On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.     

A Language for Teaching Discrete-event Simulation

Courses which teach discrete-event simulation are based on many different simulation languages. The requirements for a language to support teaching simulation are discussed. In particular, it is recommended that such languages separate into distinct modules those aspects of simulation which are taught as separate topics. Implementation of the separation is discussed. The SEESIM language, developed as a teaching aid, is described, and examples of its use are given. Straightforward use of SEESIM can be learned quickly, yet the language provides facilities for a staged introduction to advanced concepts of simulation.     

Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

The operational performance of the Yale ESTU

The ESTU began operation in 1988 and achieved the design voltage of 20 MV in 1990. Since that time, improvements to the gas handling system, negative ion injector, accelerator terminal and control system have greatly increased its capability and reliability. Today, the ESTU can efficiently produce an extensive assortment of stable ions at wide-ranging energies in support of low-energy nuclear physics.     

Infrared picosecond absorption spectroscopy of microcrystalline silicon: separation between carrier recombination in crystalline and amorphous fractions

We have studied ultra-fast carrier dynamics of photo-excited carriers in hydrogenated microcrystalline silicon prepared by a very high frequency glow-discharge technique. We report on direct observation of two types of dynamics using selective photo-excitation in picosecond pump and probe measurements. One type of the observed dynamics has been found to be independent of the sample preparation, while the other reflects the relative weights of crystalline and amorphous fractions. We propose a simple rate-equation model that describes the carrier dynamics in microcrystalline silicon in terms of the composition of those in Si microcrystallites and in the a-Si:H tissue which surrounds the microcrystallites. The model without any fitting parameters reproduces the experimental data very well when the dynamics are scaled with relative volume fractions as obtained from Raman spectra. Received: 23 November 2000 / Accepted: 17 March 2001 / Published online: 23 May 2001     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

Generic replica symmetric field-theory for short range Ising spin glasses

Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line, along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex rules are presented to help future renormalisation-group calculations. Received 9 October 2001     

Nonlinear optical parameters and optical limitation in cobalt-doped polyvinylpyrrolidone solutions

Nonlinear optical parameters (nonlinear refractive indices and nonlinear absorption coefficients) of solutions of polyvinylpyrrolidone doped by cobalt to various concentrations are measured at the lasing and second-harmonic wavelengths of a picosecond Nd:YAG laser (λ=1064 and 532 nm, respectively, and τ=35 ps). Data on optical limitation in these solutions are presented. The absence of nonlinear absorption in the IR spectral range and its significant effect in the visible range are demonstrated. Optical limitation at a wavelength of 1064 nm is related to defocusing, whereas at 532 nm, this effect is caused by two-photon absorption and partially by inverse saturated absorption and defocusing. Nonlinear optical parameters of metal-polymer complexes are reported.