On matrix mappings into some strong Cesàro sequence spaces

We determine the classes (X, Y_T) of matrix transformations from X into Y_T where X is one of the classical sequence spaces c₀, c, ?_∞ and ?₁ of all null, convergent and bounded complex sequences and all absolutely convergent complex series, T is a triangle, Y_T is the matrix domain of T in Y and Y is any of the sets of all sequences that are summable, summable to zero or bounded by the strong Cesàro method of order 1, with index 1 ? p < ∞. Furthermore, we determine the representations of the general bounded linear operators from c into Y. We also establish estimates for the norms of the operators in each case.     

Chemical characterization of the smallest S-nitrosothiol, HSNO; cellular cross-talk of H2S and S-nitrosothiols

Dihydrogen sulfide recently emerged as a biological signaling molecule with important physiological roles and significant pharmacological potential. Chemically plausible explanations for its mechanisms of action have remained elusive, however. Here, we report that H(2)S reacts with S-nitrosothiols to form thionitrous acid (HSNO), the smallest S-nitrosothiol. These results demonstrate that, at the cellular level, HSNO can be metabolized to afford NO(+), NO, and NO(-) species, all of which have distinct physiological consequences of their own. We further show that HSNO can freely diffuse through membranes, facilitating transnitrosation of proteins such as hemoglobin. The data presented in this study explain some of the physiological effects ascribed to H(2)S, but, more broadly, introduce a new signaling molecule, HSNO, and suggest that it may play a key role in cellular redox regulation.     

Cosmological expansion and local systems: a Lemaître–Tolman–Bondi model

We propose a Lemaître–Tolman–Bondi system mimicking a two-body system to address the problem of the cosmological expansion versus local dynamics. This system is strongly bound but participates in the cosmic expansion and is exactly comoving with the cosmic substratum.     

Estimation of pore size in a microstructure phantom using the optimised gradient waveform diffusion weighted NMR sequence

There has been increasing interest in nuclear magnetic resonance (NMR) techniques that are sensitive to diffusion of molecules containing NMR visible nuclei for the estimation of microstructure parameters. A microstructure parameter of particular interest is pore radius distribution. A recent in silico study optimised the shape of the gradient waveform in diffusion weighted spin-echo experiments for estimating pore size. The study demonstrated that optimised gradient waveform (GEN) protocols improve pore radius estimates compared to optimised pulse gradient spin-echo (PGSE) protocols, particularly at shorter length scales. This study assesses the feasibility of implementing GEN protocols on a small bore 9.4 T scanner and verifies their additional sensitivity to pore radius. We implement GEN and PGSE protocols optimised for pore radii of 1, 2.5, 5, 7.5, 10 μm and constrained to maximum gradient strengths of 40, 80, 200 mT m(-1). We construct microstructure phantoms, which have a single pore radius for each phantom, using microcapillary fibres. The measured signal shows good agreement with simulated signal, strongly indicating that the GEN waveforms can be implemented on a 9.4 T system. We also demonstrate that GEN protocols provide improved sensitivity to the smaller pore radii when compared to optimised PGSE protocols, particularly at the lower gradient amplitudes investigated in this study. Our results suggest that this improved sensitivity of GEN protocols would be reflected in clinical scenarios.     

On the use of intersection cuts for bilevel optimization

We address a generic mixed-integer bilevel linear program (MIBLP), i.e., a bilevel optimization problem where all objective functions and constraints are linear, and some/all variables are required to take integer values. We first propose necessary modifications needed to turn a standard branch-and-bound MILP solver into an exact and finitely-convergent MIBLP solver, also addressing MIBLP unboundedness and infeasibility. As in other approaches from the literature, our scheme is finitely-convergent in case both the leader and the follower problems are pure integer. In addition, it is capable of dealing with continuous variables both in the leader and in follower problems—provided that the leader variables influencing follower’s decisions are integer and bounded. We then introduce new classes of linear inequalities to be embedded in this branch-and-bound framework, some of which are intersection cuts based on feasible-free convex sets. We present a computational study on various classes of benchmark instances available from the literature, in which we demonstrate that our approach outperforms alternative state-of-the-art MIBLP methods.     

On the restricted evolution problem of the Einstein relativistic mechanics

This work is focused on the interior Cauchy problem for the Einstein’s field equations. Precisely, in the relativistic study of the evolution of a continuum reversible system, the Cauchy problem is broken into two separate problems: the initial data problem and the restricted problem of evolution.     

Invariants and approximate solutions for certain non-linear oscillators by means of the field method

Certain strongly non-linear conservative oscillators are approached with the field method, which is combined with the convolution integral method. A complete set of their adiabatic invariants are derived, on the basis of which approximate solutions for motion can be obtained.     

Heavy Tailed Approximate Identities and <Emphasis Type="Italic">σ</Emphasis>-stable Markov Kernels

The aim of this paper is to present some results relating the properties of stability, concentration and approximation to the identity of convolution through not necessarily mollification type families of heavy tailed Markov kernels. A particular case is provided by the kernels K _t obtained as the t mollification of L ^σ(t) selected from the family \(\mathcal {L}=\{L^{\sigma }: \widehat {L^{\sigma }}{(\xi )=e^{-|{\xi }|}}^{\sigma }, 0<\sigma <2\}\), by a given function σ with values in the interval (0,2). We show that a basic Harnack type inequality, introduced by C. Calderón in the convolution case, becomes at once natural to the setting and useful to connect the concepts of stability, concentration and approximation of the identity. Some of the general results are extended to spaces of homogeneous type since most of the concepts involved in the theory are given in terms of metric and measure.     

Water–ice phase transition probed by Raman spectroscopy

Raman spectroscopy was used to study the liquid–solid water phase transition. Special attention was devoted to the OH stretching band of the Raman spectrum, which shows monotonous changes in the temperature range between 10 and − 15 °C. The interpretation of this spectral change, as well as a careful analysis of its integrated scattered intensity, led to a spectral marker that allows the determination of the water phase (liquid or solid), and the efficient identification of the liquid–solid phase transition itself. Copyright © 2011 John Wiley & Sons, Ltd.