ON NONSYMMETRIC THEOREMS FOR (H, G)-COINCIDENCES

Let X be a compact Hausdorff space, phi: X -> S(n) a continuous map into the n-sphere S(n) that induces a nonzero homomorphism phi*: H(n)(S(n); Z(p)) -> H(n)(X; Z(p)), Y a k-dimensional CW-complex and f: X -> a continuous map. Let G a finite group which acts freely on S`. Suppose that H subset of G is a normal cyclic subgroup of a prime order. In this paper, we define and we estimate the cohomological dimension of the set A(phi)(f, H, G) of (H, G)-coincidence points of f relative to phi.

Effects of Low-Level Laser Therapy on Collagen Expression and Neutrophil Infiltrate in 5-Fluorouracil-Induced Oral Mucositis in Hamsters

Background and Objectives: Several studies have suggested that low-level laser therapy (LLLT) can ameliorate oral mucositis, however, the mechanisms involved are not well understood. The aim of this study was to investigate the mechanisms of action of LLLT on chemotherapy-induced oral mucositis, as related to effects on collagen expression and inflammation Materials and Methods: A hamster cheek pouch model of oral mucositis was used with all animals receiving intraperitoneal 5-fluorouracil, followed by surface irritation. Animals were randomly allocated into three groups, and treated with an InGaAIP diode laser at a wavelength of 660 nm and output power of 35 or 100 mW laser, or no laser Clinical severity of mucositis was assessed at four time-points by a blinded examiner Buccal pouch tissue was harvested from a subgroup of animals in each group at four time-points. Collagen was qualitatively and quantitatively evaluated after picrosinus staining. The density of the neutrophil infiltrate was also scored Results: Peak clinical severity of mucositis was reduced in the 35 mW laser group as compared to the 100 mW and control groups The reduced peak clinical severity of mucositis in the 35 mW laser group was accompanied by a decrease in the number of neutrophils and an increase in the proportion of mature collagen as compared to the other two groups. The total quantity of collagen was significantly higher in the control (no laser) group at the day 11 time-point, as compared to the 35 mW laser group, consistent with a more prolonged inflammatory response in the control group. Conclusion: This study supports two mechanisms of action for LLLT in reducing mucositis severity. The increase in collagen organization in response to the 35 mW laser indicates that LLLT promotes wound healing In addition, LLLT also appears to have an anti-inflammatory effect, as evidenced by the reduction in neutrophil infiltrate Lasers Surg Med 42 546-552, 2010. (C) 2010 Wiley-Liss, Inc.

Cyclooxygenase-2 and vascular endothelial growth factor expression in 5-fluorouracil-induced oral mucositis in hamsters: evaluation of two low-intensity laser protocols

The aim of this study was to investigate the mechanisms whereby low-intensity laser therapy may affect the severity of oral mucositis. A hamster cheek pouch model of oral mucositis was used with all animals receiving intraperitoneal 5-fluorouracil followed by surface irritation. Animals were randomly allocated into three groups and treated with a 35 mW laser, 100 mW laser, or no laser. Clinical severity of mucositis was assessed at four time-points by a blinded examiner. Buccal pouch tissue was harvested from a subgroup of animals in each group at four time-points. This tissue was used for immunohistochemistry for cyclooxygenase-2 (COX-2), vascular endothelial growth factor (VEGF), and factor VIII (marker of microvessel density) and the resulting staining was quantified. Peak severity of mucositis was reduced in the 35 mW laser group as compared to the 100 mW laser and control groups. This reduced peak clinical severity of mucositis in the 35 mW laser group was accompanied by a significantly lower level of COX-2 staining. The 100 mW laser did not have an effect on the severity of clinical mucositis, but was associated with a decrease in VEGF levels at the later time-points, as compared to the other groups. There was no clear relationship of VEGF levels or microvessel density to clinical mucositis severity. The tissue response to laser therapy appears to vary by dose. Low-intensity laser therapy appears to reduce the severity of mucositis, at least in part, by reducing COX-2 levels and associated inhibition of the inflammatory response.

Fermion perturbations in string theory black holes

In this paper we study fermion perturbations in four-dimensional black holes of string theory, obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The Dirac equation for the massless neutrino field, after conformal re-scaling of the metric, is written as a wave equation suitable to study the time evolution of the perturbation. We perform a numerical integration of the evolution equation, and with the aid of Prony fitting of the time-domain profile, we calculate the complex frequencies that dominate the quasinormal ringing stage, and also determine these quantities by the semi-analytical sixth-order WKB method. We also find numerically the decay factor of fermion fields at very late times, and show that the falloff is identical to those showing for massless fields in other four-dimensional black hole spacetimes.

