The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

The bar-radical of a class of almost alternative baric algebras

In this article we prove that, if (U, ) is a finite dimensional baric algebra of (gamma, delta) type over a field F of characteristic not equal 2,3,5 such that gamma(2) - delta(2) + delta = 1 and 0,1, then rad(U) = R(U)boolean AND(bar(U))(2), where R(U) is the nilradical (maximal nil ideal) of U.

REIDEMEISTER SPECTRUM FOR METABELIAN GROUPS OF THE FORM Q(n) x Z AND Z[1/p](n) x Z, p PRIME

In this paper, we study the Reidemeister spectrum for metabelian groups of the form Q(n) x Z and Z[1/p](n) x Z. Particular attention is given to the R(infinity)-property of a subfamily of these groups.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Crystal and molecular structures of three 2-sulphur-substituted cyclohexanones studied by X-ray crystallography and by ab initio molecular orbital calculations

The conformational features of three 2-sulphur-substituted cyclohexanone derivatives, which differ in the number of sulphur-bound oxygen atoms, i.e. zero (I), one (II) and two (III), were investigated by single crystal X-ray crystallography and geometry optimized structures determined using Hartree-Fock method. In each of (I)-(III) an intramolecular S center dot center dot center dot O(carbonyl) interaction is found with the magnitude correlated with the oxidation state of the sulphur atom, i.e. 2.838(3) angstrom in (I) to 2.924(2) angstrom in (II) to 3.0973(18) angstrom in (III). There is an inverse relationship between the strength of this interaction and the magnitude of the carbonyl bond. The supramolecular aggregation patterns are primarily determined by C-H center dot center dot center dot O contacts and are similarly influenced by the number of oxygen atoms in the molecular structures. Thus, a supramolecular chain is found in the crystal structure of (I). With an additional oxygen atom available to participate in C-H center dot center dot center dot O interactions, as in (II), a two-dimensional array is found. Finally, a three-dimensional network is found for (III). Despite there being differences in conformations between the experimental structures and those calculated in the gas-phase, the S center dot center dot center dot O interactions persist. The presence of intermolecular C-H center dot center dot center dot O interactions involving the cyclohexanone-carbonyl group in the solid-state, disrupts the stabilising intramolecular C-H center dot center dot center dot O interaction in the energetically-favoured conformation. (I): C(12)H(13)NO(3)S, triclinic space group P (1) over bar with a = 5.392(3) angstrom b = 10.731(6) angstrom, c = 11.075(6) angstrom, alpha = 113.424(4)degrees, beta = 94.167(9)degrees, gamma = 98.444(6)degrees, V = 575.5(6) angstrom(3), Z = 2, R(1) = 0.052; (II): C(12)H(13)NO(4)S, monoclinic P2(1)/n, a = 7.3506(15) angstrom, b = 6.7814(14) angstrom, c = 23.479(5) angstrom, beta = 92.94(3)degrees, V = 1168.8(4) angstrom(3), Z = 4, R(1) = 0.046; (III): C(12)H(13)NO(5)S, monoclinic P2(1)/c, a = 5.5491(11) angstrom, b = 24.146(3) angstrom, c = 11.124(3) angstrom, beta = 114.590(10)degrees, V = 1355.3(5) angstrom(3), Z = 4, R(1) = 0.051.

Chemoselective cross-coupling Suzuki-Miyaura reaction of (Z)-(2-chlorovinyl)tellurides and potassium aryltrifluoroborate salts

An ultrasound-assisted synthesis of functionalized vinylic chlorides is described by palladium-catalyzed cross-coupling reaction of potassium aryltrifluoroborate salts and (Z)-2-chloro vinylic tellurides. This procedure offers easy access to vinylic chlorides architecture that contains sterically demanding groups in good yields. (C) 2008 Elsevier Ltd. All rights reserved.

Development of a new stir bar sorptive extraction coating and its application for the determination of six pesticides in sugarcane juice

In this article, a novel polydimethylsiloxane/activated carbon (PDMS-ACB) material is proposed as a new polymeric phase for stir bar sorptive extraction (SBSE). The PDMS-ACB stir bar, assembled using a simple Teflon (R)/glass capillary mold, demonstrated remarkable stability and resistance to organic solvents for more than 150 extractions. The SBSE bar has a diameter of 2.36 mm and a length of 2.2 cm and is prepared to contain 92 mu L of polymer coating. This new PDMS-ACB bar was evaluated for its ability to determine the quantity of pesticides in sugarcane juice samples by performing liquid desorption (LD) in 200 mu L of ethyl acetate and analyzing the solvent through gas chromatography coupled with mass spectrometry (GC-MS). A fractional factorial design was used to evaluate the main parameters involved in the extraction procedure. Then, a central composite design with a star configuration was used to optimize the significant extraction parameters. The method used demonstrated a limit of quantification (LOQ) of 0.5-40 mu g/L, depending on the analyte detected; the amount of recovery varied from 0.18 to 49.50%, and the intraday precision ranged from 0.072 to 8.40%. The method was used in the analysis of real sugarcane juice samples commercially available in local markets.

Determination of fluoxetine in plasma by gas chromatography-mass spectrometry using stir bar sorptive extraction

This article presents a method employing stir bar sorptive extraction (SBSE) with in situ derivatization, in combination with either thermal or liquid desorption on-line coupled to gas chromatography-mass spectrometry for the analysis of fluoxetine in plasma samples. Ethyl chloroformate was employed as derivatizing agent producing symmetrical peaks. Parameters such as solvent polarity, time for analyte desorption, and extraction time, were evaluated. During the validation process, the developed method presented specificity, linearity (R-2 > 0.99), precision (R.S.D. < 15%), and limits of quantification (LOQ) of 30 and 1.37 pg mL(-1), when liquid and thermal desorption were employed, respectively. This simple and highly sensitive method showed to be adequate for the measurement-of fluoxetine in typical and trace concentration levels. (c) 2008 Elsevier B.V. All rights reserved.

Polydimethylsiloxane/polypyrrole stir bar sorptive extraction and liquid chromatography (SBSE/LC-UV) analysis of antidepressants in plasma samples

A new polymeric coating consisting of a dual-phase, polydimethylsiloxane (PDMS) and polypyrrole (PPY) was developed for the stir bar sorptive extraction (SBSE) of antidepressants (mirtazapine, citalopram, paroxetine, duloxetine, fluoxetine and sertraline) from plasma samples, followed by liquid chromatography analysis (SBSE/LC-UV). The extractions were based on both adsorption (PPY) and sorption (PDMS) mechanisms. SBSE variables, such as extraction time, temperature, pH of the matrix, and desorption time were optimized, in order to achieve suitable analytical sensitivity in a short time period. The PDMS/PPY coated stir bar showed high extraction efficiency (sensitivity and selectivity) toward the target analytes. The quantification limits (LOQ) of the SBSE/LC-UV method ranged from 20 ng mL(-1) to 50 ng mL(-1), and the linear range was from LOQ to 500 ng mL(-1), with a determination coefficient higher than 0.99. The inter-day precision of the SBSE/LC-UV method presented a variation coefficient lower than 15%. The efficiency of the SBSE/LC-UV method was proved by analysis of plasma samples from elderly depressed patients. (C) 2008 Elsevier B.V. All rights reserved.