Real Theta Characteristics And Automorphisms Of A Real Curve

Let X be a geometrically irreductble smooth projective cruve defined over R. of genus at least 2. that admits a nontrivial automorphism, sigma. Assume that X does not have any real points. Let tau be the antiholomorphic involution of the complexification lambda(C) of X. We show that if the action of sigma on the set S(X) of all real theta characteristics of X is trivial. then the order of sigma is even, say 2k and the automorphism tau o (sigma) over cap (lambda) of X-C has a fixed point, where (sigma) over cap is the automorphism of X x C-R defined by sigma We then show that there exists X with a real point and admitting a nontrivial automorphism sigma, such that the action of sigma on S(X) is trivial, while X/ not equal P-R(1) We also give an example of X with no real points and admitting a nontrivial automorphisim sigma such that the automorphism tau o (sigma) over cap (lambda) has a fixed point, the action of sigma on S(X) is trivial, and X/ not equal P-R(1)

Disulfide conformation and design at helix N-termini

To understand structural and thermodynamic features of disulfides within an alpha-helix, a non-redundant dataset comprising of 5025 polypeptide chains containing 2311 disulfides was examined. Thirty-five examples were found of intrahelical disulfides involving a CXXC motif between the N-Cap and third helical positions. GLY and PRO were the most common amino acids at positions 1 and 2, respectively. The N-Cap residue for disulfide bonded CXXC motifs had average values of (-112 +/- 25.2 degrees, 106 +/- 25.4 degrees). To further explore conformational requirements for intrahelical disulfides, CYS pairs were introduced at positions N-Cap-3; 1,4; 7,10 in two helices of an Escherichia coli thioredoxin mutant lacking its active site disulfide (nSS Trx). In both helices, disulfides formed spontaneously during purification only at positions N-Cap-3. Mutant stabilities were characterized by chemical denaturation studies (in both oxidized and reduced states) and differential scanning calorimetry (oxidized state only). All oxidized as well as reduced mutants were destabilized relative to nSS Trx. All mutants were redox active, but showed decreased activity relative to wild-type thioredoxin. Such engineered disulfides can be used to probe helix start sites in proteins of unknown structure and to introduce redox activity into proteins. Conversely, a protein with CYS residues at positions N-Cap and 3 of an alpha-helix is likely to have redox activity.

Conformational characteristics of asparaginyl residues in proteins

Backbone conformations at 1064 asparaginyl residues in 123 non-homologous, high-resolution X-ray structures of proteins were analysed. Asn adopts conformations in left-handed x-helical region and other partially allowed regions in the Ramachandran map more readily than any other non-glycyl residue. Asn conformational clusters in the (phi,psi) regions of left-handed alpha-helix, right-handed alpha-helix and extended (beta) strands were investigated in detail for their occurrence in various secondary structures, especially in beta-turn regions. Preferences were observed for Asn conformations in different positions in various beta-turn types, including the first and fourth positions of the turn. Asparaginyl residues with extended conformations are found to occur frequently in irregular regions, although they are expected to occur predominantly in extended strands or in the third position of type II beta-turns. Asn conformations at the N-cap positions of helices strongly prefer extended conformation than alpha(L), which seems to be characteristic of non-glycyl residues at that position. In the linkers connecting two extended strands and those connecting an alpha-helix and an extended strand, Asn with alpha(L) or alpha(R) conformation is more favoured than Asn with the beta-conformation. Analysis of Asn-Asn doublets and Asn-X-Asn triplets permitted identification of conformational families in such sequences. Results of this investigation provide useful hints in modelling Asn-rich regions in proteins such as malaria parasite coat protein. (C) Munksgaard 1994.

Studies in bubble formation — III

Bubble formation from single horizontal orifices submerged in Newtonian liquids has been investigated for such chamber volumes that both the pressure inside the chamber and flow rate into the bubble are time dependent. The data collected show that under these conditions the bubble volume decreases exponentially with increase in orifice submergence. The equations for the generalized two stage model of bubble formation, taking the variation of gas flow rate with time into account, have been derived. These equations reduce to the cases of constant gas flow rate and constant pressure when adequate constraints are imposed. The results obtained under intermediate conditions have been quantitatively explained on the basis of these equations.

Studies in bubble formation—II bubble formation under constant pressure conditions

Bubble formation under constant pressure conditions has been investigated for wide range of variation of liquid properties.Air bubbles were formed from single horizontal orifices submerged in liquids whose viscosity varied from 1·0 to 600 cPs and surface tension from 37 to 72 dyn/cm. Air flow rate was varied from 2 to 250 cm3/sec and the orifice diameter from 0·0515 to 0·4050 cm.

Anthranilic acid hydroxylase from Aspergillus niger

The in vivo conversion of radioactive tryptophan to anthranilic acid and 2,3-dihydroxybenzoic acid by submerged cultures of Claviceps paspali was shown by Groeger and his co-workers (1965). More recently, Subba Rao et al. (1967a) reported that washed mycelial felts of Aspergillus niger incorporate the radioactivity from DL-tryptophan-C14 (benzene ring-labeled) into anthranilic acid, 3-hydroxyanthranilic acid, 2,3-dihydroxybenzoic acid and catechol. However, the conversion of anthranilic acid to 2,3-dihydroxybenzoic acid by cell-free preparations has not been demonstrated. In the present paper we report the demonstration of a soluble anthranilic acid hydroxylase from Aspergillus niger which is different from the anthranilic acid hydroxylases reported so far from microbes and higher plants.

