Enhanced sensitivity for the differential pulse polarographic determination of molybdenum(VI) based on adsorption catalytic current

A differential pulse polarographic (DPP) method based on the adsorption catalytic current in a medium containing chlorate and 8-hydroxyquinoline (oxine) is suggested for the determination of molybdenum(VI). Experimental conditions such as pH and the composition of supporting electrolyte have been optimized to get a linear calibration graph at trace levels of Mo(VI). The sensitivity for molybdenum can be considerably enhanced by this method. The influence of possible interferences on the catalytic current has been investigated. The sensitivity of the method is compared with those obtained for other DPP methods for molybdenum. A detection limit of 1.0 x 10(-8) mol/L has been found.

The Adomian method applied to some extraordinary differential equations

Several ''extraordinary'' differential equations are considered for their solutions via the decomposition method of Adomian. Verifications are made with the solutions obtained by other methods.

TolA mediates the differential detergent resistance pattern between the Salmonella enterica subsp enterica serovars Typhi and Typhimurium

The tol-pal genes are essential for maintaining the outer membrane integrity and detergent resistance in various Gram-negative bacteria, including Salmonella. The role of TolA has been well established for the bile resistance of Salmonella enterica subsp. enterica serovar Typhimurium. We compared the bile resistance pattern between the S. enterica serovars Typhi and Typhimurium and observed that Typhi is more resistant to bile-mediated damage. A closer look revealed a significant difference in the TolA sequence between the two serovars which contributes to the differential detergent resistance. The tolA knockout of both the serovars behaves completely differently in terms of membrane organization and morphology. The role of the Pal proteins and difference in LPS organization between the two serovars were verified and were found to have no direct connection with the altered bile resistance. In normal Luria broth (LB), S. Typhi Delta tolA is filamentous while S. Typhimurium Delta tolA grows as single cells, similar to the wildtype. In low osmolarity LB, however, S. Typhimurium Delta tolA started chaining and S. Typhi Delta tolA showed no growth. Further investigation revealed that the chaining phenomenon observed was the result of failure of the outer membrane to separate in the dividing cells. Taken together, the results substantiate the evolution of a shorter TolA in S. Typhi to counteract high bile concentrations, at the cost of lower osmotic tolerance.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Total peroxidase activity and peroxidase isoforms as modified by salt stress in two cultivars of fox-tail millet with differential salt tolerance

The effect of NaCl on total peroxidase activity, induction of isoperoxidases and lipid peroxidation in 5-day-old seedlings of two contrasting genotypes of Setaria italica L. (Prasad, a salt tolerant cultivar and Lepakshi, a salt susceptible cultivar), was studied. Total peroxidase activity increased under NaCl salinity and the degree of elevation in the activity was salt concentration dependent. Nevertheless, a greater activity was recorded in the tolerant cultivar (cv Prasad) compared to the susceptible (cv Lepakshi) one in all days of sampling. Further, the pattern of isoperoxidases was modified during stress conditions as evident from the electrophoregrams. Although, five acidic isoforms were detected in both cultivars, differences were found between the cultivars. Furthermore, it was observed that acidic isoperoxidases were strongly expressed and an acidic isoperoxidase, A(3p) (27 kDa) is specifically found in the tolerant cultivar (cv Prasad) under NaCl stress. This isoform was partially purified and found to be thermostable with pr 5.5 and the optimum pH 7.4. A close correlation exists between the rate of lipid peroxidation in terms of malonaldehyde (MDA) content and total peroxidase activity per gram fresh weight with salt tolerance of the two cultivars. The tolerant cultivar (cv Prasad) had low MDA content and high total peroxidase activity than the susceptible variety (cv Lepakshi) during salinity stress. (C) 1999 Published by Elsevier Science Ireland Ltd. All rights reserved.

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.

Helical structures: The geometry of protein helices and nanotubes

In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A helical structure is thus generated by the repeated action of a screw transformation acting on a subunit. A plane hexagonal lattice wrapped round a cylinder provides a useful starting point for describing the helical conformations of protein molecules, for investigating the geometrical properties of carbon nanotubes, and for certain types of dense packings of equal spheres.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

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.

Encapsulation of cobalt phthalocyanine in zeolite-Y: Evidence for nonplanar geometry

Cobalt (11) phthalocyanine (CoPc) molecules have been encapsulated within the supercage of zeolite-Y. The square-planar complex, being larger than the almost spherical cage, is forced to adopt a distorted geometry on encapsulation. A comparative spectroscopic and magnetic investigation of CoPc encapsulated in zeolite-Y and in the unencapsulated state is reported. These results supported by molecular modeling have been used to understand the nature and extent of the loss of planarity of CoPc on encapsulation. The encapsulated molecule is shown to be the trans-diprotonated species in which the center of inversion is lost due to distortions required to accommodate the square complex within the zeolite. Encapsulation also leads to an enhancement of the magnetic moment of the CoPc. This is shown to be a consequence of the nonplanar geometry of the encapsulated molecule resulting in an excited high-spin state being thermally accessible.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.