Theory of A ϕ-periodic one-dimensional bundle of dielectric waveguides

Mogil' Division, Institute of Physics, Belorussian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 2, pp. 200–204, February, 1992.     

The elastoplastic stressed state of a half-plane under local nonstationary heating

We solve the thermoplastic problem for a semi-infinite plate under local nonstationary heating by heat sources. The physical equations are taken to be the relations of the nonisothermic theory of plastic flow associated with the Mises fluidity condition. The solution of the problem is constructed by the method of integral equations and the self-correcting method of sequential loading, where time is taken as the loading parameter. We carry out numerical computations of the stresses in the case of heating a plate with heat output by normal-circular heat sources. We study the problem of optimization of heating regimes in order to introduce favorable residual compressive stresses (from the point of view of hardness) in a given region of a half-plane. Two figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 29–34.     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.     

Polarizable scattering centers in a fluctuation approach to charge transport

We present a detailed derivation of the fluctuation transport theory, previously developed by Gerlach and Mycielski. The basic idea is the transformation of carrier-densities and fields into the rest frame of each type of carriers and application of the Fluctuation-Dissipation-theorem for monopolar, unscreened carrier densities. In the present paper, the theory is applied to a model system containing free electrons, rigid ions and polarizable neutral donors. We compare our results with experimental data for the polar II–VI-semiconductor Eu₁-_xSr_xS.     

Chalcogenide based all-solid-state thin electroplated ion-selective membrane for Hg(II) flow-injection determinations

The response to Hg(II) of a thin all-solid-state Te-doped silver chalcogenide membrane, described by the general formula Ag₂ + δSe_{1 − x}Te_x, which has been electrochemically prepared following a previously proposed approach, has been investigated. The kinetics of formation of the membrane's secondary dynamic response to Hg(II) has been successfully combined with the precise timing and transient signal, typical for flow-injection (FI) measurements, in developing a sensitive and reliable mercury FI detector. Under optimized stream conditions it exhibits a linear Nernstian response, with a double slope of the calibration graph of 59 mV dec⁻¹, over the mercury(II) concentration range 10⁻⁶ − 10⁻³ M, the typical sample throughput amounting to about 70 samples per hour. The observed chemical amplification of the signal is due to the specificity of the processes dominating the initial step in formation of the steady-state signal of the membrane to mercury. The analytical performance of the Hg(II) FI detector, as regards sensitivity, reproducibility, selectivity and long-term stability has been thoroughly investigated. The exact procedure for membrane electrodeposition is given and the potential of the proposed approach as a cost-effective way for preparing chalcogenides of unique structure and properties has been outlined in the above context.     

Rule-based procedures in short-term electricity load forecasting

A short-term load-forecasting system has been developed to predictload demand for the Irish Electricity Supply Board from 1 to10 days in advance. Model output is acceptably accurate at mosttimes, but special days such as public holidays and the Easterweekend etc. require individual treatment. The basic model usedin everyday load forecasting is presented first, and specialdays when this model fails in accuracy are then examined andtreated separately using rule-based procedures. These proceduresare based on identified relationships between weather conditionsand prevailing daily load shapes. Comparisons are made betweenthe forecasts for these special days as given by the standardmodel and the ruled-based procedures.