Isolation and characterization of four type 2 ribosome inactivating pulchellin isoforms from Abrus pulchellus seeds

Abrus pulchellus seeds contain at least seven closely related and highly toxic type 2 ribosome-inactivating pulchellins, each consisting of a toxic A-chain linked to a sugar binding B-chain. In the present study, four pulchellin isoforms (termed P I, P II, P III and P IV) were isolated by affinity, ion exchange and chromatofocusing chromatographies, and investigated with respect to toxicity and sugar binding specificity. Half maximal inhibitory concentration and median lethal dose values indicate that P I and P II have similar toxicities and that both are more toxic to cultured HeLa cells and mice than P III and P IV. Interestingly, the secondary structural characteristics and sugar binding properties of the respective pairs of isoforms correlate well with the two toxicity levels, in that P I/P II and P III/P IV form two specific subgroups. From the deduced amino acids sequences of the four isoforms, it is clear that the highest similarity within each subgroup is found to occur within domain 2 of the B-chains, suggesting that the disparity in toxicity levels might be attributed to subtle differences in B-chain-mediated cell surface interactions that precede and determine toxin uptake pathways.

A Single Mutation at the Sheet Switch Region Results in Conformational Changes Favoring lambda 6 Light-Chain Fibrillogenesis

Systemic amyloid light-chain (LC) amyloidosis is a disease process characterized by the pathological deposition of monoclonal LCs in tissue. All LC subtypes are capable of fibril formation although lambda chains, particularly those belonging to the lambda 6 type, are overrepresented. Here, we report the thermodynamic and in vitro fibrillogenic properties of several mutants of the lambda 6 protein 6aJL2 in which Pro7 and/or His8 was substituted by Ser or Pro. The H8P and H8S mutants were almost as stable as the wildtype protein and were poorly fibrillogenic. In contrast, the P7S mutation decreased the thermodynamic stability of 6aJL2 and greatly enhanced its capacity to form amyloid-like fibrils in vitro. The crystal structure of the P7S mutant showed that the substitution induced both local and long-distance effects, such as the rearrangement of the V(L) (variable region of the light chain)-V(L) interface. This mutant crystallized in two orthorhombic polymorphs, P2(1)2(1)2(1) and C222(1). In the latter, a monomer that was not arranged in the typical Bence-Jones dimer was observed for the first time. Crystal-packing analysis of the C222(1) lattice showed the establishment of intermolecular beta-beta interactions that involved the N-terminus and beta-strand B and that these could be relevant in the mechanism of LC fibril formation. Our results strongly suggest that Pro7 is a key residue in the conformation of the N-terminal sheet switch motif and, through long-distance interactions, is also critically involved in the contacts that stabilized the V(L) interface in lambda 6 LCs. (C) 2009 Elsevier Ltd. All rights reserved.

Neopaleozoic striated surfaces in the granitic basement and clast pavement remains of Salto, SP

Near Guarau Ceramic, localized southwest of Salto city in the State of Sao Paulo, two granite outcrops, distant some tens of meters from each other, display Neopaleozoic striated surfaces. These surfaces are in contact with diamictites from the Itarare Subgroup. The striae correspond to sub parallel grooves with millimetric spacing and depth, oriented about N48E and dipping 12 degrees to 42 degrees towards SE. Observed features and association with diamictites indicate an origin by glacial abrasion due to ice movement from southeast towards northwest. About 1.8 km east of Salto, unconsolidated material containing flat-iron-shaped and striated clasts was found on top of granite outcrops, interpreted as clasts pavement remains.

HFD groups in the Solovay model

Hajnal and Juhasz proved that under CH there is a hereditarily separable, hereditarily normal topological group without non-trivial convergent sequences that is countably compact and not Lindelof. The example constructed is a topological subgroup H subset of 2(omega 1) that is an HFD with the following property (P) the projection of H onto every partial product 2(I) for I is an element of vertical bar omega(1)vertical bar(omega) is onto. Any such group has the necessary properties. We prove that if kappa is a cardinal of uncountable cofinality, then in the model obtained by forcing over a model of CH with the measure algebra on 2(kappa), there is an HFD topological group in 2(omega 1) which has property (P). Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

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.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

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.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

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).