Krull–Schmidt reduction of principal bundles in arbitrary characteristic

Let M be an irreducible projective variety defined over an algebraically closed field k, and let E_G be a principal G-bundle over M, where G is a connected reductive linear algebraic group defined over k. We show that for E_G there is a naturally associated conjugacy class of Levi subgroups of G. Given a Levi subgroup H in this conjugacy class, the principal G-bundle E_G admits a reduction of structure group to H. Furthermore, this reduction is unique up to an automorphism of E_G.     

Quantum chemical study on enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine. Part 3. Properties of intermediates during hydride transfer

In the current article, the structures and properties of intermediates during the hydride transfer for the prior coordination of the carbonyl oxygen of keto oxime ether at B(2) of oxazaborolidine are discussed. All the structures are optimized completely by means of the Hartree–Fock (HF) and the density functional methods at the HF/6‐31G(d) and Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP)/6‐31G(d) levels. The hydride transfer from BH₃ to the carbonyl carbon in oxazaborolidine‐borane‐keto oxime ether adduct results in the formation of the adduct 4a* with a seven‐membered ring. This adduct has four stable structures. Another hydride of BH₂ transfers to the oxime carbon in 4a* , leading to the adduct 5a* , which has also four stable structures. Among all the structures of 5a* , the most stable structure can generate (1S, 2R)‐cis amino alcohol, which is in agreement with that obtained in the experiment. This enantioselective reduction may go through the process in which oxazaborolidine‐borane‐keto oxime ether adduct is directly transformed into the adduct 4a* with a seven‐membered ring. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 307–316, 2003     

Preparation of 14,36-didehydro pristinamycins IIs

The first successful preparation of 14,36-didehydro pristinamycins II_A and II_B is reported via different strategies.     

Application of metalloporphyrins and methylviologen-pendent iron porphyrin to reduction of diphenylsulfoxide

In the two-electron reduction of diphenylsulfoxide to diphenylsulfide, which is considered a model reaction of sulfite reduction catalyzed by sulfite reductase, methylviologen-pendent iron(III) porphyrin exhibits much higher catalytic activity than usual iron(III) and manganese(III) tetraphenylporphyrins, while cobalt(II) tetraphenylporphyrin exhibits much less catalytic activity than the others. Discussion about the active species and the reason of the acceleration by methylviologen-pendent is presented.     

High-pressure clathrate hydrate of acetone

X-ray diffraction study of quenched sample of acetone clathrate hydrate synthesized at 0.8 GPa was carried out. It was shown that the host frameworks of the hydrate comprise uniform cavities which are similar to that of recently characterized structure of high-pressure tetrahydrofurane hydrate. The unique peculiarity of investigated hydrate is decrease in the crystallographic symmetry of the hydrate arising from ordering in guest subsystem.     

Singular Reduction of Poisson Manifolds

The conditions under which it is possible to reduce a Poisson manifold via a regular foliation have been completely characterized by Marsden and Ratiu. In this Letter we show that this characterization can be generalized in a natural way to the singular case and, as a corollary, we obtain that when the singular distribution is given by the tangent spaces to the orbits created by a Hamiltonian Lie group action, one reproduces the Universal Reduction Procedure of Arms, Cushman, and Gotay.     

Synthesis and reduction of 5-halo-and 5-nitro-1-(benzofuran-3-yl)-2-phenylethanones

Novel 1-(2-alkylbenzofuran-3-yl)-2-(4-methoxyphenyl)ethanones having a halogen or nitro group in position 5 of the benzofuran ring were synthesized starting with the corresponding 2-(2-formylphenoxy)alkanoic acids. 1-(2-Alkylbenzofuran-3-yl)-2-phenylethanols containing bromine or chlorine atom were prepared in high yields by reduction of the corresponding ethanones with lithium aluminum hydride. Selective catalytic reduction of nitro 1-(2-alkylbenzofuran-3-yl)-2-(4-methoxyphenyl)ethanones to the corresponding amino compounds under Pd/C in room temperature was achieved. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1158–1166, August, 2006.     

Charge and structural ordering in the brownmillerite phases: La1−xSrxMnO2.5 (0.2<x<0.4)

The topotactic reduction of La_1−xSr_xMnO₃ (0.2<x<0.4) perovskite phases to the corresponding La_1−xSr_xMnO_2.5 brownmillerite phases with NaH is described. Neutron and electron diffraction data show the x=0.25 and 0.2 phases adopt structures with an unusual ordered L-R-L-R alternation of twisted chains of Mn(II) tetrahedra within each anion-deficient layer. This is accompanied by Mn(II)/(III) charge ordering within the remaining MnO₆ octahedral layers. In contrast, the x=0.4 phase adopts a structure in which the twisted chains of tetrahedra are disordered.     

Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. Research partially supported by the MIUR FIRB Project RBNE01WBBB “Large-Scale Nonlinear Optimization.”     

Field Profile Synthesis with an Antenna Array

Two algorithms for the synthesis of a microwave beam with desired characteristics are discussed. The beam is composed by an array of either identical or non-identical antennas. In an example, the application of those algorithms for wireless power transmission is demonstrated.