Rains of solitons in a figure-of-eight passively mode-locked fiber laser

We report experimental observation of rains of solitons in figure-of-eight fiber laser passively mode-locked through nonlinear optical loop mirror. Soliton pulses are created from an extended noisy background and drift until they reach a condensed phase comprising several tens of aggregated solitons. The observation of this dynamics tends to strengthen the idea of the universality of the collective behavior of solitons.     

Characterization of an ytterbium-doped double-clad fiber laser passively mode-locked by nonlinear polarization rotation

The properties of an ytterbium-doped double-clad fiber laser, passively mode-locked by nonlinear polarization rotation are investigated in this work. Cartographies of mode-locking regime versus halfwave plates orientations are presented for several values of the total cavity dispersion and for different pump powers. Bistability between the continuous and the mode-locking regimes is pointed out. The effect of the total group velocity dispersion is described with a master mode-locking equation. PACS 42.55.Wd; 42.65.Re     

Dynamic Bivariate Mortality Modelling

The dependence structure of the life statuses plays an important role in the valuation of life insurance products involving multiple lives. Although the mortality of individuals is well studied in the literature, their dependence remains a challenging field. In this paper, the main objective is to introduce a new approach for analyzing the mortality dependence between two individuals in a couple. It is intended to describe in a dynamic framework the joint mortality of married couples in terms of marginal mortality rates. The proposed framework is general and aims to capture, by adjusting some parametric form, the desired effect such as the “broken-heart syndrome”. To this end, we use a well-suited multiplicative decomposition, which will serve as a building block for the framework to relate the dependence structure and the marginals, and we make the link with existing practice of affine mortality models. Finally, given that the framework is general, we propose some illustrative examples and show how the underlying model captures the main stylized facts of bivariate mortality dynamics.

     

Nested Heuristic Methods for the Location-Routeing Problem

The concept of ‘nested methods’ is adopted to solve the location-routeing problem. Unlike the sequential and iterative approaches, in this method we treat the routeing element as a sub-problem within the larger problem of location. Efficient techniques that take into account the above concept and which use a neighbourhood structure inspired from computational geometry are presented. A simple version of tabu search is also embedded into our methods to improve the solutions further. Computational testing is carried out on five sets of problems of 400 customers with five levels of depot fixed costs, and the results obtained are encouraging.     

A Convenient One-Step Synthesis of 5-(α-alkanonyl) and 5-(α-Cyclanonyl)-4-Pentanolides

The thermolysis of t-butyl perpent-4-enoate in ketones leads to the formation of 5-(α-alkanonyl) and 5-(α-cyclanonyl)-4-pentanolides with fairly good yields.     

High-Q factor single mode circular photonic crystal nano-resonator

In this work, the analysis, fabrication and optical characterization of a two-dimensional circular photonic crystal (2D-CPC) nano-resonator based on an air/GaAs/air slab waveguide are presented. Four InAs/InGaAs quantum dots (QDs) stacked layers emitting around 1300 nm at room temperature were embedded in a GaAs waveguide layer grown on an Al_0.7Ga_0.3As layer and GaAs substrate. The patterning of the structure and the membrane release were achieved by using electron beam lithography, ICP plasma etching and selective wet etching of the AlGaAs sacrificial layer. The micro-luminescence spectrum recorded from the fabricated nano-cavity shows a narrow optical transition at the resonance wavelength of about 1282 nm with a FWHM and Q-factor of 6.2 Å and more than 2000, respectively.     

A Fully Nonlinear Nonhomogeneous Neumann Problem

Let Ω be an open bounded set in ℝ^N, N≥3, with connected Lipschitz boundary ∂Ω and let a(x,ξ) be an operator of Leray–Lions type (a(⋅,∇u) is of the same type as the operator |∇u|^p−2∇u, 1<p<N). If τ is the trace operator on ∂Ω, [φ] the jump across ∂Ω of a function φ defined on both sides of ∂Ω, the normal derivative ∂/∂ν_a related to the operator a is defined in some sense as 〈a(⋅,∇u),ν〉, the inner product in ℝ^N, of the trace of a(⋅,∇u) on ∂Ω with the outward normal vector field ν on ∂Ω. If β and γ are two nondecreasing continuous real functions everywhere defined in ℝ, with β(0)=γ(0)=0, f∈L¹(ℝ^N), g∈L¹(∂Ω), we prove the existence and the uniqueness of an entropy solution u for the following problem,

Integrating heuristic information into exact methods: The case of the vertex p-centre problem

We solve the vertex p-centre problem optimally using an exact method that considers both upper and lower bounds as part of its search engine. Tight upper bounds are generated quickly via an efficient three-level heuristic, which are then used to derive potential ‘lower bounds’ accordingly. These two pieces of information when used together make our chosen exact method more efficient at obtaining optimal solutions relatively quickly. The proposed implementation produced excellent results when tested on the OR Library data set. This integrated approach can be adopted for those exact methods that consider both upper and lower bounds within their search engine and hence provide a wider spectrum of applicability in other hard combinatorial problems.