A Stochastic Analysis of a Staffing Problem

Consider an organization with several categories of staff, each having a specified number of members. The age of entry into service and the age of retirement are both specified. Withdrawals occur at time-independent rates. Under this set-up, the authors have computed the maximum ages at which promotions should take place, assuming that the staff members continuing at various ages are random. Some illustrative calculations have been carried out.     

A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

填充式方钴矿化合物CeOs4Sb12近藤相互作用的非弹性中子散射研究

CeOs₄Sb₁₂晶体中由于导电电子与Ce³⁺ 4f¹电子之间存在c-f杂化作用导致费米面附近存在能量间隙.这种c-f近藤相互作用和能量间隙是理解CeOs₄Sb₁₂物理性质，如近藤绝缘体行为、Ce³⁺磁矩在低温下猝灭以及重费米性等电、磁性质的关键.当用LAM-D中子谱仪对粉末CeOs₄Sb₁₂进行测量时，可以得到不同温度下CeOs₄Sb₁₂的非弹性中子散射谱.结果表明CeOs₄Sb₁₂中存在近藤相互作用，其作用强度为3.1 meV，证实了CeOs₄Sb₁₂为近藤绝缘体.中子测量得出CeOs₄Sb₁₂德拜温度为317 K. 关键词： 非弹性中子散射 填充式方钴矿 近藤绝缘体     

On a class of operators related to second-order differential equations

In the present paper, we find a class of linear homogeneous differential equations of order n + 1 (n > 1) whose fundamental system of solutions is constructed from the fundamental system of solutions of a second-order differential equation. The spectral properties of differential operators generated by these differential expressions are investigated. In particular, sufficient conditions are obtained for the coefficients of a second-order differential equation under which the case of maximal deficiency indices is realized. Dedicated to the memory of B. M. Levitan     

Enantiodiscrimination of racemic electrophiles by diketopiperazine enolates: asymmetric synthesis of methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates

Enolates of (S)-N,N′-bis-(p-methoxybenzyl)-3-iso-propylpiperazine-2,5-dione exhibit high levels of enantiodiscrimination in alkylations with (RS)-1-aryl-1-bromoethanes and (RS)-2-bromoesters, affording substituted diketopiperazines containing two new stereogenic centres in high de. Deprotection and hydrolysis of the resultant substituted diketopiperazines provides a route to the asymmetric synthesis of homochiral methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates in high de and ee.     

High pressure X-ray diffraction study of CdAl2Se4 and Raman study of AAl2Se4 (A=Hg, Zn) and CdAl2X4 (X=Se, S)

We report the results of an X-ray diffraction study of CdAl₂Se₄ and of Raman studies of HgAl₂Se₄ and ZnAl₂Se₄ at room temperature, and of CdAl₂S₄ and CdAl₂Se₄ at 80 K at high pressure. The ambient pressure phase of CdAl₂Se₄ is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl₂Se₄ and ZnAl₂Se₄ reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl₂S₄ and CdAl₂Se₄, which shows a very weak temperature dependence of the Raman-active phonon modes.     

Optimal Harvesting in an Age-Structured Predator–Prey Model

We investigate optimal harvesting control in a predator–prey model in which the prey population is represented by a first-order partial differential equation with age-structure and the predator population is represented by an ordinary differential equation in time. The controls are the proportions of the populations to be harvested, and the objective functional represents the profit from harvesting. The existence and uniqueness of the optimal control pair are established.     

Structural and electronic properties of graphite layers grown on SiC(0 0 0 1)

Photoelectron spectroscopy, low-energy electron diffraction, and scanning probe microscopy were used to investigate the electronic and structural properties of graphite layers grown by solid state graphitization of SiC(0 0 0 1) surfaces. The process leads to well-ordered graphite layers which are rotated against the substrate lattice by 30°. On on-axis 6H-SiC(0 0 0 1) substrates we observe graphitic layers with up to several 100 nm wide terraces. ARUPS spectra of the graphite layers grown on on-axis 6H-SiC(0 0 0 1) surfaces are indicative of a well-developed band structure. For the graphite/n-type 6H-SiC(0 0 0 1) layer system we observe a Schottky barrier height of ?_B,n = 0.3 ± 0.1 eV. ARUPS spectra of graphite layers grown on 8° off-axis oriented 4H-SiC(0 0 0 1) show unique replicas which are explained by a carpet-like growth mode combined with a step bunching of the substrate.     

Wavelength and power monitoring of DWDM systems using scanning F–P filter calibrated with a F–P laser

A novel technique to overcome the long-term drift and hysteresis of a scanning Fabry–Perot filter was developed and applied to wavelength and power monitoring of DWDM system. By using the comb peaks generated by a temperature-stabilized, near threshold-biased Fabry–Perot diode laser as wavelength reference for the scanning Fabry–Perot filter, wavelength and power measurement accuracy of better than ±10 pm and 0.2 dB, respectively, were achieved.