On maximizing measures of homeomorphisms on compact manifolds

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g : X -> R, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral integral(X) g d mu, considered as a function on the space of all T-invariant Borel probability measures mu, attains its maximum on a measure supported on a periodic orbit.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Immobilized analogues of sunflower trypsin inhibitor-1 constitute a versatile group of affinity sorbents for selective isolation of serine proteases

Sunflower trypsin inhibitor-1 (SFI-1), a natural 14-residue cyclic peptide, and some of its synthetic acyclic variants are potent protease inhibitors displaying peculiar inhibitory profiles. Here we describe the synthesis and use of affinity sorbents prepared by coupling SFTI-1 analogues to agarose resin. Chymotrypsinand trypsin-like proteases could then be selectively isolated from pancreatin; similarly, other proteases were obtained from distinct biological sources. The binding capacity of [Lys5]-SFTI-1-agarose for trypsin was estimated at over 10 mg/mL of packed gel. SFTI-1-based resins could find application either to improve the performance of current purification protocols or as novel protease-discovery tools in different areas of biological investigation. (C) 2009 Elsevier B.V. All rights reserved.

Paleomagnetism of the Santa Fe Group, central Brazil: Implications for the late Paleozoic apparent polar wander path for South America

Paleomagnetic and rockmagnetic data are reported for the Floresta Formation (Santa Fe Group) of the Sanfranciscana Basin, central Brazil. This formation represents the Permo-Carboniferous glacial record of the basin and comprises the Brocoto (diamictites and flow diamictites), Brejo do Arroz (red sandstones and shales with dropstones and invertebrate trails), and Lavado (red sandstones) members, which crop out near the cities of Santa Fe de Minas and Canabrava, Minas Gerais State. Both Brejo do Arroz and Lavado members were sampled in the vicinities of the two localities. Alternating field and thermal demagnetizations of 268 samples from 76 sites revealed reversed components of magnetization in all samples in accordance with the Permo-Carboniferous Reversed Superchron. The magnetic carriers are magnetite and hematite with both minerals exhibiting the same magnetization component, suggesting a primary origin for the remanence. We use the high-quality paleomagnetic pole for the Santa Fe Group (330.9 degrees E 65.7 degrees S; N = 60; alpha(95) = 4.1 degrees; k = 21) in a revised late Carboniferous to early Triassic apparent polar wander path for South America. On the basis of this result it is shown that an early Permian Pangea A-type fit is possible if better determined paleomagnetic poles become available.

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.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

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.