Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Protein variation in blood-dwelling schistosome worms generated by differential splicing of micro-exon gene transcripts

Schistosoma mansoni is a well-adapted blood-dwelling parasitic helminth, persisting for decades in its human host despite being continually exposed to potential immune attack. Here, we describe in detail micro-exon genes (MEG) in S. mansoni, some present in multiple copies, which represent a novel molecular system for creating protein variation through the alternate splicing of short (<= 36 bp) symmetric exons organized in tandem. Analysis of three closely related copies of one MEG family allowed us to trace several evolutionary events and propose a mechanism for micro-exon generation and diversification. Microarray experiments show that the majority of MEGs are up-regulated in life cycle stages associated with establishment in the mammalian host after skin penetration. Sequencing of RT-PCR products allowed the description of several alternate splice forms of micro-exon genes, highlighting the potential use of these transcripts to generate a complex pool of protein variants. We obtained direct evidence for the existence of such pools by proteomic analysis of secretions from migrating schistosomula and mature eggs. Whole-mount in situ hybridization and immunolocalization showed that MEG transcripts and proteins were restricted to glands or epithelia exposed to the external environment. The ability of schistosomes to produce a complex pool of variant proteins aligns them with the other major groups of blood parasites, but using a completely different mechanism. We believe that our data open a new chapter in the study of immune evasion by schistosomes, and their ability to generate variant proteins could represent a significant obstacle to vaccine development.

Dinuclear Azide-Bridged Copper(II) Complex as Building Block for the Assembly of a 2D-Supramolecular Array

A novel Schiff base-copper(II) complex [Cu(2)L(2)(N(3))(2)](ClO(4))(2) 1, where L = (4-imidazolyl)ethylene-2-amino-1-ethylpyridine (apyhist), containing azide-bridges between adjacent copper ions in a dinuclear arrangement was isolated and characterized both in the solid state and in solution by X-ray crystallography and different spectroscopic techniques. Azide binding constants were estimated from titrations of the precursor [CuL(H(2)O)(2)](2+) solutions with sodium azide, giving rise to the azido-bridged species, [Cu(2)L(2)(N(3))(2)](2+). Raman spectra showed asymmetric stretching band at 2060 cm(-1), indicating the presence of azido ligands with a symmetric mu(1,) (1) binding geometry. EPA spectra, in frozen methanol/water solutions at 77 K, exhibited characteristic features of copper centers in tetragonal pyramidal coordination geometry, exhibiting magnetic interactions between them. Further, in solid state, two different values for magnetic coupling in this species were obtained, J/k = -(5.14 +/- 0.02) cm(-1) attributed to the mu(1, 1) azide-bridge mode, and J`z`/k = -(2.94 +/- 0.11) cm(-1) for the interaction between dinuclear moieties via water/perchorate bridges. Finally, an attempt was made to correlate structure and magnetic data for this dinuclear asymmetric end-on azido bridged-copper(II) 1 complex with those of another correlated dinuclear system, complex [Cu(2)L(2)Cl(2)](ClO(4))(2) 2, containing the same tridentate diimine ligand, but with chloro-bridged groups between the copper centres.

