear on the vertices. In this paper, we investigate the...

Yersinia pestis, the agent of plague, forms a biofilm in its flea vector to enhance transmission. Y. pestis biofilm development is positively regulated by hmsT and hmsD, encoding diguanylate cyclases (DGCs) involved in synthesis of the bacterial second messenger c-di-GMP. rcsA, encoding an auxiliary protein in Rcs phosphorelay, is nonfunctional in Y. pestis, while in Yersinia pseudotuberculosis...