Limit theorems for Hilbert space-valued linear processes under long range dependence

Let ${\left(X_k\right)}_{k\in \mathbb{Z}}$ be a linear process with values in a separable Hilbert space $\mathbb{H}$ given by $X_k={\sum }_{j=0}^{\infty }{(j+1)}^{?N}{\epsilon }_{k?j}$ for each $k\in \mathbb{Z}$, where $N:\mathbb{H}\to \mathbb{H}$ is a bounded, linear normal operator and ${\left({\epsilon }_k\right)}_{k\in \mathbb{Z}}$ is a sequence of independent, identically distributed $\mathbb{H}$-valued random variables with $E{\epsilon }_0=0$ and $E6{\epsilon }_0{6}^2<\infty$. We investigate the central and the functional central limit theorem for ${\left(X_k\right)}_{k\in \mathbb{Z}}$ when the series of operator norms ${\sum }_{j=0}^{\infty }6{(j+1)}^{?N}{6}_{op}$ diverges. Furthermore, we show that the limit process in case of the functional central limit theorem generates an operator self-similar process.     

On the use of graphs in discrete tomography

In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with scheduling and timetabling applications. The complexity status of these problems is studied and we exhibit some polynomially solvable cases. We show how various classical techniques of operations research like matching, 2-SAT, network flows are applied to derive some of these results.     

Derivation of Feynman–Kac and Bloch–Torrey Equations in a Trapping Medium

Methodology and Computing in Applied Probability - We derive rigorously the fractional counterpart of the Feynman–Kac equation for a transport problem with trapping events characterized by...     

Pyrene-sensitised near-IR luminescence from ytterbium and neodymium complexes

Ytterbium and neodymium have been shown to exhibit sensitised emission following excitation of pyrene chromophores. Sensitised emission is demonstrated in self-assembled complexes and in azamacrocycle derivatives bearing pendent pyrene groups. Energy transfer in these systems is dependent on the nature of the link between the ligand and the complex.     

The wave-particle dualism in 1992: A summary

We review the past and present theoretical and experimental situations relating to wave-particle dualism. New tests aimed at enlightening the individual behavior as awave, then as aparticle, of asingle quantum mechanical system in the same experimental run are presented. The related epistemological, philosophical, and historical backgrounds are presented in a twofold exposition taking into account thepositivistic standard Copenhagen interpretation as well as therealist de Broglian point of view.     

Bounds and Heuristics for the Shortest Capacitated Paths Problem

Given a graph G, the Shortest Capacitated Paths Problem (SCPP) consists of determining a set of paths of least total length, linking given pairs of vertices in G, and satisfying capacity constraints on the arcs of G.We formulate the SCPP as a 0-1 linear program and study two Lagrangian relaxations for getting lower bounds on the optimal value. We then propose two heuristic methods. The first one is based on a greedy approach, while the second one is an adaptation of the tabu search meta-heuristic.     

Viscosity of aqueous mixtures of silver and thallium nitrates with calcium or cadmium nitrates from pure fused salt to pure water

Fused salt-water systems extending from pure fused salt to pure water have been less studied than dilute aqueous solutions, despite their practical and theoretical importance. Even fewer studies have been made regarding the influence of the temperature upon transport properties. The present publication brings new interesting information on the viscous flow properties of the following two fused nitrate-water systems containing monovalent and divalent cations: AgNO₃–TINO₃–M(NO₃)₂–H₂O where M=Ca or Cd, with the TINO₃ and M(NO₃)₂ mole fractions in the anhydrous salt fixed at 0.436 and 0.100, respectively. The parameters in the Arrhenius, Eyring, Batschinski and the Abraham and Abraham equations are found to be well correlated with the properties of the components of the melts. The temperature effect allows a discussion to be made in terms of structural features such as holes and free volumes.     

Kinetic Limit of N-Body Description of Wave–Particle Self-Consistent Interaction

A system of N particles $\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z ^(N)(0), ξ ^N (0)), it evolves according to Hamiltonian dynamics to (Z ^(N)(t), ξ ^N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z ^(∞)(0), f(0)) evolve to (Z ^(∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution f ^N(0) → f(0) weakly and with Z ^(N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z ^(N)(t), f ^N(t)) converges weakly to (Z ^(∞)(t), f(t)).     

Fragmentation characteristics of permethylated oligosaccharides using a matrix-assisted laser desorption/ionization two-stage time-of-flight (TOF/TOF) tandem mass spectrometer

Matrix-assisted laser desorption/ionization two-stage time-of-flight (MALDI-TOF/TOF) tandem mass spectrometry (MS/MS) was applied to characterize permethylated oligosaccharides. Under these ionization conditions such derivatives yield intense signals corresponding to sodium-cationized molecular species. A systematic study was conducted on a series of neutral and sialylated permethylated oligosaccharides to allow rationalization of the fragmentation processes. The major fragments observed in the MALDI-TOF/TOF-MS/MS spectra result from cleavage of glycosidic bonds, preferentially at N-acetylhexosamine and sialic acid residues. The fragments originating from both the reducing and the non-reducing ends of the glycan yield information on sequence and branching. Cross-ring cleavages, which are very informative of the linkages of the monosaccharide residues constituting these oligosaccharides, and 'internal' cleavage ions which are derived from elimination of substituents from around the pyranose ring, were also observed. This extensive fragmentation was shown to be useful for the structural characterization of oligosaccharides. MALDI-TOF/TOF-MS/MS of permethylated oligosaccharides appears to be a powerful tool for carbohydrate structural analysis.