Isopropylation of indoline

The composition of the reaction products was ascertained, and the kinetics of the alkylation of indoline with isopropyl alcohol in 90% sulfuric acid at 60C were studied. The reactivities of indoline and its carbocyclic analogs are compared.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 920–922, July, 1991.     

Ethyl α-cyanoacrylate in the Michael reaction

Ethyl -cyanocarylate undergoes the Michael reaction with strong CH-acids (pK _a < 13) in the presence of strong basic amines such as butylamine, piperidine, and triethylamine. Only polymerization of ethyl -cyanoacrylate occurs under the same conditions with weaker CH-acids in the presence of less basic amines such as aniline, N-methylaniline, and pyridine.A. N. Nesmeyanov Institute of Organometallic Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 10, pp. 2449–2452, October, 1992.     

Two-dimensional nuclear Overhauser enhancement NMR experiments on pelargonidin-3-glucopyranoside, an anthocyanin of low molecular mass.

Pelargonidin-3-glucoside has been isolated from the acidified methanolic extract of strawberries (Fragaria anannassa variety Corona) by successive application of an ion-exchange resin, droplet-counter chromatography and gel filtration. The pigment in acidified methanolic solution was studied by means of the two-dimensional nuclear Overhauser enhancement NMR technique, and the sugar unit was found to be attached to the 3-position on the aglycone. At +20 degrees C the pigment was found to be in the extreme narrowing limit where the NOESY cross-peaks are negative. However, at -20 degrees C this low-mass anthocyanin could be studied in the slow motion regime where the NOESY cross-peaks are positive. With a mixing time of 0.3 s, the glucose H1"-H4" proton pair was measured in the initial cross-relaxation rate and their cross-peak volume corresponded to the H1"-H4" distance found in a 4C1 chair conformation.     

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.     

Existence of Cesàro limit of bounded solution of evolution equation in banach space

An existence criterion for the Cesàro limit of a bounded solution y(t) of the problem dy(t)/dt = Ay(t), y(0)=y₀, t [O, ), where A is a closed linear operator with dense domain of definition D(A) in a reflexive Banach space E, is obtained under the condition that there exists a sufficiently small interval (O, ) belonging to the set of the regular points (A) of the operator A.Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1279–1280, September, 1992.     

Inverse problems of the theory of separately continuous mappings

The present paper investigates the problem of constructing a separately continuous function defined on the product of two topological spaces that possesses a specified set of points of discontinuity and the related special problem of constructing a pointwise convergent sequence of continuous functions that possesses a specified set of points of nonuniform convergence and set of points of discontinuity of a limit function. In the metrizable case the former problem is solved for separable F-sets whose projections onto every cofactor is of the first category. The second problem is solved for a pair of embedded F.Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1209–1220, September, 1992.     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which interpolate between the zonal spherical functions of related real andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.     

Electroproduction of strangeness

Formalism for the electroproduction of strange particles based on the one photon exchange approximation and the Feynman diagrams representation of hadron current is reviewed. Different photoproduction models are compared with available photo and electroproduction data. New experiments are proposed that may resolve existing uncertainties and inconsistencies. The formation of hypernuclei via kaon electroproduction is investigated theoretically and compared with other reactions involving purely hadronic processes.