The local polynomial hull near a degenerate CR singularity: Bishop discs revisited

Let be a smooth real surface in and let be a point at which the tangent plane is a complex line. How does one determine whether or not is locally polynomially convex at such a p-i.e. at a CR singularity? Even when the order of contact of with at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study non-parabolic CR singularities. We show that the presence or absence of Bishop discs around certain non-parabolic CR singularities is completely determined by a Maslov-type index. This result subsumes all known facts about Bishop discs around order-two, non-parabolic CR singularities. Sufficient conditions for Bishop discs have earlier been investigated at CR singularities having high order of contact with . These results relied upon a subharmonicity condition, which fails in many simple cases. Hence, we look beyond potential theory and refine certain ideas going back to Bishop.

AIWIN - A fast and jigless inspection technique for machined parts

Precision inspection of manufactured components having multiple complex surfaces and variable tolerance definition is an involved, complex and time-consuming function. In routine practice, a jig is used to present the part in a known reference frame to carry out the inspection process. Jigs involve both time and cost in their development, manufacture and use. This paper describes 'as is where is inspection' (AIWIN), a new automated inspection technique that accelerates the inspection process by carrying out a fast registration procedure and establishing a quick correspondence between the part to inspect and its CAD geometry. The main challenge in doing away with a jig is that the inspection reference frame could be far removed from the CAD frame. Traditional techniques based on iterative closest point (ICP) or Newton methods require either a large number of iterations for convergence or fail in such a situation. A two-step coarse registration process is proposed to provide a good initial guess for a modified ICP algorithm developed earlier (Ravishankar et al., Int J Adv Manuf Technol 46(1-4):227-236, 2010). The first step uses a calibrated sphere for local hard registration and fixing the translation error. This transformation locates the centre for the sphere in the CAD frame. In the second step, the inverse transformation (involving pure rotation about multiple axes) required to align the inspection points measured on the manufactured part with the CAD point dataset of the model is determined and enforced. This completes the coarse registration enabling fast convergence of the modified ICP algorithm. The new technique has been implemented on complex freeform machined components and the inspection results clearly show that the process is precise and reliable with rapid convergence. © 2011 Springer-Verlag London Limited.

Cis-trans peptide variations in structurally similar proteins

The presence of energetically less favourable cis peptides in protein structures has been observed to be strongly associated with its structural integrity and function. Inter-conversion between the cis and trans conformations also has an important role in the folding process. In this study, we analyse the extent of conservation of cis peptides among similar folds. We look at both the amino acid preferences and local structural changes associated with such variations. Nearly 34% of the Xaa-Proline cis bonds are not conserved in structural relatives; Proline also has a high tendency to get replaced by another amino acid in the trans conformer. At both positions bounding the peptide bond, Glycine has a higher tendency to lose the cis conformation. The cis conformation of more than 30% of beta turns of type VIb and IV are not found to be conserved in similar structures. A different view using Protein Block-based description of backbone conformation, suggests that many of the local conformational changes are highly different from the general local structural variations observed among structurally similar proteins. Changes between cis and trans conformations are found to be associated with the evolution of new functions facilitated by local structural changes. This is most frequent in enzymes where new catalytic activity emerges with local changes in the active site. Cis-trans changes are also seen to facilitate inter-domain and inter-protein interactions. As in the case of folding, cis-trans conversions have been used as an important driving factor in evolution.

H-1, C-13, N-15 assignment and secondary structure determination of glutamine amido transferase subunit of gaunosine monophosphate synthetase from Methanocaldococcus jannaschii

Sequence specific resonance assignments have been obtained for H-1, C-13 and N-15 nuclei of the 21 kDa (188 residues long) glutamine amido transferase subunit of guanosine monophosphate synthetase from Methanocaldococcus jannaschii. From an analysis of H-1 and C-13(alpha), C-13(beta) secondary chemical shifts, (3) JH(N)H(alpha) scalar coupling constants and sequential, short and medium range H-1-H-1 NOEs, it was deduced that the glutamine amido transferase subunit has eleven strands and five helices as the major secondary structural elements in its tertiary structure.

