Numerical methods for finding multiple eigenvalues of matrices depending on parameters

Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods. Received December 19, 1994 / Revised version received January 18, 1996     

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     

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.     

Hydroxyl-containing mesogens. Synthesis and liquid-crystalline properties of 2-o-hydroxyarylpyrimidines

We have synthesized 5-alkyl(alkoxy)-2-(o-lzydroxy-p-alkoxyphenyl)pyrimidines and considered the effect of the OH group on the inesomorphism. We have found that in binuclear o-hydroxyarylpyrimidines, an ortho OH group forming an intramolecular hydrogen bond increases T_mp, inhibits the appearance of nematic properties, and promotes the appearance of a smectic A.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 30, No. 1, pp. 90–92, January, 1994.     

Effect of infection byVerticillium dahliae on the lipid complex of cotton seeds from varieties with contrasting resistance

The yields and fatty acid compositions of the free lipids and lipids weakly and strongly bound to proteins from seeds of cottonplant varieties resistant and susceptible to verticillium wilt have been determined and the changes in these indices in the seeds of the infected plants have been measured. It has been established that the seeds of healthy plants of the two varieties are similar in the qualitative compositions of the lipids and fatty acids but differ with respect the amounts of lipids in them bound with protein in different ways and with respect to the amounts of the individual fatty acids. The observed changes in the lipid and fatty-acid compositions depend on the degree of resistance of the variety to wilt.     

Flavonoids and xanthones ofHedysarum connatum andH. alpinum

State Scientific Center for Drugs, Khar'kov. Ukrainian Pharmaceutical Academy, Khar'kov. Botanical Gardem, Russian Academy of Sciences, St. Petersburg. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 564–565, July–August, 1994.     

Lipids of cottonseed and palm oils and compositions based on them

The phsicochemical indices and the fatty-acid and triacylglycerol compositions of cottonseed and palm oils, of cottonseed oil hydrogenate, and of compositions based on them have been determined with the aid of IR and UV spectroscopies, GLC analysis, and chemical transformations. The compositions and amounts of the main classes of lipids in the initial oils and the hydrogenate have been studied. It has been found that in the process of hydrogenation the amount of oxygenated components falls. The work was conducted with the financial support of the Uzbek Fund for Fundamental Investigations.     

Rhamnose orthoacetates of aconitine and imperialine

The preparation and spectral properties of rhamnose orthoacetates of aconitine and imperialine are described.Tashkent Pharmaceutical Institute. Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 743–746, September–October, 1993.     

Isolation of phospholipase A2 from the venom of the green toadBufo viridis

Phospholipase A₂ has been isolated fromthe venom of he Central Asian green toad Bufo viridis in the electroophoretically homogeneous state for the first time by biospecific absorption chromatography. The affinity sorbent used was Affi-Gel 10 with covalently bound phosphatidylserine (PDS). The chemical inertness of the bound PDS to the hydrolytic action of phospholipase A2 and its high tendency to form biospecific complexes have been shown. Some biochemical characteristics of the enzyme isolated have been studied: influence of the pH and of the Ca²⁺ concentration and dependence of activity on substrate concentration.A. S. Sadykov Institute of Bioorganic Chemistry, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax 627071. Tashkent State University, fax 462472. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 105–109, January–February, 1994.