Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

Effect of substitution of Y on the structural, magnetic, and thermal properties of hexagonal DyMnO3 single crystals

We investigate the structural, magnetic, and specific heat behavior of the hexagonal manganite Dy0.5Y0.5MnO3 in order to understand the effect of dilution of Dy magnetism with nonmagnetic yttrium. In this compound, the triangular Mn lattice orders antiferromagnetic at T-N(Mn) approximate to 68 K observed experimentally in the derivative of magnetic susceptibility as well as in specific heat. In addition, a low-temperature peak at T-N(Dy) similar to 3 K is observed in specific heat which is attributed to rare earth order. The T-N(Mn) increases by 9 K compared to that of hexagonal (h) DyMnO3 while T-N(Dy) is unchanged. A change in slope of thermal evolution of lattice parameters is observed to occur at temperature close to T-N(Mn). This hints at strong magnetoelastic coupling in this geometric multiferroic. In magnetization measurements, steplike features are observed when the magnetic field is applied along the c axis which shift to higher fields with temperature and vanish completely above 40 K. The presence of different magnetic phases at low temperature and strong magnetoelastic effects can lead to such field-induced transitions which resemble metamagnetic transitions. This indicates the possibility of strong field-induced effects in dielectric properties of this material, which is unexplored to date.

Analysis of geometric and strain effects in homo-Diels-Alder reactions

Molecular mechanics calculations have been carried out to quantify the key geometric and strain effects which are likely to control the homo-Diels-Alder reactivity of 1,4-dienes. The criteria considered include C1..C5 and C2..C4 distances in the diene, twist angle of the two pi units, and the magnitude of strain increase as a result of cycloaddition. By first considering these factors in a number of non-conjugated dienes with known reactivity, the ranges of values within which the reaction is favoured are proposed. Calculations are also reported on several substrates which have not been investigated so far. Promising systems for experimental study are suggested which, in addition to being intrinsically interesting, would place the present proposals on a firm basis.

Line clipping revisited: Two efficient algorithms based on simple geometric observations

Two new line clipping algorithms, the opposite-corner algorithm and the perpendicular-distance algorithm, that are based on simple geometric observations are presented. These algorithms do not require computation of outcodes nor do they depend on the parametric representations of the lines. It is shown that the opposite-corner algorithm perform consistently better than an algorithm due to Nicholl, Lee, and Nicholl which is claimed to be better than the classic algorithm due to Cohen-Sutherland and the more recent Liang-Barsky algorithm. The pseudo-code of the opposite-corner algorithm is provided in the Appendix.

Preparation of a soluble 58kDa-3-hydroxy-3-methylglutaryl CoA reductase from liver microsomes and its inhibition by ethoxysilatrane, a hypocholesterolemic compound

On repeated thawing at room temperature of frozen preparations of heavy microsomes from rat livers, HMGCoA reductase activity was solubilized due to limited proteolysis. This soluble enzyme was partially purified by fractionation with ammonium sulfate and filtration on Sephacryl S-200 column. The active enzyme was coeluted with a major 92 kDa-protein and was identified as a 58kDa-protein after separation by SDS-PAGE and immunoblotting. Ethoxysilatrane, a hypocholesterolemic compound, which decreased the liver-microsomal activity of HMGCoA reductase on intra-peritonial treatment of animals, showed little effect on the enzyme activity with isolated microsomes or the 50kDa-soluble enzyme when added in the assay. But it was able to inhibit the activity of the soluble 58kDa-enzyme in a concentration-dependent, reversible manner. Cholesterol and an oxycholesterol were without effect whereas chlorophenoxyisobutyrate and ubiquinone showed small inhibition under these conditions. The extra region that links the active site domain (50kDa protein) to the membrane, present in the 58kDa-protein appears to be involved in mediating the inhibition by silatrane.

On some geometric invariants associated to the space of flat connections on an open space

A geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

Effect of Constant and Cyclic Current Stressing on the Evolution of Intermetallic Compound Layers

In this paper the effects of constant and cyclic power loads on the evolution of interfacial reaction layers in lead-free solder interconnections are presented. Firstly, the differences in the growth behavior of intermetallic compound (IMC) layers at the cathode and anode sides of the interconnections are rationalized. This is done by considering the changes in the intrinsic fluxes of elements owing to electromigration as well as taking into account the fact that the growth of Cu3Sn and Cu6Sn5 are coupled via interfacial reactions. In this way, better understanding of the effect of electron flux on the growth of each individual layer in the Cu-Sn system can be achieved. Secondly, it is shown that there is a distinct difference between steady-state current stressing (constant current, constant temperature) and power cycling with alternating on- and off-cycle periods (accompanied by a change of temperature). The reasons behind the observed differences are subsequently discussed. Finally, special care is taken to ensure that the current densities are chosen in such a way that there is no risk for even partial melting of the solder interconnections.