Formation of out of plane oxime metallacycles in [Cu(2)] and [Cu(4)] complexes

The reaction Of Cu(ClO(4))(2)center dot 6H(2)O with dimethylglyoxime (H(2)dmg) in a 1:1 mole ratio in aqueous methanol at room temperature affords the dinuclear complex [Cu(2)(mu-Hdmg)(4)] (1). Reaction of 1 with [Cu(bpy)(H(2)O)(2)](ClO(4))(2) (bpy = 2,2`-bipyridine) in a 1:1 mole ratio in aqueous methanol at room temperature yields the tetranuclear complex [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](ClO(4))(2) (2). The direct reaction of Cu(ClO(4))(2)center dot 6H(2)O with H(2)dmg and bpy in a 2:21 mole ratio in aqueous methanol at room temperature also yields 2 quantitatively. The complexes 1 and 2 were structurally characterized by X-ray crystallography. Unlike the binding in Ni/Co-dmg, two different types of N-O bridging modes during the oxime based metallacycle formation and stacking of square planar units have been identified in these complexes. The neutral dinuclear complex 1 has CuN(4)O coordination spheres and complex 2 consists of a dicationic [Cu(2)(mu-HdMg)(2)(mu-dMg)(2)(bpy)(2)(H(2)O)(2)](2+) unit and two uncoordinated ClO(4)(-) anions having CuN(4)O and CuN(2)O(3) coordination spheres. The two copper(II) ions are at a distance of 3.846(8) angstrom in 1 for the trans out of plane link and at 3.419(10) and 3.684(10) angstrom in 2 for the trans out of plane and cis in plane arrangements, respectively. The average Cu-N(oxime) distances are 1.953 and 1.935 angstrom, respectively. The average basal and apical Cu-N(oxime) distances are 1.945, 2.295 and 2.429 angstrom. The UV-Vis spectra of 2 is similar to the spectrum of the reaction mixture of 1 and [Cu(bpy)(H(2)O)(2)](2+). Variable temperature magnetic properties measurement shows that the interaction between the paramagnetic copper centers in complex I is antiferromagnetic in nature. The EPR spectra of frozen solution of the complexes at 77 K consist of axially symmetric fine-structure transitions (Delta M(S) = 1) and half-field signals (Delta M(S) = 2) at ca. 1600 G, suggesting the presence of appreciable Cu-Cu interactions. (C) 2009 Elsevier Ltd. All rights reserved.

Raman spectroscopy of a sulfur dioxide visual sensor: The origin of the two colors in the solid sample

The vibrational spectroscopic characterization of a sulfur dioxide visual sensor was carried out using a Raman microscope system. It was observed the formation of two distinct complexes, that were characterized by the position and relative intensities of the bands assigned to the symmetric stretching, nu(s)(SO(2)),of the linked SO(2) molecules. In fact, in the yellowish orange complex, that corresponds to the 1:1 stoichiometry, only one band is observed, assigned to nu(s)(SO(2)) at ca. 1080 cm-(1) and, in the deep red complex, that corresponds to the 1:2 complex, at ca. 1070 and 1090 cm(-)1 are observed. The variation of the relative intensities of the bands assigned to nu(s)(SO(2)) present in the Ni(II)center dot SO(2) complex, in different points of the sample, shows clearly the requirement of the Raman microscope in the vibrational characterization of this kind of molecular sensor. (C) 2008 Elsevier B.V. All rights reserved.

Theoretical Characterization of Hydrogen Polyoxides: HOOH, HOOOH, HOOOOH, and HOOO

We have investigated the polyoxides HOOH, HOOOH, HOOOOH, and HOOO employing the CCSD(T) methodology, and the correlation consistent basis sets. For all molecules, we have computed fundamental vibrational frequencies, structural parameters, rotational constants, and rotation-vibration corrections. For HOOOH, we have obtained a good agreement between our results and microwave and infrared spectra measurements, although for the symmetric OO stretch some important differences were found. Heats of formation were computed using atomization energies, and our recommendation is as follows: Delta H degrees(f,298)(HOOOH) = -21.50 kcal/mol and Delta H degrees(f,298)(HOOOOH) = -10.61 kcal/mol. In the case of HOOO, to estimate the heat of formation, we have constructed three isodesmic reactions to cancel high order correlation effects. The results obtained confirmed that the latter effects are very important for HOOO. The new Delta H degrees(f,298)(HOOO) obtained is 5.5 kcal/mol. We have also calculated the zero-point energies of DO and DOOO to correct the experimental lower limit determined for the Delta H degrees(f,298)(HOOO). The Delta(Delta ZPE) decreases the binding energy of HOOO by 0.56 kcal/mol. Employing the latter value, the new experimental lower limit for Delta H degrees(f,298)(HOOO) is 3.07 kcal/mol, just 2.4 kcal/mol lower than our determination. We expect that the fundamental vibrational frequencies and rotational constants determined for HOOOOH and DOOOOD contribute to its identification in the gas phase. The vibrational spectrum of HOOOOH shows some overlapping with that of HOOOH thus indicating that one may encounter some difficulties in its characterization. We discuss the consequences of the thermochemical properties determined in this work, and suggest that the amount of HOOO present in the atmosphere is smaller than that proposed recently in this journal (J. Phys. Chem A 2007, 111, 4727).