An (s,S) random lifetime inventory model with a positive lead time

Positive lead times substantially complicate the modeling and analysis of inventory systems with finite shelf lifetimes and they have not been sufficiently addressed in the existing literature. In this paper, we analyze an (s, S) continuous review model with a positive lead time. We assume an exponential lifetime and an exponential lead time. Matrix-geometric solutions can be obtained for the steady state probability distribution of the inventory level. We then derive the total expected cost function. We carry out numerical studies and gain insights to the selection of system parameters. The findings on the impact of a positive lead time on the optimal reorder point and reorder batch size will be useful in developing strategies in handling inventory problems with finite lifetimes and positive lead times.     

Intertwined Basins of Attraction in Systems of O.D.E.

We investigate the basins of attraction in two dimensional ordinary differential equations (O.D.E.), and show that under certain conditions the basins of attraction are of fine and intertwined structure, which giving rise to an obstruction to predictability.     

Stereoselective synthesis of sterically constrained dipeptides. Part 2

The alkylation of the diastereomeric mixture of lactims 2 and 3 occurs in total regioselectivity and good to high facial stereoselectivity (d.s. ranging from 82 to 97%). Cleavage of the lactim 4e gives enantiomerically pure dipeptide 12, sterically constrained at the α-carbon. The absolute configuration of the new stereocentres has been assigned on the basis of ¹H-NMR data and NOE measurements.     

Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité

We examine the exact controllability of the solution of the linear elasticity system with evolutive Ventcel conditions in a bounded domain of ø³. We use the Hubert uniqueness method (HUM) of Lions [7]; some multipliers are defined on the boundary: the curvature tensor [3] appears when computing some boundary integrals.     

Temperature and excitation energy of hot nuclei in the reaction of 40Ar+197Au at 25 MeV/nucleon

The coincidence measurements between heavy fission fragments and light charged particles with Z ⩽ 2 were carried out for the ⁴⁰Ar+¹⁹⁷Au reaction at 25 MeV/nucleon, to study the properties of hot nuclei in heavy ion induced reactions. The linear momentum transfers (LMTs) were deduced from the folding angle and the time-of-flight difference between two fission fragments of heavy residues. The relationship of the nuclear temperature (slope parameter of the energy spectrum) and the excitation energy was determined independently from the measurement of the kinetic energy spectra in the frames of the emitting sources and from the LMT analysis. Both the temperature and the excitation energy increase with decreasing impact parameter, which suggests that a plateau temperature of 5.5 MeV is reached at an excitation energy of 3.1 MeV/nucleon. The result was also compared with various statistical models that explain the plateau by the multifragmentation process, where the excitation energy is assumed to be stored in compression and expansion effects.     

The eigenstates and tunnelling time in an interdiffused AlGaAs/GaAs quantum well by the transfer matrix method

A matrix method has been used for the determination of the confined eigenstates and their corresponding tunnelling times in an interdiffused AlGaAs/GaAs single quantum well structure. The nonlinear confinement potential profile of the disordered quantum well is due to the interdiffusion of the constituent Al and Ga atoms and is modeled here by an error function. The results indicate that the interdiffusion, as well as the applied electric field, affect the tunnelling times and the energy linewidths of the corresponding states. The results are compared with those for an AlGaAs/GaAs as-grown single square quantum well without any interdiffusion.     

Characteristic polynomial and higher order traces of third order three dimensional tensors

Eigenvalues of tensors play an increasingly important role in many aspects of applied mathematics. The characteristic polynomial provides one of a very few ways that shed lights on intrinsic understanding of the eigenvalues. It is known that the characteristic polynomial of a third order three dimensional tensor has a stunning expression with more than 20000 terms, thus prohibits an effective analysis. In this article, we are trying to make a concise representation of this characteristic polynomial in terms of certain basic determinants. With this, we can successfully write out explicitly the characteristic polynomial of a third order three dimensional tensor in a reasonable length. An immediate benefit is that we can compute out the third and fourth order traces of a third order three dimensional tensor symbolically, which is impossible in the literature.