Estimates on the Green’s Function and Existence of Positive Solutions of Nonlinear Singular Elliptic Equations in the Half Space

We establish a new 3G-Theorem for the Green’s function for the half space We exploit this result to introduce a new class of potentials that we characterize by means of the Gauss semigroup on . Next, we define a subclass of and we study it. In particular, we prove that properly contains the classical Kato class . Finally, we study the existence of positive continuous solutions in of the following nonlinear elliptic problem

Molecular recognition of nucleobases and amino acids by sulphonato-calixnaphthalene-capped silver nanoparticles

The plasmon resonances of sulphonato-calixnaphthalene-capped silver nanoparticles have been used to study the complexation of the nanoparticles with nucleobases and amino acids. Only in the case of the nanoparticles capped with oxacalix[4]naphthalenesultone, does complexation of both nucleobases and certain amino acids occur. The complexation of the aromatic amino acids, phenylalanine and tryptophan, has previously not been observed for calixarene-capped silver nanoparticles.     

Optical Emission Spectroscopy Measurements and Simulation of Radioelement Volatility During Radioactive Waste Treatment by Plasma

An optical emission spectroscopy (OES) method has been used to measure the concentration above the melt of some radioelements, ¹³⁷Cs, ⁶⁰Co and ¹⁰⁶Ru during the vitrification of radioactive wastes by thermal plasma. This method allows the study of non homogeneous optically thin plasmas exhibiting a symmetry plane without sophisticated tomographic systems. Local plasma temperatures above the melt have been evaluated using measured relative intensities of spectral lines of the plasma-forming gas. Radioelement concentrations in the plasma are deduced from the intensity ratio of the radioelement–gas spectral lines. A computer model is used to simulate the volatility of ¹³⁷Cs, ⁶⁰Co and ¹⁰⁶Ru, during the treatment of radioactive wastes by thermal plasma. This model is based on the calculation of system composition using the free enthalpy minimization method, coupled with the equation of mass transfer at the reactional interface. In this study, the OES measurements and the computer model allowed the determination of this radioelement volatility depending on the parameters like plasma current, and the nature of atmosphere furnace. The results of the model are compared to those obtained by OES measurements.     

The indecomposable tournaments T with |W5(T)|=|T|−2

We consider a tournament $T=(V,A)$. For $X?V$, the subtournament of T induced by X is $T[X]=(X,A\cap (X\times X))$. An interval of T is a subset X of V such that, for $a,b\in X$ and $x\in V?X$, $(a,x)\in A$ if and only if $(b,x)\in A$. The trivial intervals of T are ?, $\{x\}(x\in V)$ and V. A tournament is indecomposable if all its intervals are trivial. For $n?2$, $W_{2n+1}$ denotes the unique indecomposable tournament defined on $\{0,\dots ,2n\}$ such that $W_{2n+1}[\{0,\dots ,2n?1\}]$ is the usual total order. Given an indecomposable tournament T, $W_5(T)$ denotes the set of $v\in V$ such that there is $W?V$ satisfying $v\in W$ and $T[W]$ is isomorphic to $W_5$. Latka [6] characterized the indecomposable tournaments T such that $W_5(T)=?$. The authors [1] proved that if $W_5(T)\ne ?$, then $|W_5(T)|?|V|?2$. In this note, we characterize the indecomposable tournaments T such that $|W_5(T)|=|V|?2$.     

Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times

In this paper, we study the identical parallel machine scheduling problem with a planned maintenance period on each machine to minimize the sum of completion times. This paper is a first approach for this problem. We propose three exact methods to solve the problem at hand: mixed integer linear programming methods, a dynamic programming based method and a branch-and-bound method. Several constructive heuristics are proposed. A lower bound, dominance properties and two branching schemes for the branch-and-bound method are presented. Experimental results show that the methods can give satisfactory solutions.     

Order Extensions and the Fixed Point Property

The purpose of this paper is to investigate how the fixed point property and its negation behave when a covering relation is added to the order. We prove that every finite ordered set which is not totally ordered and which is dismantlable by retractables, respectively by irreducibles, has an upper cover (in its extension lattice) which is also dismantlable by retractables, respectively by irreducibles. We also provide examples of finite ordered sets having the fixed point property so that none of their upper covers has the fixed point property. Part of this work was done while the author was visiting Brandon University. The author thanks M. Roddy for his hospitality and financial support.     

Indecomposability graph and critical vertices of an indecomposable graph

Given a directed graph G=(V,A), the induced subgraph of G by a subset X of V is denoted by G[X]. A subset X of V is an interval of G provided that for a,b∈X and x∈V?X, (a,x)∈A if and only if (b,x)∈A, and similarly for (x,a) and (x,b). For instance, 0?, V and {x}, x∈V, are intervals of G, called trivial intervals. A directed graph is indecomposable if all its intervals are trivial, otherwise it is decomposable. Given an indecomposable directed graph G=(V,A), a vertex x of G is critical if G[V?{x}] is decomposable. An indecomposable directed graph is critical when all its vertices are critical. With each indecomposable directed graph G=(V,A) is associated its indecomposability directed graph defined on V by: given x≠y∈V, (x,y) is an arc of if G[V?{x,y}] is indecomposable. All the results follow from the study of the connected components of the indecomposability directed graph. First, we prove: if G is an indecomposable directed graph, which admits at least two non critical vertices, then there is x∈V such that G[V?{x}] is indecomposable and non critical. Second, we characterize the indecomposable directed graphs G which have a unique non critical vertex x and such that G[V?{x}] is critical. Third, we propose a new approach to characterize the critical directed graphs.     

Singular limits solution for two-dimensional elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights

Given Ω bounded open regular set of ${\mathbb{R}^2}$ , ${q_1,\ldots, q_K \in \Omega}$ , ${\varrho : \Omega \longrightarrow [0,+\infty)}$ a regular bounded function and ${V: \Omega \longrightarrow [0,+\infty)}$ a bounded fuction. We give a sufficient condition for the model problem $$(P):\qquad-{\Delta}u -{\lambda}\varrho(x)|{\nabla}u|^2 = \varepsilon^{2}V(x)e^u$$ to have a positive weak solution in Ω with u = 0 on ?Ω, which is singular at each q _i as the parameters ${\varepsilon}$ and λ tend to 0, essentially when the set of concentration points q _i and the set of zeros of V are not necessarily disjoint.