Albedo enhancement over land to counteract global warming: impacts on hydrological cycle

A recent modelling study has shown that precipitation and runoff over land would increase when the reflectivity of marine clouds is increased to counter global warming. This implies that large scale albedo enhancement over land could lead to a decrease in runoff over land. In this study, we perform simulations using NCAR CAM3.1 that have implications for Solar Radiation Management geoengineering schemes that increase the albedo over land. We find that an increase in reflectivity over land that mitigates the global mean warming from a doubling of CO2 leads to a large residual warming in the southern hemisphere and cooling in the northern hemisphere since most of the land is located in northern hemisphere. Precipitation and runoff over land decrease by 13.4 and 22.3%, respectively, because of a large residual sinking motion over land triggered by albedo enhancement over land. Soil water content also declines when albedo over land is enhanced. The simulated magnitude of hydrological changes over land are much larger when compared to changes over oceans in the recent marine cloud albedo enhancement study since the radiative forcing over land needed (-8.2 W m(-2)) to counter global mean radiative forcing from a doubling of CO2 (3.3 W m(-2)) is approximately twice the forcing needed over the oceans (-4.2 W m(-2)). Our results imply that albedo enhancement over oceans produce climates closer to the unperturbed climate state than do albedo changes on land when the consequences on land hydrology are considered. Our study also has important implications for any intentional or unintentional large scale changes in land surface albedo such as deforestation/afforestation/reforestation, air pollution, and desert and urban albedo modification.

2,3-Unsaturated enoses. A Pummerer rearrangement route to sugar vinyl sulfides and synthesis of 3-deoxy-3-alkyl/arylsulfinyl pyranosides

A Pummerer rearrangement of 2,3-dideoxy-3-alkyl/arylsulfinyl-arabino-hexopyranosides is reported. Treatment of sulfinyl-arabino-hexopyranoside derivatives, obtained through oxidation of the corresponding thio-derivatives, with trifluoroacetic anhydride (TFAA)/pyridine led to a facile formation of 2,3-dideoxy-3-alkyl/arylthio-hex-2-enopyranosides. Upon conversion of sugar vinyl sulfides to vinyl sulfoxides, conjugate addition reactions were conducted with alkoxides, to afford 3-deoxy-3-alkyl/arylsulfinyl pyranosides, in the manno-configuration exclusively. Whereas the conjugate addition reaction did not proceed with ether protecting groups, ester protecting groups and free hydroxyl groups in the sugar vinyl sulfoxide permitted the reaction. (C) 2012 Elsevier Ltd. All rights reserved.

Comparison of rhodamine B degradation under UV irradiation by two phases of titania nano-photocatalyst

Titania (TiO2) nano-photocatalysts, with different phases, prepared using a modified sol-gel process were employed in the degradation of rhodamine at 10 mg L-1 concentration. The degradation efficiency of these nano-photocatalysts was compared to that of commercial Degussa P25 titania. It was found that the nanocatalysts calcined at 450 degrees C and the Degussa P25 titania had similar photoreactivity profiles. The commercial Degussa P25 nanocatalysts had an overall high apparent rate constant of (K-app) of 0.023 min(-1). The other nanocatalyst had the following rate constants: 0.017, 0.0089, 0.003 and 0.0024 min(-1) for 450, 500, 550 and 600 degrees C calcined catalysts, respectively. This could be attributed to the phase of the titania as the anatase phase is highly photoactive than the other phases. Furthermore, characterisation by differential scanning calorimetry showed the transformation of titania from amorphous to anatase and finally to rutile phase. SEM and TEM characterisations were used to study the surface morphology and internal structure of the nanoparticles. BET results show that as the temperature of calcinations was raised, the surface area reduced marginally. X-ray diffraction was used to confirm the different phases of titania. This study has led to a conclusion that the anatase phase of the titania is the most photoactive nanocatalyst. It also had the highest apparent rate constant of 0.017 min(-1), which is similar to that of the commercial titania.

