Katznelson-Tzafriri type theorems for individual solutions of evolution equations

In this paper we present an extension of the Katznelson-Tzafriri Theorem to the asymptotic behavior of individual solutions of evolution equations . The obtained results do not require the uniform continuity of solutions as well as the well-posedness of the equations. The method of study is based on a recently developed approach to the spectral theory of functions that is direct and free of -semigroups.

     

Chemical constituents from the leaves of Manglietia phuthoensis and their effects on osteoblastic MC3T3-E1 cells

Two new phenyl glycosides, mangliesides A and B (1, 2), a new ionol glycoside, manglieside C (3), two new lignan glycosides, mangliesides D and E (4, 5), were isolated from the leaves of Manglietia phuthoensis, along with two known lignans, 3-methoxymagnolol (6) and obovatol (7). Their structures were established by means of 1D and 2D NMR, electrospray ionization (ESI)-MS and HR-ESI-MS experiments. Among them, compounds 2 and 5 significantly (p<0.05) increased the growth and differentiation of osteoblastic MC3T3-E1 cells in vitro.     

Bounds of <Emphasis Type="Italic">p</Emphasis>-adic weighted Hardy-Cesàro operators and their commutators on <Emphasis Type="Italic">p</Emphasis>-adic weighted spaces of Morrey types

In this paper we aim to investigate the boundedness of the p-adic weighted Hardy-Cesàro operators and their commutators on weighted functional spaces of Morrey type. In each case, we obtain the corresponding operator norms.     

A note on Lipschitzian stability of variational inequalities over perturbed polyhedral convex sets

In the previous paper (Optim lett 6:749–762, 2012), under some technical assumptions, we proved that the solution mapping of variational inequalities over perturbed polyhedral convex sets is not Lipschitz-like around points at which the positively linear dependence of the active vectors defining the constraint set is valid. This note shows that the result holds without such assumptions. In addition, for more deeply understanding the results on the Lipschitz-like stability, some examples have been presented.     

The Extension of Distributions on Manifolds,a Microlocal Approach

Let M be a smooth manifold, \({I\subset M}\) a closed embedded submanifold of M and U an open subset of M. In this paper, we find conditions using a geometric notion of scaling for \({t\in \mathcal{D}^{\prime}(U{\setminus} I)}\) to admit an extension in \({\mathcal{D}^\prime(U)}\). We give microlocal conditions on t which allow to control the wave front set of the extension generalizing a previous result of Brunetti–Fredenhagen. Furthermore, we show that there is a subspace of extendible distributions for which the wave front of the extension is minimal which has applications for the renormalization of quantum field theory on curved spacetimes.     

Infinite Volume Limit for Correlation Functions in the Dipole Gas

We study a classical lattice dipole gas with low activity in dimension \({d \geq 3}\). We investigate long distance properties by a renormalization group analysis. We prove that various correlation functions have an infinite volume limit. We also get estimates on the decay of correlation functions.     

Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems

In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution maps for optimization problems, variational inequalities and fixed-point problems are derived.     

Continuity properties of solution maps of parametric lexicographic equilibrium problems

Inspired by the great importance of equilibrium problems and the lexicographic order, we consider a parametric lexicographic equilibrium problem. Sufficient conditions for the upper semicontinuity, closedness, and continuity of solution maps are established. Many examples are provided to ensure the essentialness of the imposed assumptions. Applications to lexicographic variational inequalities and lexicographic optimization problems are discussed.