Two modifications of the least cost per period heuristic for dynamic lot-sizing

This paper proposes two constructive heuristics for the well-known single-level uncapacitated dynamic lot-sizing problem. The proposed heuristics, called net least period cost (nLPC) and nLPC(i), are developed by modifying the average period cost concept from Silver and Meal's heuristic, commonly known as least period cost (LPC). An improved tie-breaking stopping rule and a locally optimal decision rule are proposed in the second heuristic to enhance performance. We test the effectiveness of the proposed heuristics by using 20 benchmarking test problems frequently used in the literature. Furthermore, we perform a large-scale simulation study involving three factors, 50 experimental conditions, and 100?000 randomly generated problems to evaluate the proposed heuristics against LPC and six other well-known constructive heuristics in the literature. The simulation results show that both nLPC and nLPC(i) produce average holding and setup costs lower than or equal to those of LPC in every one of the 50 experimental conditions. The proposed heuristics also outperform each of the six other heuristics evaluated in all experimental conditions, without an increase in computational requirements. Lastly, considering that both nLPC and nLPC(i) are fairly simple for practitioners to understand and that lot-sizing heuristics have been commonly used in practice, there should be a very good chance for practical applications of the proposed heuristics.     

Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

Specific features of photoisomerization of provitamin D 3 in a nematic liquid crystal

Photoisomerization of provitamin D ₃ (7-dehydrocholesterol) in a nematic liquid crystal (ZLI-1695, Merck) is investigated in detail by UV absorption spectroscopy. It is found that dissolution of chiral molecules of provitamin D ₃ induces the cholesteric phase in a nematic. The spectral kinetics of photoisomerization in this phase changes significantly from that in an ethanol solution. A sharp nonmonotonic dependence of the increase in accumulation of trans isomer tachysterol in a liquid crystal matrix with a decrease in the induced cholesteric pitch from 2200 to 25 μm is revealed.     

Metastable States in Antiprotonic Helium Atoms: An Island of Stability in a Sea of Continuum

 In this contribution we consider a phenomenon of metastable states in antiprotonic helium atoms, precise spectroscopy of these states and a present-day study of the electromagnetic properties of antiprotons. Received October 16, 2001; accepted for publication November 13, 2001     

Effect of hydrogen on the photoelectronic properties of GaAs/InGaAs quantum-well heterostructures with an island palladium layer on the surface

The effect of hydrogen on the photoluminescence and planar conductivity of GaAs/InGaAs quantum-well heterostructures with an island Pd layer at the anodically oxidized surface was studied. Unlike continuous deposited Pd layers, island layers do not cause the formation of defects in the GaAs surface region and yet the Pd layer maintains high catalytic activity with respect to hydrogen. It is found that the thermal treatment of such a structure in a hydrogen atmosphere causes atomic-hydrogen passivation of the defects in quantum wells. Studies of the characteristics of planar photoresistors with an island Pd layer acting as hydrogen sensors show that their hydrogen detectivity is approximately two orders of magnitude higher than that of diode structures with continuous Pd layers.     

Why and how to avoid standard kinetic equations I. Principles and band conduction problem

A review of ideas leading to full rejection of any finite or partially-infinite order kinetic equation linearized in external field is given on grounds of the time-convolution Generalized Master Equations (GME). By two examples (two-level and band conduction problem), it is shown how standard kinetic equations result from GME in the lowest order approximations which obscure, however, a direct correspondence with the Kubo linear response theory. Without approximations, on the other hand, the rigorous approach is shown to be fully equivalent with the Kubo results. It is argued and illustrated that usual technical simplicity and seeming physical lucidity of standard theories (connected with the presence of field-independent transfer or scattering rates in the fielddependent linearized theory) are just owing to structural features which are solely due to the lowest order approximations involved. These features (i.e. also the possibility of standard physical interpretation of kinetic phenomena) are proved to disappear completely as far as the theory goes properly to higher orders.     

Universal algebras

A survey of the development of the theory of universal algebras in the years 1976–1988. Such basic directions of development of this theory as classes of universal algebras (varieties, quasivarieties, etc.), Mal'tsev conditions, congruences, sheaves, homomorphisms, subalgebras, products of algebras, clones of operations, completeness, systems of equations in algeberas, and connections with computer mathematics show up in it. Considerable attention is given to concrete classes of algebras (p-algebras, BCK-algebras, unary algebras, etc.).Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 27, pp. 45–124, 1989.