Variation of Snowline and Mass Balance of Glaciers of Warwan and Bhut Basins of Western Himalaya Using Remote Sensing Technique

Glaciers are natural reservoirs of fresh water in frozen state and sensitive indicators of climate change. Among all the mountainous glaciated regions, glaciers of Himalayas form one of the largest concentrations of ice outside the Polar Regions. Almost all the major rivers of northern India originate from these glaciers and sustain perennial flow. Therefore, in view of the importance and role of the glaciers in sustaining the life on the Earth, monitoring the health of glaciers is necessary. Glacier's health is monitored in two ways (i) by mapping the change in extent of glaciers (ii) by finding variation in the annual mass balance. This paper has been discussed the later approach for monitoring the health of glaciers of Warwan and Bhut basins. Mass balance of glaciers of these two basins was determined based on the extraction of snow line at the end of ablation season. A series of satellite images of AWiFS sensor were analysed for extraction of snowline on the glaciers for the period of 2005, 2006 and 2007. The snow line at the end of ablation season is used to compute accumulation area ratio (AAR = Accumulation area/Glacier area) for each glacier of basins. An approach based on relationship of AAR to specific mass balance (computed in field) for glaciers of Basapa basin was employed in the present study. Mean of specific mass balance of individual glacier for the year 2005, 2006 and 2007 of Warwan basin was found to be -ve 0.19 m, -ve 0.27 m and -ve 0.2 m respectively. It is 0.05 m, -ve 0.11 m and -ve 0.19 m for Bhut basin. The analysis suggests a loss of 4.3 and 0.83 kmA(3) of glacier in the monitoring period of 3 years for Warwan and Bhut basins respectively. The overall results suggest that the glaciers of Warwan basin and Bhut basins have suffered more loss of ice than gain in the monitoring period of 3 years.

Cubicity and Bandwidth

A unit cube in (or a k-cube in short) is defined as the Cartesian product R (1) x R (2) x ... x R (k) where R (i) (for 1 a parts per thousand currency sign i a parts per thousand currency sign k) is a closed interval of the form a (i) , a (i) + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G is the minimum k such that G has a k-cube representation. From a geometric embedding point of view, a k-cube representation of G = (V, E) yields an embedding such that for any two vertices u and v, ||f(u) - f(v)||(a) a parts per thousand currency sign 1 if and only if . We first present a randomized algorithm that constructs the cube representation of any graph on n vertices with maximum degree Delta in O(Delta ln n) dimensions. This algorithm is then derandomized to obtain a polynomial time deterministic algorithm that also produces the cube representation of the input graph in the same number of dimensions. The bandwidth ordering of the graph is studied next and it is shown that our algorithm can be improved to produce a cube representation of the input graph G in O(Delta ln b) dimensions, where b is the bandwidth of G, given a bandwidth ordering of G. Note that b a parts per thousand currency sign n and b is much smaller than n for many well-known graph classes. Another upper bound of b + 1 on the cubicity of any graph with bandwidth b is also shown. Together, these results imply that for any graph G with maximum degree Delta and bandwidth b, the cubicity is O(min{b, Delta ln b}). The upper bound of b + 1 is used to derive upper bounds for the cubicity of circular-arc graphs, cocomparability graphs and AT-free graphs in terms of the maximum degree Delta.

Spectral analysis on SL(2, R)

Let G be the group . For this group we prove a version of Schwartz's theorem on spectral analysis for the group G. We find the sharp range of Lebesgue spaces L (p) (G) for which a smooth function is not mean periodic unless it is a cusp form. Failure of the Schwartz-like theorem is also proved when C (a)(G) is replaced by L (p) (G) with suitable p. We show that the last result is linked with the failure of the Wiener-tauberian theorem for G.

