Diazaphospholene and Diazaarsolene Derived Homogeneous Catalysis

The past 20 years has seen significant advances in main group chemistry and their use in catalysis. This Minireview showcases the recent emergence of phosphorus and arsenic containing heterocycles as catalysts. With that, we discuss how the Group 15 compounds diazaphospholenes, diazaarsolenes, and their cationic counterparts have proven to be highly effective catalysts for a wide range of reduction transformations. This Minireview highlights how the initial discovery by Gudat of the hydridic nature of the P−H bond in these systems led to these compounds being used as catalysts and discusses the wide range of examples currently present in the literature.     

Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some existence results like Bahri-Coron theorem. Furthermore, we consider the approximate subcritical problem and we construct some solutions which blow up at two different points, one of them lay on the boundary and the other one is an interior point.     

On nonhomogeneous singular elliptic equations with cylindrical weights

In this paper, we establish the existence of multiple solutions for nonhomogeneous singular elliptic equations with cylindrical weights, by using Ekeland??s variational principle and mountain pass theorem without Palais?CSmale condition.     

Calculating safety stocks for assembly systems with random component procurement lead times: A branch and bound algorithm

In this paper, a discrete single-level multi-component inventory control model for assembly systems with random component procurement lead times is considered. The economic order quantity (EOQ) policy is used for a type of finished product. The requirements of the components are constant and cyclic (periodic), and their values per period are deduced from the EOQ for the finished product. The paper focuses on the components safety stock calculation. The objective is to minimise the average holding cost of the components while keeping the desired service level for the finished product. For this, an upper bound, two lower bounds, two dominance properties and an efficient branch and bound algorithm are suggested. Several tests are executed and conclusions are drawn. The proposed model provides a substantial saving for assembly systems with a large number and unreliable delivery of components as in semi-conductor and automotive industries.     

The one machine scheduling problem: Insertion of a job under the real-time constraint

We consider a single resource that performs a set of jobs, each job being defined by its operation time and its due date. Jobs are not preemptive, which means that a job that starts cannot be interrupted before completion. These jobs have been scheduled so as to minimize the total tardiness, and the schedule is known.     

Effect of process parameters on the EHD airflow

This work deals with the assessment by numerical investigations of the electrohydrodynamic enhancement of heat transfer in a channel. In order to get a better understanding of the phenomena, we developed an original numerical approach. The model handles the couplings between a non-isothermal turbulent flow and corona discharges from multiple wires. The typical configuration consists in a channel where air enters at a given velocity. In the channel, the ionic wind is produced by multiple coronating wires. In this study, the model is used in order to analyse the effect of some process parameters (inter-electrode distance, wire radius, applied voltage) on the flow and on the convective heat transfer enhancement. We firstly confirm that the model operates well and permits selection of the best parameters in a specific configuration. The model reveals that similar flows could be obtained with different combinations between the inter-electrode distance and the applied voltage. In a second stage, the distance between adjacent wires is discussed. Synergetic effects are obtained for close wires; they locally lead to a tenfold increase of the heat transfer enhancement.     

Méthode des éléments finis multi-échelles pour le problème de Stokes

This work consists of a numerical study of a multi-scale finite element method for a Stokes-type problem with highly oscillating coefficients. The objective of this method is to capture the multi-scale structure of the solution via local basis functions calculated in advance, which contain the essential information on small scales.     

Ball Milling for Heterocyclic Compounds Synthesis in Green Chemistry: A Review

This review aims to present the application of ball milling for the synthesis ofdifferent heterocyclic compounds in very good yields. The method is a simple, economical, and ecofriendly process for synthesizing heterocycles, which is a large family of organic compounds. They are extremely important and have wide-ranging pharmaceutical and industrial applications.     

Existence and Comparison of Green Kernels for Some Elliptic Operators on (0, ∞)

In this paper we give necessary and sufficient conditions for the existence and the comparability of Green kernels for second order elliptic operators in the one dimensional case.