Maximal subclasses of local fitting classes

A Fitting class $ \mathfrak{F} A Fitting class is said to be π-maximal if is an inclusion maximal subclass of the Fitting class of all finite soluble π-groups. We prove that is a π-maximal Fitting class exactly when there is a prime p ∊ π such that the index of the -radical in G is equal to 1 or p for every π-subgroup of G. Hence, there exist maximal subclasses in a local Fitting class. This gives a negative answer to Skiba’s conjecture that there are no maximal Fitting subclasses in a local Fitting class (see [1, Question 13.50]). Original Russian Text Copyright ? 2008 Savelyeva N. V. and Vorob’ev N. T. __________ Vitebsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1411–1419, November–December, 2008.     

The SC property of an expected residual function arising from stochastic complementarity problems

The stochastic nonlinear complementarity problem has been recently reformulated as an expected residual minimization problem which minimizes an expected residual function defined by an NCP function. In this work, we show that the expected residual function defined by the Fischer–Burmeister function is an function.     

Algorithms for finding clique-transversals of graphs

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τ _c of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τ _c . This algorithm is employed for finding the minimum cardinality clique-transversal of [`(3K₂)]\overline{3K_{2}} -free circular-arc graphs in O(n ⁴) time. Further we describe an algorithm for determining τ _c of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n ²) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n ²) time.     

Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids

The class of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety of . Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of . We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain the structure theorems of various generalized orthogroups. Partially supported by a UGC (HK) grant #2060123 (04-05).     

Wavelength dependence of matrix-assisted laser desorption and ionization using a tunable mid-infrared laser

Matrix-assisted laser desorption and ionization by infrared laser (IR-MALDI) is expected to be an effective methods for soft-ionization of high-molecular weight proteins and intracellular proteins. IR-MALDI is not widely used because its low sensitivity, complexity, high cost, and as it does not work well on commercial MALDI time-of-flight mass spectrometers (TOFMSs). We employed a tunable mid-infrared (MIR) laser as a light source for MALDI to investigate the IR-MALDI. The laser wavelength can be tuned within a range from 5.5 to 10.0 μm, and included several biomaterial group vibration modes. We evaluated the wavelength dependence of ionization in IR-MALDI for four matrices: succinic acid, urea, 3,5-dimethoxy-4-hydroxycinnamic acid (sinapic acid) and 2,5-dihydroxybenzoic acid (DHB). These matrices contained various groups of vibration modes, and absorbed an infrared (IR) energy at a specific wavelength. The mass spectra of angiotensin II was obtained at a specific wavelength corresponding to the CO stretching and benzene ring vibration mode. In IR-MALDI, we considered the strong molecular bond attracting an electron from a neighboring hydrogen atom, possibly protonating the hydrogen atom.     

Majorization of regular measures and weights with finite and positive critical exponent

For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω.     

A remark on Andrews-Askey integral

In this paper, we use the Andrews-Askey integral and the q-Chu-Vandermonde formula to derive a more general integral formula. Applications of the new integral formula are also given, which include to derive the q-Pfaff-Saalschütz formula and the terminating Sears's transformation formula.     

Pyrolysis of poly(phenylene vinylene)s with polycaprolactone side chains

The thermal degradation characteristics of a new macromonomer poly(-caprolactone) with central 4,4′-dicarbaldehyde terphenyl moieties and poly(phenylene vinylene)s with well defined (-caprolactone), (PPV/PCL) as lateral substituents were investigated via direct pyrolysis mass spectrometry. The unexpectedly high thermal stability of the macromonomer was attributed to intermolecular acetylation of benzaldehyde yielding a hemiacetal and causing a crosslinked structure during the pyrolysis. Increased thermal stability of the PCL chains was detected for all samples. The increase in stability of PCL chains was much more pronounced than was detected for poly(p-phenylene)-graft-poly(-caprolactone) copolymer (PPP/PCL); the upward temperature shift was about 100 °C for PPV/PCL and only 20 °C for PPP/CL. This pronounced effect may be due to higher thermal stability of PPV compared to PPP and the decrease in steric hindrance for PPV with PCL side chains.     

Evaluation of recurrence relationships and numerical solutions for finite rotation matrix elements by using auxiliary functions

In this article, we derived several new recurrence relations of the rotation matrix elements by using Gauss’ recurrence formulas for hypergeometric functions and auxiliary functions , and . The aim of this contribution is to obtain general algorithm to compute the rotation matrix elements, paying attention to the use recurrence relationships of the auxiliary functions that allow the treatment of the functions with high angular momentum quantum numbers.     

Functionalized fluoroalkyl and alkenyl silanes: Preparations, reactions, and synthetic applications

Preparations, reactions, and synthetic applications of functionalized fluoroalkyl and alkenyl silanes have been summarized. This review focuses mainly on the chemistries of (1) 1-substituted difluoromethylsilanes (XCF₂SiR₃), (2) 1-substituted 2,2-difluorovinylsilanes (CF₂CXSiR₃), (3) trifluoroisopropenyl, trifluoroacetimidoyl, and trifluoroacetyl silanes [CF₃C(SiR₃)X, XCH₂, NAr, O] and (4) other fluorinated alicyclic silanes.