A note on the acyclicity of the Koszul complex of a module

We prove the vanishing of the Koszul homology group H _μ(Kos(M)_μ), where μ is the minimal number of generators of M. We give a counterexample that the Koszul complex of a module is not always acyclic and show its relationship with the homology of commutative rings.     

Designing a majorization scheme for the recourse function in two-stage stochastic linear programming

We discuss issues pertaining to the domination from above of the second-stage recourse function of a stochastic linear program and we present a scheme to majorize this function using a simpler sublinear function. This majorization is constructed using special geometrical attributes of the recourse function. The result is a proper, simplicial function with a simple characterization which is well-suited for calculations of its expectation as required in the computation of stochastic programs. Experiments indicate that the majorizing function is well-behaved and stable.     

Study of perfection of layers of AlGaSb(AS) solid solution

Studies have been carried out on the perfection of then-Al_xGa_1–xSb_1–yAs_y (0.12x0.26) layer grown on GaSb substrates under different conditions of lattice matching. During the relaxation of the mechanical stresses at first a system of tilt dislocations with a density of up to 5 · 10⁵ cm^–2 is formed while in thick layers (h 20 m) a network of misfit dislocations parallel to the heteroboundary is formed. The time required to dissolve a weighed amount of GaAs in the melt is shown to be of major importance for obtaining layers of a solid solution that are isoperiodic with the substrate. The entry of arsenic only in the initial portion of the epitaxial layer can reduce the dislocation density in the layer without decreasing the measured value of Aa. Dissolution of a weighed amount of GaAs in a Ga + Sb melt for two hours at T=730–750°C is sufficient to obtain layers of Al_xGa_1–xSb_1–yAs_y solid solution that are isoperiodic with the substrate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 84–89, January, 1988.In conclusion, we thank L. V. Druzhinina for useful discussions as well as Z. V. Korotchenko, L. S. Khludkova, and F. S. Kim for assistance in the performance of the experiments.     

Coherence of synchrotron radiation

Gal'tsov et al. [Vestn. Mosk. Gos. Univ., Fiz., Astron.,14, No. 5, 614 (1973)] studied the radiation spectrum of N equally spaced charges moving along a circle. In particular, it was shown that as N the intensity of the radiation from the system of charges vanishes. The present study will consider the radiation spectrum of N charges moving along an arbitrary closed curve, randomly distributed in the vicinity of equally spaced points. The coherency factor will be found for the assumption that: a) the distributions of individual charges are not intercorrelated; b) the charge distribution is such that in the vicinity of a given point only one charge is found. It will be shown that as N the radiation intensity tends to a finite limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 8–11, March, 1988.     

A topological characterization of classical BRST cohomology

The recent identification of classical BRST cohomology with the vertical cohomology of a certain fibration is used to compute it in terms of the classical observables and the topology of the gauge orbits. When the gauge orbits are compact and orientable, a duality theorem is exhibited.     

Static cylindrically symmetric solution of the Kaluza-Klein equations

In this paper we investigate the (static) solution of the Kaluza-Klein equations for a cylindrically symmetric current distribution. Specifically, we are interested in the fields generated by a long, cylindrical solenoid. We shall examine in some detail the concept of effective mass of a charged test particle. We shall show that, for a certain charge-to(rest)mass ratio of the test particle, the effective mass becomes imaginary at a certain distance from the axis of our solenoid.     

Laser properties of coactivated YAP: Nd free of colour centres

YAP:Nd, Cr grown under Ar-H₂ or Ar-He-H₂ atmosphere possesses good energy transfer from Cr³⁺ to Nd³⁺ but suffers from the colour centre formation. The centre formation was completely prevented using further admixture of Ce³⁺ and 10^–4–10^–3 wt. % Fe. Small luminescence quenching of Cr³⁺ or Nd³⁺ due to iron ions is negligible in the presence of Ce³⁺. The crystals may be also heavily doped with Nd³⁺ because the increased pumping efficiency compensates the shortening of the luminescence lifetime. YAP: Nd, Ce, Cr, Fe is advisible active laser material particularly for all the types of pulsed lasers.     

Preparation,characterization and a kinetic study oftrans-[Ru(NH3)4L(H2O)](PF6)2 [L=PPh3, AsPh3, or SbPh3]

Summary The complexestrans-[Ru(NH₃)₄(H₂O)PPh₃](PF₆)₂ and [Ru(NH₃)₅L](PF₆)₂, (L=AsPh₃ or SbPh₃) have been isolated and characterized by microanalysis, cyclic voltammetry and ultraviolet-visible spectroscopy. The specific rate constants for the aquation of [Ru(NH₃)₅L]²⁺ totrans-[Ru(NH₃)₄L(H₂O)]²⁺ are (2.5±0.1)×10^–5s^–1 and (1.8±0.1)×10^–5s^–1 for L=AsPh₃ and SbPh₃, respectively, at 25.0±0.1°C; =0.10 mol dm^–3, NaO₂CCF₃. Under the same conditions, the second-order rate constants for the substitution of water intrans-[Ru(NH₃)₄(H₂O)L]²⁺ by isonicotinamide (isn) are 1.2±0.1, (6.3±0.3)×10^–2 and (3.8±0.2)×10^–2 m ^–1s^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of decreasingtrans-effect is: PPh₃AsPh₃>SbPh₃. The formation constants for thetrans-[Ru(NH₃)₄L(isn)]²⁺ complexes are 75±3, (1.40±0.01)×10³ and (1.80±0.02)×10³M^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of increasingtrans-influence is: SbPh₃3PPh₃.     

Some trends in the development of microplasmas for spectrochemical analysis

The development of microplasmas for spectrochemical analysis by optical methods is discussed. Recent achievements in miniaturization are highlighted, especially for three types of plasmas, namely high-frequency plasmas, dc-discharges and microwave plasmas. The potentials of each of these groups of plasmas as sources for atomic emission spectrometry are discussed. Literature citations and experiments indicate that the plasmas are also very useful as atom reservoirs for atomic absorption spectrometry. Methods of sampling, including feeding with gas chromatography effluents, the use of electrothermal vaporization, and the evolution of gaseous species (as shown for the case of Hg vapor), are discussed as prominent interfaces to make use of these sources for elemental analysis.