On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Evolved gas analysis (EGA) of brick clays

Using a system based on non-dispersive infrared (NDIR) detectors, evolved gas analysis (EGA) was able to identify and quantify the principal volatiles produced by heating powdered samples of UK brick clays. From these results, atmospheric emissions likely to result from brick production can be predicted. In addition, EGA results for extruded brick clay test pieces are significantly different from those of powdered samples. Within an extruded brick clay body, evolved gases are contained within a pore system and evolved gas-solid phase reactions also occur. This EGA study provides further evidence on the nature of firing reactions within brick clay bodies. The qualitative and quantitative influence of heating rate — a key process condition in brick manufacture — on gas release is also outlined.Dedicated to Dr. Robert Mackenzie on the occasion of his 75th birthday     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

A poincaré-bendixson theorem for analytic families of vector fields

We provide a characterization of the limit periodic sets for analytic families of vector fields under the hypothesis that the first jet is non-vanishing at any singular point. Also, applying the family desingularization method, we reduce the complexity of some of these sets.     

Experimental studies of microwave amplification in the ion-focusedregime

Studies of microwave amplification with an in-focused electron beam drawn from an induction injector are reported. A free-electron laser (FEL) operating at 9.4 GHz and employing ion-focusing within the interaction region has achieved power in excess of 30 MW at 9.4 GHz, with a beam energy of 0.8 MeV and current of 0.7 kA. Peak gain is 20 dB/m, with no saturation after 15 wiggler periods. Also reported are the first evolution and detuning data for an ion-channel laser/maser (ICL). Two shortcomings of the prematurely halted ICL studies are poor frequency discrimination and a large axial plasma gradient. Prospects for operation with an upgraded 1.6 MeV accelerator are discussed     

Synthesis,structure, and chemical properties of some N-(3-chloro-2-quinoxalyl)arylsulfonamides

We have developed a method for synthesis of N-(3-clzloro-2-quinoxalyl)sulfonamides by reaction of 2,3-dichloroquinoxaline with substituted arylsufonamides. Based on the IR spectra, we have established that in the solid state, the synthesized compounds exist in the form of amide tautomers. Alkylation of these compounds leads to N-metliyl-N-(3-chloro-2-quinoxalyl)arylsulfonamides. We demonstrate the possibility of nucleophilic substitution of the halogen upon treatment with O- and N-nucleophiles. The use of bifunctional nucleophiles leads to condensed quinoxalines.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 30, No. 3, pp. 387–392, March, 1994.     

5-[5-R-furfurylidene]-2,2-dimethyl-1,3-dioxane-4,6-diones 5. Nucleophilic replacement of halogen in the furan ring

Halogen in positions 3 and 5 of the furan ring in ftirfurylidenedioxanediones is readily replaced by dithiocarbonate, dithiocarbatnate, dithiophosphate, thiocyanate, and azide anions, and by thiourea, and secondary and tertiary amines. The conformation of the initial halogen derivative is retained in the substitution products.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 327–334, March, 1994.