Production under periodic demand update prior to a single selling season: A decomposition approach

This paper focuses on dynamic, continuous-time production control problems in the fashion industry. Similar to the classical news-vendor problem, we consider a single product-type and the cumulative demand for items is not known until the end of the production horizon and therefore must be forecasted. Since there are periodic updates before a single selling season, actual demand during a period of time can only be determined by the end of the period. If the overall demand is overestimated, excessive inventory holding and production costs are paid and surpluses are sold at low prices at the end of the production horizon. If it is under-estimated, then sales are lost. The objective is to dynamically determine production orders which minimize overall expected costs. Since the optimal feedback for such a problem is characterized by thresholds evolving with time and system states, there is a significant computational burden in determining them. With the aid of the variational analysis and a decomposition, we derive a closed-form solution for the thresholds. A numerical study carried out to compare the decomposition and straightforward simulation-based solutions indicates the high accuracy of the suggested approach while the computational burden is dramatically reduced.     

Propagation of electromagnetic waves over a foamed sea surface

We study the propagation of electromagnetic waves over a smooth sea surface with impedance fluctuations due to copious foaming. This problem is solved analytically with allowance for multiple scattering at small grazing angles. An analytical expression for the effective impedance of the mean field is found in the case of large variance in the perturbation of the dielectric properties of the interface. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 5, pp. 438–451, May 1999.     

The Ion-optical scheme of a portable mass spectrometer

An ion-optical scheme for a portable magnetic double-focusing mass spectrometer that makes it possible to analyze several components simultaneously over a wide mass range (the mass-spectrograph operating mode) is proposed. This scheme effectively solves the research and technological problems involving the analysis of rapidly varying compositions.     

Classification of Curves in 2D and 3D via Affine Integral Signatures

We propose new robust classification algorithms for planar and spatial curves subjected to affine transformations. Our motivation comes from the problems in computer image recognition. To each planar or spatial curve, we assign a planar signature curve. Curves, equivalent under an affine transformation, have the same signature. The signatures are based on integral invariants, which are significantly less sensitive to small perturbations of curves and noise than classically known differential invariants. Affine invariants are derived in terms of Euclidean invariants. We present two types of signatures: the global and the local signature. Both signatures are independent of curve parameterization. The global signature depends on a choice of the initial point and, therefore, cannot be used for local comparison. The local signature, albeit being slightly more sensitive to noise, is independent of the choice of the initial point and can be used to solve local equivalence problem. An experiment that illustrates robustness of the proposed signatures is presented.     

2-(N-tosylamino)benzaldehyde thiobenzoylhydrazone and its complexes with copper(II) and zinc(II): Synthesis and structures

2-(N-Tosylamino)benzaldehyde thiobenzoylhydrazone and its copper(II) and zinc(II) complexes with dimethylformamide (DMF) and methanol, [CuL(DMF)] and [ZnL(CH₃OH)], respectively, were synthesized. The structures of the copper(II) complex and the cyclic product of hydrazone oxidation (1,3,4-thiadiazole derivative) were determined by X-ray diffraction analysis.     

Quasiequilibrium Knudsen boundary layer on a nonisothermal porous body

The state of a gas near a permeable nonisothermal body with ultrathin pores, that is, pores in which the motion of molecules is not accompanied by intermolecular collisions, is studied. A boundary layer of a new type, namely, the quasiequilibrium Knudsen boundary layer on the porous body surface, is investigated. It is formed on condition that within the body there is a heat flux, even when the body is in an equilibrium gas. The statistical methods for solving the Boltzmann equation are used to determine the temperature and pressure jumps across the Knudsen layer near thin perforated and porous membranes.     

Electromagnetic-Wave Propagation in a Half-Space with a Curvilinear Impedance Boundary

We study propagation of electromagnetic waves in a vacuum half-space with a one-dimensional distortion of the impedance boundary whose profile is smooth on the wavelength scale. We suggest a method allowing one to obtain the solution of this problem on the basis of a more simple boundary-value problem with the same geometry of the boundary, but with a zero Dirichlet boundary condition.     

On the deconstruction of time

In this note we discuss the possibility of getting a time rather than space in the scenario of (de)construction of a new dimension.     

Dynamic zigzag pricing of resalable goods with no depreciation and intergroup externalities

This paper addresses the pricing policy of durable value goods that do not depreciate over time. This implies that demands for this type of goods fluctuate with respect to their market price and social interactions between customers rather than with respect to the time elapsed since they have been produced or created. We suggest an analytical approach for optimally setting durable value product prices with respect to the interdependency between two customer groups characterized by asymmetric intergroup externalities. We demonstrate that cyclic pricing policies of harmonic form become optimal when the company is prepared to compromise its short-run net profit to ensure its lasting reputation. Furthermore, we show that the greater the difference between the product of the price and the externality effect of the two customer groups, the greater the frequency of the harmonic fluctuation.