A natural compound, methyl angolensate, induces mitochondrial pathway of apoptosis in Daudi cells

Natural products discovered from medicinal plants have played an important role in the treatment of cancer. In an effort to identify novel small molecules which can affect the proliferation of lymphoma cells, we tested methyl angolensate (MA), a plant derived tetranortriterpenoid, purified from the crude extract of the root callus of Soymida febrifuga commonly known as Indian red wood tree. We have tested MA for its cytotoxic properties on Burkitt's lymphoma cell lines, using various cellular assays. We observed that MA induces cytotoxicity in Daudi cells in a dose-dependent manner using trypan blue, MTT and LDH assays. We find that the treatment with MA led to activation of DNA double-strand break repair proteins including KU70 and KU80, suggesting the activation of nonhomologous DNA end joining pathway in surviving cells. Further, we find that methyl angolensate could induce apoptosis by cell cycle analysis, annexin V-FITC staining, DNA fragmentation and PARP cleavage. Besides, MA treatment led to reactive oxygen species generation and loss of mitochondrial transmembrane potential. These results suggest the activation of mitochondrial pathway of apoptosis. Hence, we identify MA as a potential chemotherapeutic agent against Daudi cells.

Structural instability of the charge ordered compound Nd0.5Sr0.5MnO3 under a magnetic field

We report an anomalous magnetostriction behavior of the charge ordered compound Nd0.5Sr0.5MnO3. We have found that the applied magnetic field not only gives rise to a large negative magnetoresistance but also produces a huge positive magnetovolume effect. This unusual effect is explained considering that the applied magnetic field induces a structural transition at which the volume drastically increases. This effect is also seen in the anisotropic magnetostriction which shows clear anomalies at the field induced transition.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Direct and sensitized (energy and electron transfer) geometric isomerization of stilbene within zeolites: a comparison between solution and zeolite as reaction media

The trans- and cis-stilbenes upon inclusion in NaY zeolite are thermally stable. Direct excitation and triplet sensitization results in geometric isomerization and the excited state behavior under these conditions are similar to that in solution. Upon direct excitation, a photostationary state consisting of 65% cis and 35% trans isomers is established. Triplet sensitization with 2-acetonaphthone gave a photostationary state consisting of 63% cis and 37% trans isomers. These numbers are similar to the ones obtained in solution. Thus, the presence of cations and the confined space within the zeolite have very little influence on the overall chemistry during direct and triplet sensitization. However, upon electron transfer sensitization with N-methylacridinium (NMA) as the sensitizer within NaY, isomerization from cis-stilbene radical cation to trans-stilbene occurs and the recombination of radical ions results in triplet stilbene. Prolonged irradiation gave a photostationary state (65% cis and 35% trans) similar to triplet sensitization. This behavior is unique to the zeolite and does not take place in solution. Steady state fluorescence measurements showed that the majority of stilbene molecules are close to the N-methylacridinium sensitizer. Diffuse reflectance flash photolysis studies established that independent of the isomer being sensitized only trans radical cation is formed. Triplet stilbene is believed to be generated via recombination of stilbene radical cation and sensitizer radical anion. One should be careful in using acidic HY zeolite as a medium for photoisomerization of stilbenes. In our hands, in these acidic zeolites isomerization dominated the photoisomerization. (C) 2002 Elsevier Science B.V. All rights reserved.

Light-induced geometric isomerization of 1,2-diphenylcyclopropanes included within Y zeolites: Role of cation-guest binding

Through a systematic study of several diphenylcyclopropane derivatives, we have inferred that the cations present within a zeolite control the excited-state chemistry of these systems. In the parent 1,2-diphenylcylopropane, the cation binds to the two phenyl rings in a sandwich-type arrangement, and such a mode of binding prevents cis-to-trans isomerization. Once an ester or amide group is introduced into the system (derivatives of 2beta,3beta-diphenylcyclopropane-1alpha-carboxylic acid), the cation binds to the carbonyl group present in these chromophores and such a binding has no influence on the cis-trans isomerization process. Cation-reactant structures computed at density functional theory level have been very valuable in rationalizing the observed photochemical behavior of diphenylcyclopropane derivatives included in zeolites. While the parent system, 1,2-diphenyleylopropane, has been extensively investigated in the context of chiral induction in solution, owing to its failure to isomerize from cis to trans, the same could not be investigated in zeolites. However, esters of 2beta,3beta-diphenylcyclopropane-1alpha-carboxylic acid could be studied within zeolites in the context of chiral induction. Chiral induction as high 20% ee and 55% de has been obtained with selected systems. These numbers, although low, are much higher than what has been obtained in solution with the same system or with the parent system by other investigators (maximum similar to10% ee).

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.