Algorithms for central-median paths with bounded length on trees

The location of path-shaped facilities on trees has been receiving a growing attention in the specialized literature in the recent years. Examples of such facilities include railroad lines, highways and public transit lines. Most of the papers deal with the problem of locating a path on a tree by minimizing either the maximum distance from the vertices of the tree to the facility or of minimizing the sum of the distances from all the vertices of the tree to the path. However, neither of the two above criteria alone capture all essential elements of a location problem. The sum of the distances criterion alone may result in solutions which are unacceptable from the point of view of the service level for the clients who are located far away from the facilities. On the other hand, the criterion of the minimization of the maximum distance, if used alone, may lead to very costly service systems. In the literature, there is just one paper that considers the problem of finding an optimal location of a path on a tree using combinations of the two above criteria, and efficient algorithms are provided. In particular, the cases where one criterion is optimized subject to a restriction on the value of the other are considered and linear time algorithms are presented. However, these problems do not consider any bound on the length or cost of the facility. In this paper we consider the two following problems: find a path which minimizes the sum of the distances such that the maximum distance from the vertices of the tree to the path is bounded by a fixed constant and such that the length of the path is not greater than a fixed value; find a path which minimizes the maximum distance with the sum of the distances being not greater than a fixed value and with bounded length. From an application point of view the constraint on the length of the path may refer to a budget constraint for establishing the facility. The restriction on the length of the path complicates the two problems but for both of them we give O(n log² n) divide-and-conquer algorithms.     

Arithmetic of algebraic curves from diophantus to Poincaré

This article contains an analysis of the methods for solving diophantine equations of second and third degrees in two unknowns, from the most ancient times to Poincaré. Special attention is paid to the works of Fermat, Euler, and Jacobi.     

τ→μγ and μ→eγ as probes of neutrino mass models

We discuss the possibility of discriminating between different supersymmetric see-saw models by improving the experimental sensitivity to charged lepton flavour violating processes. Assuming a hierarchical neutrino mass spectrum, we classify see-saw models according to how the hierarchy Δm²Δm²_atm is generated, and study the predictions of each class for the branching ratios of τ→μγ and μ→eγ. The process τ→μγ is found to be a particularly promising tool to probe the fundamental see-saw parameters, and especially to identify the origin of the large atmospheric mixing angle. Predictions for μ→eγ are more model-dependent. We point out that, even with an improvement of the experimental sensitivities by three orders of magnitude, both τ→μγ and μ→eγ could escape detection in models where Δm²_atm is determined by one of the lightest right-handed neutrinos.     

Surface Adsorption and Photo-Reactivity of Sulfonylurea Herbicides

Photodegradation of two sulfonylurea herbicides, triasulfuron and thifensulfuron-methyl adsorbed on Preveza or Nea Malgara soils (Greece) was studied in outdoor and laboratory experiments. Herbicides on adsorbed phase and kept in the dark were characterised by a high reactivity, giving depletion curves that can be all described by a first order equation. In the irradiation experiments the kinetic behaviour of photodegradation was complex and characterised by a double step photoreaction. After a first period varying from 8 to 24 h the rate of reaction was reduced to 7-31% of the initial rate. The kinetic constant related to the degradation of triasulfuron practically showed the same values of those obtained for thifensulfuron-methyl. The half-lives obtained on Nea Malgara soil were generally higher than those obtained using Preveza soil. The observed behaviour is explained considering the photochemical properties of the herbicides, and the organic matter content of the soils.     

Local and global solutions for some parabolic nonlocal problems

We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a “Newtonian” nonlocal term.     

Stability of a Continuous Reaction-Diffusion Cournot-Kopel Duopoly Game Model

In order to take into account the territory in which the outputs are in the market and the time-depending firms’ strategies, the discrete Cournot duopoly game (with adaptive expectations, modeled by Kopel) is generalized through a non autonomous reaction-diffusion binary system of PDEs, with self and cross diffusion terms. Linear and nonlinear asymptotic L ²-stability, via the Liapunov Direct Methot and a nonautonomous energy functional, are investigated.     

Titanium-Promoted Acylation of Sulfonamides to N-Acylsulfonamide PPARα Antagonists

The direct acylation of sulfonamides by esters represents an attractive strategy in organic chemistry, being an interesting alternative to classical approaches to N-acylsulfonamides. Here is described a simple and effective method to obtain N-acylsulfonamides of pharmaceutical interest, in a reaction promoted by titanium(IV) chloride. This strategy was successfully applied to the synthesis of a peroxisome proliferator–activated receptor α antagonist with a benzenesulfonimide moiety, ensuring an excellent yield of product. The reaction was further studied to explore the behavior of different α-bromoesters and esters and the effects of para-substitution in the benzenesulfonamide moiety.     

Assessment of the Arsenic Removal From Water Using Lanthanum Ferrite

The catalytic performance of a perovskite-type lanthanum ferrite LaFeO₃ to remove arsenic from water has been investigates for the first time. LaFeO₃ was prepared by citrate auto-combustion of dry gel obtained from a solution of the corresponding nitrates poured into citric acid solution. Kinetic studies were performed in the dark with As(V) and in the dark and under UV-C irradiation at pH 6–7 with As(III) (both 1 mg L⁻¹), and As : Fe molar ratios (MR) of 1 : 10 and 1 : 100 using the LaFeO₃ catalyst. As(V) was removed from solution after 60 min in the dark in 7 % and in 47 % for MR=1 : 10 and MR=1 : 100, respectively, indicating the importance of the amount of the iron material on the removal. Oxidation of As(III) in the dark was negligible after 60 min in contact with the solid sample, but complete removal of As(III) was observed within 60 min of irradiation at 254 nm, due to As(III) photooxidation to As(V) and to As(III) sorption to a minor extent. Morphological and microstructural studies of the catalyst complement the catalytic testing. This work demonstrates that LaFeO₃ can be used for the removal of As(III) from highly arsenic contaminated water.     

Wavelength stabilized 980 nm uncooled pump laser modules for erbium-doped fiber amplifiers

We review the development of wavelength stabilized 980 nm pump laser modules without active temperature stabilization for applications in erbium-doped fiber amplifiers. Operation over a wide temperature range with an output power exceeding 400 mW at an ambient temperature of 70°C is demonstrated. The overall reliability of uncooled modules is estimated to be well below 500 FIT at all operating conditions. Such devices are made possible by continuous development and steady improvement of the pump laser chip, the optimization of the fiber Bragg grating stabilization scheme, careful design of the module package, and extended reliability analysis on the basis of stress tests as well as field data.