Brumadoite, a new copper tellurate hydrate, from Brumado, Bahia, Brazil

Brumadoite, ideally Cu(2)Te(6+)O(4)(OH)(4)center dot 5H(2)O, is a new mineral from Pedra Preta mine, Serra das Eguas, Brumado, Bahia, Brazil. It occurs as microcrystalline aggregates both on and, rarely, pseudomorphous after coarse-grained magnesite, associated with mottramite and quartz. Crystals are platy, subhedral, 1-2 mu m in size. Brumadoite is blue (near RHS 114B), has a pale blue streak and a vitreous lustre. It is transparent to translucent and does not fluoresce. The empirical formula is (Cu(2.90)Pb(0.04)Ca(0.01))(Sigma 2.95) (Te(0.93)(6+)Si(0.05))(Sigma 0.98)O(3.92)(OH)(3.84)center dot 5.24H(2)O. Infrared spectra clearly show both (OH) and H(2)O. Microchemical spot tests using a KI Solution show that brumadoite has tellurium in the 6(+) state. The mineral is monoclinic, P2(1)/m or P2(1). Unit-cell parameters refined from X-ray powder data are a 8.629(2) angstrom, b 5.805(2) angstrom, c 7.654(2) angstrom, beta 103.17(2)degrees, V 373.3(2) angstrom(3), Z = 2. The eight strongest X-ray powder-diffraction lines [d in angstrom, (l),(hkl)] are: 8.432,(100),(100); 3.162,(66),((2) over bar 02); 2.385,(27),(220); 2.291,((1) over bar 12),(22); 1.916,(11),(312); 1.666,(14),((4) over bar 22,114); 1.452,(10), (323, 040); 1.450,(10),(422,403). The name is for the type locality, Brumado, Bahia, Brazil. The new mineral species has been approved by the CNMNC (IMA 2008-028).

Footemineite, the Mn-analog of atencioite, from the Foote mine, Kings Mountain, Cleveland County, North Carolina, USA, and its relationship with other roscherite-group minerals

Footemineite, ideally Ca2Mn2+square Mn22+Be4(PO4)(6)(OH)(4)-6H(2)O, triclinic, is a new member of the roscherite group. It occurs on thin fractures crossing quartz-microcline-spodumene pegmatite at the Foote mine, Kings Mountain, Cleveland County, North Carolina, U.S.A. Associated minerals are albite, analcime, eosphorite, siderite/rhodochrosite, fairfieldite, fluorapatite, quartz, milarite, and pyrite. Footemineite forms prismatic to bladed generally rough to barrel-shaped crystals up to about 1.5 mm long and I mm in diameter. Its color is yellow, the streak is white, and the luster is vitreous to slightly pearly. Footemineite is transparent and non-fluorescent. Twinning is simple, by reflection, with twin boundaries across the length of the crystals. Cleavage is good on {0 (1) over bar1}) and {100}. Density (calc.) is 2.873 g/cm(3). Footemineite is biaxial (-), n(alpha) = 1.620(2), n(beta) = 1.627(2), n(gamma) = 1.634(2) (white light). 2V(obs) = 80 degrees, 2V(calc) = 89.6 degrees. Orientation: X boolean AND b similar to 12 degrees, Y boolean AND c similar to 15 degrees, Z boolean AND a similar to 15 degrees. Elongation direction is c, dispersion: r > v or r < v, weak. Pleochroism: beta (brownish yellow) > alpha = gamma (yellow). Mossbauer and IR spectra are given. The chemical composition is (EDS mode electron microprobe, Li and Be by ICP-OES, Fe3+:Fe2+ y Mossbauer, H2O by TG data, wt%): Li2O 0.23, BeO 9.54, CaO 9.43, SrO 0.23, BaO 0.24, MgO 0.18, MnO 26.16, FeO 2.77, Fe2O3 0.62, Al2O3 0.14, P2O5 36.58, SiO2 0.42, H2O 13.1, total 99.64. The empirical formula is (Ca1.89Sr0.03Ba0.02)Sigma(1.94)(Mn-0.90(2+)square(0.10))Sigma(1.00)(square 0.78Li0.17Mg0.05) Sigma(1.00)(Mn3.252+Fe0.432+ Fe0.093+Al0.03)Sigma(3.80) Be-4.30(P5.81Si0.08O24)[(OH)3.64(H2O)0.36]Sigma(4.00)center dot 6.00H(2)O . The strongest reflection peaks of the powder diffraction pattern [d, angstrom (1, %) (hkl)] are 9.575 (53) (010), 5.998 (100) (0 (1) over bar1), 4.848 (26) (021), 3.192 (44) (210), 3.003 (14) (0 (2) over bar2), 2.803 (38) ((1) over bar 03), 2.650 (29) ((2) over bar 02), 2.424 (14) (231). Single-crystal unit-cell parameters are a = 6.788(2), b = 9.972(3), c = 10.014(2) A, (x = 73.84(2), beta = 85.34(2), gamma = 87.44(2)degrees,V = 648.74 angstrom(3), Z = 1. The space group is P (1) over bar. Crystal structure was refined to R = 0.0347 with 1273 independent reflections (F > 2(5). Footemineite is dimorphous with roscherite, and isostructural with atencioite. It is identical with the mineral from Foote mine described as ""triclinic roscherite."" The name is for the Foote mine, type locality for this and several other minerals.

Random walks systems with killing on Z

We study random walks systems on Z whose general description follows. At time zero, there is a number N >= 1 of particles at each vertex of N, all being inactive, except for those placed at the vertex one. Each active particle performs a simple random walk on Z and, up to the time it dies, it activates all inactive particles that it meets along its way. An active particle dies at the instant it reaches a certain fixed total of jumps (L >= 1) without activating any particle, so that its lifetime depends strongly on the past of the process. We investigate how the probability of survival of the process depends on L and on the jumping probabilities of the active particles.

Perfect Simulation of a Coupling Achieving the (d)over-bar-distance Between Ordered Pairs of Binary Chains of Infinite Order

We explicitly construct a stationary coupling attaining Ornstein`s (d) over bar -distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of infinite order as a countable mixture of Markov transition probabilities of increasing order. Under suitable conditions on the loss of memory of the chains, this representation implies that the coupled chain can be represented as a concatenation of i.i.d. sequences of bivariate finite random strings of symbols. The perfect simulation algorithm is based on the fact that we can identify the first regeneration point to the left of the origin almost surely.

NONHOMOGENEOUS RANDOM WALKS SYSTEMS ON Z

We consider a random walks system on Z in which each active particle performs a nearest-neighbor random walk and activates all inactive particles it encounters. The movement of an active particle stops when it reaches a certain number of jumps without activating any particle. We prove that if the process relies on efficient particles (i.e. those particles with a small probability of jumping to the left) being placed strategically on Z, then it might survive, having active particles at any time with positive probability. On the other hand, we may construct a process that dies out eventually almost surely, even if it relies on efficient particles. That is, we discuss what happens if particles are initially placed very far away from each other or if their probability of jumping to the right tends to I but not fast enough.

On the Derived Categories and Quasitilted Algebras

In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable objects in these categories, using homological properties. Given a complex X*, we consider the set J(X*) = {i is an element of Z vertical bar H(i)(X*) not equal 0} and we define the application l(X*) = maxJ(X*) - minJ(X*) + 1. We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras.

An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

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.