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.     

Error analysis: a tool for selecting travel demand models

In developing travel demand models it is generally assumed that the base-year data used in developing the parameters, as well as the forecasted data to be used as independent variables for the design year, are of acceptable quality. The purpose of this paper is to present the application of error propagation theory in assesing the predictive quality of one type of travel demand forecasting model (multinomial logit models) and to demonstrate how error considerations can be used as a tool for identifying the optimal model. The general conclusions of this study are that: (1) it is indeed possible to quantify errors in dependent variables in logit models as a consequence of errors in independent variables; and (2) error consideration can be used as a tool for identifying the optimal model from a set of candidate models. Further research is recommended to develop better insights into the phenomenon of error propagation so that the consideration of errors can be a factor in decisions on model selection.     

τ-CHEBYSHEV AND τ-COCHEBYSHEV SUBPSACES OF BANACH SPACES

The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi^[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.     

Schmidt analysis of pure-state entanglement

We examine the application of Schmidt mode analysis to pure-state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of entanglement.     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.     

Advantages of NIR radiation use for optical determination of skin horny layer thickness with embedded TiO2 nanoparticles during tape stripping procedure

The tape stripping technique is an experimental method frequently used for reconstruction of the in-depth distribution of various topically administered substances within the horny layer of human skin, e.g., compounds contained in sunscreens. Titanium dioxide (TiO₂) nanoparticles (25–200 nm in diameter) are one such compound. Optical techniques which apply blue light are found to be suitable for reconstruction. However, the presence of particles affects the light propagation within the skin and therefore causes incorrect determination of strip thickness, leading to an improper reconstructed distribution of nanoparticle concentration revealed from the experimental data. This study evaluates the errors emerging from the use of blue (400 nm) and NIR (800 nm) radiation and finds the use of longer wavelength light more advantageous. Particles of different diameters are considered, and it is revealed that the application of small particles (25–60 nm) results in the lowest rate of error.     

The square lattice shuffle

We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

On construction of symmetries from integrals of hyperbolic partial differential systems

An algorithm is proposed which allows one to construct higher symmetries of arbitrary order for some special classes of hyperbolic systems possessing integrals. The Pohlmeyer-Lund-Regge system and the open two-dimensional Toda lattices are shown to belong to the class of systems where our algorithm is applicable. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.