A discrete time markovian inventory model for perishable commodities

In this paper, we analyze a Markovian inventory model for perishable commodities, in which the arrivals of items into the system as well as the demands for these items are assumed to be discrete r.v.'s having a common support {0, 1,…}. Each item in the system is classified into one of N age categories. New items arriving in the system are placed into the first age category. Items of age category j, j = 1,…, N-l, which have not been removed by demand during a day, are placed into age category j+1 at the beginning of the next day. Items of age N, which have not been removed by demand, are registered as outdates. Results concerning the characteristics of such a model are derived for the case of two and three age categories.     

Geometry and Excitation Energy Fluctuations of NMA in Aqueous Solution with CHARMM, AMBER, OPLS, and GROMOS Force Fields: Implications for Protein Ultraviolet Spectra Simulation

EPR experiments carried out at various temperatures for partially hydroxylated nanocrystalline MgO exposed to atomic hydrogen reveal that the entrapped electrons arising from spontaneous dissociation of hydrogen atoms exhibit an antiferromagnetic ordering. The measured magnetic data is found to be compatible with a phenomenological model of interacting paramagnetic centres at high temperature, and with a Pauli like behaviour below a certain temperature. This is further corroborated with density functional calculations of the effective magnetic coupling parameter for Heisenberg model between entrapped electrons on suitable embedded cluster models of MgO nanocrystals.     

Optimal Group Testing with Processing Times and Incomplete Identification

We consider the group testing problem for a finite population of possibly defective items with the objective of sampling a prespecified demanded number of nondefective items at minimum cost. Group testing means that items can be pooled and tested together; if the group comes out clean, all items in it are nondefective, while a contaminated group is scrapped. Every test takes a random amount of time and a given deadline has to be met. If the prescribed number of nondefective items is not reached, the demand has to be satisfied at a higher (penalty) cost. We derive explicit formulas for the distributions underlying the cost functionals of this model. It is shown in numerical examples that these results can be used to determine the optimal group size.     

Synthesis and characterization of poly(phosphon acetal) derivatives of poly(vinyl alcohol)

Preparation of poly(phosphonoacetals) (PPA) by transacetalation of poly(vinyl alcohol) with diethyl-phosphonoacetal is described. PPA with a degree of substitution of 60% is an alcoholsoluble polymer with a glass transition temperature (T_g) of 67°C. High resolution ¹H and ¹³C NMR spectra reveal the presence of hemiacetals alongside the six-membered acetal ring with an approximate ratio of 2:8 of these substituents. A possible correlation between the microtacticity of the parent PVA and the structure of PPA is indicated; the syndiotactic and isotactic sequences on the parent polymer controls the relationship between the two pendant groups.     

Constrained thermal denaturation of DNA under fixed linking number

A DNA molecule with freely fluctuating ends undergoes a sharp thermal denaturation transition upon heating. However, in circular DNA chains and some experimental setups that manipulate single DNA molecules, the total number of turns (linking number) is constant at all times. The consequences of this additional topological invariant on the melting behaviour are nontrivial. Below, we investigate the melting characteristics of a homogeneous DNA where the linking number along the melting curve is preserved by supercoil formation in duplex portions. We obtain the mass fraction and the number of loops and supercoils below and above the melting temperature. We also argue that a macroscopic loop appears at T _c and calculate its size as a function of temperature.     

Transport and percolation in disordered systems—A self-consistent time-local approach

A new self-consistent equation for the transport of excitations in disordered systems, which forms the basis for a new class of time-domain coherent potential approximations, is developed. As an example, we calculate the probability of remaining in the original site G₀(t) as well as the second moment of the distribution of excitations r²(t) for a random mixture of donors which satisfy a master equation with short-range transition rates. A percolation-type transition is observed and its characteristics are analyzed both above and below the transition point.Alfred P. Sloan fellow, Camille and Henry Dreyfus teacher-scholar.     

Stochastic Liouville equations for hydrogen-bonding fluctuations and their signatures in two-dimensional vibrational spectroscopy of water

The effects of hydrogen-bond forming and breaking kinetics on the linear and coherent third-order infrared spectra of the OH stretch of HOD in D2O are described by Markovian, not necessarily Gaussian, fluctuations and simulated using the stochastic Liouville equations. Slow (0.5 ps) fluctuations are represented by a collective electrostatic coordinate, whereas fast (<100 fs) frequency fluctuations are described using either a second collective electrostatic coordinate or a four-state jump (FSJ) model for hydrogen-bonding configurations. Parameters for both models were obtained using a 1-ns molecular-dynamics trajectory calculated using the TIP4P force field combined with an electrostatic ab initio map. The asymmetry of the photon-echo spectra (larger linewidth on the blue side than on the red side) predicted by the FSJ is in better agreement with recent experiments.     

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.