Partial remission in patients newly diagnosed with type 1 diabetes is a period of good glucose control that can last from several weeks to over a year. The clinical significance of the remission period is that patients might be more responsive to immunotherapy if treated within this period. This article provides clinical data that indicates the level of glucose control and insulin-secreting β-c...

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

This paper deals with the description of the overall effect of pinning conditions in discrete systems. We study a variational problem on the discrete in which pinning sites are modeled as network subsets on which concentrated forces are imposed. We want to determine the asymptotic effect of pinning conditions on a periodic lattice as its size vanishes. Our analysis is performed in the framework...

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations. We employ the direct method of the calculus of variations, i.e. we obtain solutions minimizing certain functional I. We give conditions which ensure that I is finitely defined and differentiable on certain subsets of Orlicz-Sobolev spaces W L associated to an N -function Φ. We show that, in ...

We show that Bowen’s equation, which characterises the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered c...

Let Q(S) be the moduli space of area one holomorphic quadratic differentials for an oriented surface S of genus g ≥ 0 with m ≥ 0 punctures and 3g − 3 + m ≥ 2. We show that for every compact subset K of Q(S) the as-ymptotic growth rate δ(K) of the number of periodic orbits of the Teichmüller flow Φ t which are contained in K is not bigger than h = 6g − 6 + 2m, and sup K δ(K) = h. Similarly, h is...

We study spectra of alloy-type random Schrödinger operators on metric graphs. For finite edge subsets we prove a Wegner estimate which is linear in the volume (i.e. the total length of the edges) and the length of the energy interval. The single site potential needs to have fixed sign, the metric graph does not need to have a periodic structure. A further result is the existence of the integrat...

We study two widely used algorithms, Glauber dynamics and the Swendsen-Wang algorithm, on rectangular subsets of the hypercubic lattice Z. We prove that under certain circumstances, the mixing time in a box of side length L with periodic boundary conditions can be exponential in L. In other words, under these circumstances, the mixing in these widely used algorithms is not rapid; instead, it is...