Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Z(p). This is done by defining an index preserving morphism s: Br(<(K(X))over cap>)` --> Br(K(X))` which splits res : Br(K (X)) --> Br(<(K(X))over cap>), where <(K(X))over cap> is the completion of K (X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over <(K(X))over cap>. (C) 2010 Elsevier Inc. All rights reserved.

Hyperbolic unit groups and quaternion algebras

We classify the quadratic extensions K = Q[root d] and the finite groups G for which the group ring o(K)[G] of G over the ring o(K) of integers of K has the property that the group U(1)(o(K)[G]) of units of augmentation 1 is hyperbolic. We also construct units in the Z-order H(o(K)) of the quaternion algebra H(K) = (-1, -1/K), when it is a division algebra.

NEONATAL HANDLING AND THE MATERNAL ODOR PREFERENCE IN RAT PUPS: INVOLVEMENT OF MONOAMINES AND CYCLIC AMP RESPONSE ELEMENT-BINDING PROTEIN PATHWAY IN THE OLFACTORY BULB

Early-life environmental events, such as the handling procedure, can induce long-lasting alterations upon several behavioral and neuroendocrine systems. However, the changes within the pups that could be causally related to the effects in adulthood are still poorly understood. In the present study, we analyzed the effects of neonatal handling on behavioral (maternal odor preference) and biochemical (cyclic AMP response element-binding protein (CREB) phosphorylation, noradrenaline (NA), and serotonin (5-HT) levels in the olfactory bulb (OB)) parameters in 7-day-old male and female rat pups. Repeated handling (RH) abolished preference for the maternal odor in female pups compared with nonhandled (NH) and the single-handled (SH) ones, while in RH males the preference was not different than NH and SH groups. In both male and female pups, RH decreased NA activity in the OB, but 5-HT activity increased only in males. Since preference for the maternal odor involves the synergic action of NA and 5-HT in the OB, the maintenance of the behavior in RH males could be related to the increased 5-HT activity, in spite of reduction in the NA activity in the OB. RH did not alter CREB phosphorylation in the OB of both male and females compared with NH pups. The repeated handling procedure can affect the behavior of rat pups in response to the maternal odor and biochemical parameters related to the olfactory learning mechanism. Sex differences were already detected in 7-day-old pups. Although the responsiveness of the hypothalamic-pituitary-adrenal axis to stressors is reduced in the neonatal period, environmental interventions may impact behavioral and biochemical mechanisms relevant to the animal at that early age. (C) 2009 IBRO. Published by Elsevier Ltd. All rights reserved.

Nitrogen Metabolism in leaves of a tank epiphytic bromeliad: Characterization of a spatial and functional division

The leaf is considered the most important vegetative organ of tank epiphytic bromeliads due to its ability to absorb and assimilate nutrients. However, little is known about the physiological characteristics of nutrient uptake and assimilation. In order to better understand the mechanisms utilized by some tank epiphytic bromeliads to optimize the nitrogen acquisition and assimilation, a study was proposed to verify the existence of a differential capacity to assimilate nitrogen in different leaf portions. The experiments were conducted using young plants of Vriesea gigantea. A nutrient solution containing NO(3)(-)/NH(4)(+) or urea as the sole nitrogen source was supplied to the tank of these plants and the activities of urease, nitrate reductase (NR), glutamine synthetase (GS) and glutamate dehydrogenase (NADH-GDH) were quantified in apical and basal leaf portions after 1, 3, 6, 9, 12, 24 and 48 h. The endogenous ammonium and urea contents were also analyzed. Independent of the nitrogen sources utilized, NR and urease activities were higher in the basal portions of leaves in all the period analyzed. On the contrary. GS and GDH activities were higher in apical part. It was also observed that the endogenous ammonium and urea had the highest contents detected in the basal region. These results suggest that the basal portion was preferentially involved in nitrate reduction and urea hydrolysis, while the apical region could be the main area responsible for ammonium assimilation through the action of GS and GDH activities. Moreover, it was possible to infer that ammonium may be transported from the base, to the apex of the leaves. In conclusion, it was suggested that a spatial and functional division in nitrogen absorption and NH(4)(+) assimilation between basal and apical leaf areas exists, ensuring that the majority of nitrogen available inside the tank is quickly used by bromeliad`s leaves. (C) 2011 Elsevier GmbH. All rights reserved.

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

CoMFA and CoMSIA 3D QSAR Models for a Series of Cyclic Imides with Analgesic Activity

Three-dimensional quantitative structure-activity relationships (3D-QSAR) were performed for a series of analgesic cyclic imides using the CoMFA and CoMSIA methods. Significant correlation coefficients ( CoMFA, r(2) = 0.95 and q(2) = 0.72; CoMSIA, r(2) = 0.96 and q(2) = 0.76) were obtained, and the generated models were externally validated using test sets. The final QSAR models as well as the information gathered from 3D contour maps should be useful for the design of novel cyclic imides having improved analgesic activity.

Classical and fragment-based hologram structure-activity relationships for a series of analgesic cyclic imides

Cyclic imides have been widely employed in drug design research due to their multiple pharmacological and biological properties. In the present study, two-dimensional quantitative structure-activity relationship (2D QSAR) studies were conducted on a series of potent analgesic cyclic imides using both classical and hologram QSAR (HQSAR) methods, yielding significant statistical models (classical QSAR, q(2) = 0.80; HQSAR, q(2) = 0.84). The models were then used to evaluate an external data test, and the predicted values were in good agreement with the experimental results, indicating their consistency for untested compounds.

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.

On cohomologies and extensions of cyclic groups

Cohomology groups H(s)(Z(n), Z(m)) are studied to describe all groups up to isomorphism which are (central) extensions of the cyclic group Z(n) by the Z(n)-module Z(m). Further, for each such a group the number of non-equivalent extensions is determined. (C) 2011 Elsevier B.V. All rights reserved.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

COMMUTATIVE FINITE-DIMENSIONAL ALGEBRAS SATISFYING x(x(xy))=0 ARE NILPOTENT

We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic not equal 2 is solvable. We prove that every commutative finite-dimensional algebra u over a field F of characteristic not equal 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.