COINCIDENCES OF FIBREWISE MAPS BETWEEN SPHERE BUNDLES OVER THE CIRCLE

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles SrM of a Riemannian manifold (M,g) of dim ≥ 3, assuming different variable radius functions r and weighted Sasaki metrics induced by the conformal class of g. New examples are shown of manifolds with constant positive or with constant negative scalar curvature which are not Einstein. Recalling results on the associated almost complex structure I^G and symplectic structure ω^G on the manifold TM , generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds TM and SrM.

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Metallochlorophylls of magnesium, copper and zinc: evaluation of the influence of the first coordination sphere on their solvatochromism and aggregation properties

In this study the role of different metal centers (magnesium, zinc and copper) on the enhancement of the hydrophilic character of metallochlorophylls, was evaluated. The solvatochromism as well as the aggregation process for these compounds in water/ethanol mixtures at different volume ratios were evaluated using Fluorescence, and Resonant Light Scattering (RLS) measurements, aiming to characterize the behavior of these compounds. Independently on the studied metallochlorophyll, the presence of at least 60% of water results in a considerable increase in the fluorescence emission, probably a direct consequence of a lower aggregation of these compounds, which is confirmed by the results from RLS measurements. Additionally, the results suggest that magnesium and zinc chlorophyll should be promising phototherapeutic agents for Photodynamic Therapy.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

On the applicability of the Aris' equivalent sphere in multicomponent reacting systems

The validity of the concept of equivalent sphere introduced by Aris in 1957 to multicomponent reacting systems is investigated in this paper. A network of C6 hydrocarbon reforming reaction and a fixed bed reactor are taken as the model reaction network and the reactor configuration, respectively.

Electrophysiological characteristics of the Marshall bundle in humans

BACKGROUND Marshall bundles (MBs) are the muscle bundles within the ligament of Marshall. OBJECTIVE This trial sought to the electrophysiological characteristics of the MB and the anatomical connections between MB and left atrium (LA) in patients with persistent atrial fibrillation (AF). METHODS We enrolled 72 patients (male: female 59: 13, age 59.9 +/- 9.4 years) who underwent MB mapping and ablation for AF. MB mapping was done via an endocardial or epicardial approach during sinus rhythm and AF. RESULTS Recordings were successful in 64 of 72 patients (89%). A single connection was noted in 11 of 64 patients between the MB and the coronary sinus (CS) muscle sleeves. The MB recordings showed distinct MB potentials with a proximal-to-distal activation pattern during sinus rhythm. During AF, organized passive activations and dissociated slow MB ectopic activities were commonly observed in this type of connection. Double connections to both CS and LA around left pulmonary veins were noted in 23 of 64 patients (36%). After the ablation of the distal connection, MB recording showed typical double potentials as in single connection. Multiple connections were noted in 30 of 64 patients (47%). During sinus rhythm, the earliest activation was in the middle of the MB. The activation patterns were irregular and variable in each patient. During AF, rapid and fractionated complex activations were noted in all patients of this group. CONCLUSION We documented 3 different types of MB-LA connections. Rapid and fractionated activations were most commonly observed in the MB that had multiple LA connections.

The medial forebrain bundle mediates cardiovascular responses to electrical stimulation of the medial prefrontal cortex

The medial prefrontal cortex (MPFC) is involved in cardiovascular control. MPFC electrical stimulation has been reported to cause depressor and bradycardic responses in anesthetized rats. Although the pathway involved is yet unknown, there is evidence indicating the existence of a relay in the lateral hypothalamus (LH). The medial forebrain bundle (MFB) that courses in the lateral portion of the LH carries the vast majority of telencephalic afferent as well efferent projections, including those from the MPFC. To evaluate if the hypotensive pathway originating in the MPFC courses the MFB, we studied the effect of coronal or sagittal knife cuts through the LH and other brain areas on the cardiovascular responses to MPFC electrical stimulation. Knife cuts were performed using blades I to 6 mm wide. Results indicate that the neural pathway descending from the MFB decussates early in the vicinity of MPFC, crossing the midline within the corpus callosurn and yielding two descending pathways that travel rostro-caudally in the lateral portion of the LH, within the MFB. The decussation was confirmed by histological analysis of brain sections processed after the injection of biotinilated dextran amine in the site of the stimulation in the MPFC. Because knife cuts through the LH ipsilateral had minimal effects on the cardiovascular responses and knife cuts performed contralateral to the stimulated MPFC had no effect on the response to MPFC stimulation, data indicate that the contralateral limb of the pathway may be only activated as an alternative pathway when the ipsilateral pathway is blocked. (c) 2009 Elsevier B.V. All rights reserved.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Evaluation of estrogen neuroprotective effect on nigrostriatal dopaminergic neurons following 6-hydroxydopamine injection into the substantia nigra pars compacta or the medial forebrain bundle

Studies involving estrogen treatment of ovariectomized rats or mice have attributed to this hormone a neuroprotective effect on the substantia nigra pars compacta (SNpc) neurons. We investigated the effect of estradiol replacement in ovariectomized rats on the survival of dopaminergic mesencephalic cell and the integrity of their projections to the striatum after microinjections of 1 mu g of 6-hydroxydopamine (6-OHDA) into the right SNpc or medial forebrain bundle (MFB). Estradiol replacement did not prevent the reduction either in the striatal concentrations of DA and metabolites or in the number of nigrostriatal dopaminergic neurons following lesion with 1 mu g of 6-OHDA into the SNpc. Nevertheless, estradiol treatment reduced the decrease in striatal DA following injection of 1 mu g of 6-OHDA into the MFB. Results suggest therefore that estrogen protect nigrostriatal dopaminergic neurons against a 6-OHDA injury to the MFB but not the SNpc. This may be due to the distinct degree of lesions promoted in these different rat models of Parkinson`s disease.