Sufficient conditions for a strong relative minimum in an optimal control problem

In this paper, on the basis of Young's method (Ref. 1), sufficient conditions for a strong relative minimum in an optimal control problem are given. Young's method generalizes geodesic coverings and the simplest Hilbert integral from the standard variational calculus. This paper carries Young's method over to nonparametric problems.     

Influence of Water Vapor on CCl4 and CHCl3 Conversion in Gliding Discharge

The effect of initial concentration of tetrachloromethane and trichloromethane on their conversion in gliding discharge was determined. The conversion of CCl₄ and CHCl₃ was carried out in air containing 20 or 8000 ppm of water vapor. The flow rate of the air containing 1.2, 2.5, or 6.0 vol% of CCl₄ or CHCl₃ was 200 Nl/h. The amount of tetrachloromethane and trichloromethane reacted was determined for a constant value of specific energy which was varied with 2.0 and 4.0 VAh/Nl. The amounts of CCl₄ and CHCl₃ reacted were a linear function of the initial concentration of these compounds in the inlet gas. The results obtained have shown that water vapor present in the air has a favorable effect on the conversion of tetrachloromethane and trichloromethane in gliding discharge.     

Crystallization and second harmonic generation in thermally poled niobium borophosphate glasses

Crystallization of glasses with compositions (1−x)(0.95 NaPO₃+0.05 Na₂B₄O₇)+xNb₂O₅, x=0.4, 0.43, 0.45, 0.48 was investigated by differential scanning calorimetry and X-ray powder diffraction. Crystallization of two phases was observed in the glasses with x=0.43-0.48. First phase is a sodium niobate with the structure of tetragonal tungsten bronze () and second phase is Na₄Nb₈P₄O₃₂ (). The crystallization of sodium niobate is correlated with increasing of nonlinear optical efficiency reported for thermally poled glasses with x>0.4. The results of Raman spectroscopy show the formation of three-dimensional (3D) niobium oxide framework in the glasses with increase of niobium concentration. This framework is supposed to have tetragonal tungsten bronze structure and to be responsible for nonlinear optical properties of the glass. Second harmonic generation signals of as prepared and crystallized glass after thermal poling are compared. The nucleation and crystallization do not improve the NLO properties of the glasses under study.     

Strukturelle Untersuchungen einiger neutraler Komplexe des zweiwertigen Molybdäns

Unit cell parameters have been calculated from x-ray powder diffraction data of Mo₂Br₄ Py ₄ (A), Mo₂I₄ Py ₄ (B), Mo₂I₄ Pic ₄ (C), Mo₂(SCN)₄ Py ₄ (D) and Mo₂(SCN)₄ Pic ₄ (E), A, B and C crystallize tetragonal. A witha=9,4₂,c=15,O₂ Å; B witha=9,4₆,c=14,9₈ Å and C witha=9,6₆ andc=15,7₂ Å D and E crystallize orthorhombic. D witha=10,0₉,b=9,1₄,c=15,0₈ Å; E witha=10,2₂,b=9,4₁ andc=15,1₅ Å.Py=pyridine,Pic=4-methylpyridine.

     

Substitution of phosphine in the complex [RhCl(cyclooctadiene)(phosphine)] by 1-hexene

Summary The substitution of phosphine in the [RhCl(COD)(phosphine)] complex (1), where phosphine is PPh₃ or 1/2 BPS-2 [bis(diphenylphosphinoethyl)tetramethyldisiloxane] and COD is cycloocta-1,5-diene, by 1-hexene is a two-step reversible reaction. All individual rate constants and equilibrium constants were determined spectrophotometrically and associative mechanism occurring via the formation of five-coordinated [RhCl(COD)(phosphine)(1-hexene)] (2) was inferred. The rate-determining step changes from the first- to the second-one as the concentration of 1-hexene increases. An excess of phosphine shifts the equilibrium towards complex (2).     

Multipeak distributions of first passage times in bistable dynamics in a model of a thermochemical system.

A master equation is used to study transitions between the stable limit cycle and stable focus in the two-variable bistable system. The distribution function of the mean first passage time between these attractors and the relative dispersion of the mean first return time from the stable focus to itself as a function of the intensity of fluctuations are calculated and discussed. A coherence resonance is observed for the return time from the focus to itself.     

The endomorphism spectrum of an ordered set

Theendomorphism spectrum of an ordered setP, spec(P)={|f(P)|:f End(P)} andspectrum number, sp(P)=max(spec(P)\{|P|}) are introduced. It is shown that |P|>(1/2)n(n – 1) ^{n – 1} implies spec(P) = {1, 2, ...,n} and that if a projective plane of ordern exists, then there is an ordered setP of size 2n ²+2n+2 with spec(P)={1, 2, ..., 2n+2, 2n+4}. Lettingh(n)=max{|P|: sp(P)n}, it follows thatc ₁ n ²h(n)c ₂ n ⁿ⁺¹ for somec ₁ andc ₂. The lower bound disproves the conjecture thath(n)2n. It is shown that if |P| – 1 spec(P) thenP has a retract of size |P| – 1 but that for all there is a bipartite ordered set with spec(P) = {|P| – 2, |P| – 4, ...} which has no proper retract of size|P| – . The case of reflexive graphs is also treated.Partially supported by a grant from the NSERC.Partially supported by a grant from the NSERC.     

On gauge invariance of Breit-Wigner propagators

We present an approach to bosonic (Z ^o,W ^±) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for theZ ^o-boson propagator we extend previous analyses and show that the part proportional tok k _v /M ² must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.