Classical and non-classical solutions of a prescribed curvature equation

We discuss existence and multiplicity of positive solutions of the one-dimensional prescribed curvature problem

depending on the behaviour at the origin and at infinity of the potential . Besides solutions in W^2,1(0,1), we also consider solutions in which are possibly discontinuous at the endpoints of [0,1]. Our approach is essentially variational and is based on a regularization of the action functional associated with the curvature problem.     

Martingale and stationary solutions for stochastic Navier-Stokes equations

Summary We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness.     

Application of high-resolution magic-angle spinning NMR spectroscopy to define the cell uptake of MRI contrast agents

A new method, based on proton high-resolution magic-angle spinning ((1)H HR-MAS) NMR spectroscopy, has been employed to study the cell uptake of magnetic resonance imaging contrast agents (MRI-CAs). The method was tested on human red blood cells (HRBC) and white blood cells (HWBC) by using three gadolinium complexes, widely used in diagnostics, Gd-BOPTA, Gd-DTPA, and Gd-DOTA, and the analogous complexes obtained by replacing Gd(III) with Dy(III), Nd(III), and Tb(III) (i.e., complexes isostructural to the ones of gadolinium but acting as shift agents). The method is based on the evaluation of the magnetic effects, line broadening, or induced lanthanide shift (LIS) caused by these complexes on NMR signals of intra- and extracellular water. Since magnetic effects are directly linked to permeability, this method is direct. In all the tests, these magnetic effects were detected for the extracellular water signal only, providing a direct proof that these complexes are not able to cross the cell membrane. Line broadening effects (i.e., the use of gadolinium complexes) only allow qualitative evaluations. On the contrary, LIS effects can be measured with high precision and they can be related to the concentration of the paramagnetic species in the cellular compartments. This is possible because the HR-MAS technique provides the complete elimination of bulk magnetic susceptibility (BMS) shift and the differentiation of extra- and intracellular water signals. Thus with this method, the rapid quantification of the MRI-CA amount inside and outside the cells is actually feasible.     

Study on Planar Whispering Gallery Dielectric Resonators. I. General Properties

Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric losses, respectively, are obtained in terms of the complex dielectric constant of the involved media. The same approach is employed in the analysis of the limit allowed frequencies of a fixed family of mode, leading to the definition of the ideal frequency band. The role of the transverse mode is then discussed, and the effective frequency band is introduced and determined both in simple disc and circular ring resonators. The extension of the effective band is limited at least by a factor 3, in terms of decades, in comparison to the extension of the ideal one; this limitation, due to the presence of transverse modes, can be overcome using suitable designed nonhomogeneous resonators, as discussed in a following companion paper.     

Minimum sum set coloring of trees and line graphs of trees

In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.     

Auger electron emission in proton-induced interactions in living matter: A TILDA-V Monte Carlo tracking

The present work focuses on studying the contribution of the Auger electron emission in proton-induced interactions in biological matter. The Monte Carlo track-structure code, TILDA-V, was then used for modeling the protons beams of 10 keV to 100 MeV in biological matter, namely, water vapor and hydrated DNA. The main ionizing processes are described by means of an extensive set of ab initio differential and total cross sections computed within a quantum-mechanical CDW-EIS approximation.     

The Kramer–Mesner method with tactical decompositions: some new unitals on 65 points

We propose a combination of two known computational methods for the construction of designs with prescribed groups of automorphisms: the Kramer–Mesner method and the method of tactical decompositions. This combined method is used to construct new unitals with parameters 2‐(65, 5, 1). © 2011 Wiley Periodicals, Inc. J Combin Designs 19:290‐303, 2011     

A semi-Markov process with an inverse Gaussian distribution as sojourn time

Let X_n denote the state of a device after n repairs. We assume that the time between two repairs is the time τ taken by a Wiener process {W(t), t ? 0}, starting from w₀ and with drift μ < 0, to reach c ∈ [0, w₀). After the nth repair, the process takes on either the value X_n?1 + 1 or X_n?1 + 2. The probability that X_n = X_n?1 + j, for j = 1, 2, depends on whether τ ? t₀ (a fixed constant) or τ > t₀. The device is considered to be worn out when X_n ? k, where k ∈ {1, 2, …}. This model is based on the ones proposed by Rishel (1991) [1] and Tseng and Peng (2007) [2]. We obtain an explicit expression for the mean lifetime of the device. Numerical methods are used to illustrate the analytical findings.