Studies in bubble formation - IV: bubble formation at porous discs

Bubble formation from porous discs submerged in liquids of different physical properties has been investigated. It is found the number of sites effective for bubble formation is much smaller than the total potentially available sites. The number of effective sites is found to be a function of the surface tension, viscosity, and density of the liquid and the gas flow rate through the disc. A model proposed on the basis of bubble formation from an isolated nozzle and the close packed arrangement of the formed bubbles, explains the phenomenon adequately. © 1970.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

A unified approach to bubble and drop formation

An approach, starting with the bubble formation model of Khurana and Khumar, has been presented, which is found to be reasonably applicable to the formation of both bubbles and drops from single submerged nozzles. The model treats both the phenomena jointly as the formation of a dispersed phase entity resulting from injection, whose size depends upon operating parameters and physical properties.

A Note on Diffraction of Water Waves by a Nearly Vertical Barrier

A simplified perturbational analysis is employed, together with the application of Green's theorem, to determine the first-order corrections to the reflection and transmission coefficients in the problem of diffraction of surface water waves by a nearly vertical barrier in two basically important cases: (i) when the barrier is partially immersed and (ii) when the barrier is completely submerged. The present analysis produces the desired results fairly easily and relatively quickly as compared with the known integral equation approach to this class of diffraction problems.

Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs

Let G - (V, E) be a weighted undirected graph having nonnegative edge weights. An estimate (delta) over cap (u, v) of the actual distance d( u, v) between u, v is an element of V is said to be of stretch t if and only if delta(u, v) <= (delta) over cap (u, v) <= t . delta(u, v). Computing all-pairs small stretch distances efficiently ( both in terms of time and space) is a well-studied problem in graph algorithms. We present a simple, novel, and generic scheme for all-pairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for all-pairs t-stretch distances for a whole range of stretch t, and we also answer an open question posed by Thorup and Zwick in their seminal paper [J. ACM, 52 (2005), pp. 1-24].

Experimental estimation of friction force in lubricated cutting of steel

Friction force generated in lubricated cutting of steel is experimentally estimated by recording the tangential force experienced by the spherical face of a pin rubbing against a freshly cut surface. The pin and the cutting tool are both submerged in the lubricant and the pin is situated on the cut-track to record the force. The recording shows an instantaneous achievement of a peak in the force curve followed by a decline in time to a steady state value. The peak and not the steady state friction was found to be sensitive to the structure of the hydrocarbon and addition of additive to the oil. The configuration was designed and tested to demonstrate the influence of a reaction film which develops during cutting, on cutting tool friction. Given the strong correlation between the peak friction and the existence of a tribofilm in the cutting zone, the configuration is used to determine the lower limit of a cutting speed regime, which marks the initiation of lubricant starvation, in cutting of steel using an emulsion as a cutting fluid. (C) 2010 Elsevier B.V. All rights reserved.

Analysis of transients in a canal network

A generalised formulation of the mathematical model developed for the analysis of transients in a canal network, under subcritical flow, with any realistic combination of control structures and their multiple operations, has been presented. The model accounts for a large variety of control structures such as weirs, gates, notches etc. discharging under different conditions, namely submerged and unsubmerged. A numerical scheme to compute and approximate steady state flow condition as the initial condition has also been presented. The model can handle complex situations that may arise from multiple gate operations. This has been demonstrated with a problem wherein the boundary conditions change from a gate discharge equation to an energy equation and back to a gate discharge equation. In such a situation the wave strikes a fixed gate and leads to large and rapid fluctuations in both discharge and depth.

Heterogeneous nucleation of solidification of cadmium particles embedded in an aluminium matrix

A hypomonotectic alloy of Al-4.5wt%Cd has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. As-melt spun hypomonotectic Al-4.5wt%Cd consists of a homogeneous distribution of faceted 5 to 120 nm diameter cadmium particles embedded in a matrix of aluminium, formed during the monotectic solidification reaction. The cadmium particles exhibit an orientation relationship with the aluminium matrix of {111}Al//{0001}Cd and lang110rangAlAl//lang11¯20> Cd, with four cadmium particle variants depending upon which of the four {111}Al planes is parallel to {0001}Cd. The cadmium particles exibit a distorted cuboctahedral shape, bounded by six curved {100}Al//{20¯23}Cd facets, six curved {111}Al/{40¯43}Cd facets and two flat {111}Al//{0001}Cd facets. The as-melt spun cadmium particle shape is metastable and the cadmium particles equilibrate during heat treatment below the cadmium melting point, becoming elongated to increase the surface area and decrease the separation of the {111}Al//{0001}Cd facets. The equilibrium cadmium particle shape and, therefore, the anisotropy of solid aluminium-solid cadmium and solid aluminium -liquid cadmium surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 420 °C. The anisotropy of solid aluminium-solid cadmium surface energy is constant between room temperature and the cadmium melting point, with the {100}Al//{20¯23}Cd surface energy on average 40% greater than the {111}Al//{0001}Cd surface energy, and 10% greater than the {111}Al//{40¯43Cd surface energy. When the cadmium particles melt at temperatures above 321 °C, the {100}Al//{20¯23}Cd facets disappear and the {111}Al//{40¯43}Cd and {111}A1//{0001}Cd surface energies become equal. The {111}Al facets do not disappear when the cadmium particles melt, and the anisotropy of solid aluminium-liquid cadmium surface energy decreases gradually with increasing temperature above the cadmium melting point. The kinetics of cadmium solidification have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Cadmium particle solidification is nucleated catalytically by the surrounding aluminium matrix on the {111}Al faceted surfaces, with an undercooling of 56 K and a contact angle of 42 °. The nucleation kinetics of cadmium particle solidification are in good agreement with the hemispherical cap model of heterogeneous nucleation.