Studies on lithium L-ascorbate dihydrate: An interesting chiral nonlinear optical crystal

Lithium L-Ascorbate dihydrate (LLA) is a new metal organic nonlinear optical crystal belonging to the saccharide family. Single crystals of LLA were grown from aqueous solution. Solubility of the crystal has a positive temperature coefficient facilitating growth by slow cooling. Rietveld refinement was used to confirm the phase formation. The crystal has prismatic habit with (010), (001) and (10-1) prominent faces. Thermal analysis shows that the crystal is stable up to 102 degrees C. Transmission spectrum of the crystal extends from 302 nm to 1600 nm. Dielectric spectroscopic analysis revealed Cole Cole behaviour and prominent piezoelectric resonance peaks were observed in the range of 100-200 kHz. Second harmonic generation (SHG) conversion efficiency of up to 2.56 times that of a phase matched KDP crystal was achieved when the (010) plate of LLA single crystal was rotated about the +ve c axis, by 9.4 degrees in the clockwise direction. We also observed SHG conical sections which were attributed to noncollinear phase matching. The observation of the third conical section suggests very high birefringence and large nonlinear coefficients. A detailed study of surface laser damage showed that the crystal has high multiple damage thresholds of 9.7 GW cm(-2) and 42 GW cm(-2) at 1064 nm and 532 nm radiation respectively. (C) 2012 Elsevier B.V. All rights reserved.

Influence of nature of support on the catalytic activity of supported molybdenum-oxo species in benzyl alcohol conversion

Supported catalysts containing 15 wt.% of molybdenum have been prepared by the incipient wetness impregnation method. CaO, MgO, Al2O3, Zr(OH)4 and Al(OH)3 have been used as supports for the preparation of supported Mo catalysts. Characterisation of all the materials prepared has been carried out through BET surface area measurement, X-ray diffractometry and FT-IR spectroscopy. Catalytic activity measurements have been carried out with reference to structure-sensitive benzyl alcohol conversion in the liquid phase. The percentage conversion of benzyl alcohol to benzaldehyde and toluene varied over a large range depending on the support used for the preparation of catalysts, indicating the importance of the support on catalytic activity of Mo catalysts. Al(OH)3 has been found to be the best support for molybdenum among all the supports used. Support–metal interaction (SMI) has been found to play an important role in determining the catalytic activity of supported catalysts.

An experiment that shaped the physics of the century

In this article it is pointed out how the different layers of substructure of matter were revealed to us by experiments which were essentially very similar to the famous α-particle scattering experiment performed by Rutherford. This experiment, which revealed the nuclear structure of an atom, paved the way towards our current understanding of the fundamental constituents of matter and shaped the course of physics for the 20th century.

Organophotocatalysis in nanostructured soft gel materials as tunable reaction vessels: comparison with homogeneous and micellar solutions

Riboflavin tetraacetate-catalyzed aerobic photooxidation of 1-(4-methoxyphenyl)ethanol was investigated as a model reaction under blue visible light in different soft gel materials, aiming to establish their potential as reaction vessels for photochemical transformations. Three strategies involving different degrees of organization of the catalyst within the gel network were explored, and the results compared to those obtained in homogeneous and micellar solutions. In general, physical entrapment of both the catalyst and the substrate under optimized concentrations into several hydrogel matrices (including low-molecular-weight and biopolymer-based gels) allowed the photooxidation with conversions between 55 and 100% within 120 min (TOF similar to 0.045-0.08 min(-1); k(obs) similar to 0.011-0.028 min(-1)), albeit with first-order rates ca. 1-3-fold lower than in solution under comparable non-stirred conditions. Remarkably, the organogel made of a cyclohexane-based bisamide gelator in CH3CN not only prevented the photodegradation of the catalyst but also afforded full conversion in less than 60 min (TOF similar to 0.167 min(-1); k(obs) similar to 0.073 min(-1)) without the need of additional proton transfer mediators (e. g., thiourea) as it occurs in CH3CN solutions. In general, the gelators could be recycled without detriment to their gelation ability and reaction rates. Moreover, kinetics could be fine-tuned according to the characteristics of the gel media. For instance, entangled fibrillar networks with relatively high mechanical strength were usually associated with lower reaction rates, whereas wrinkled laminated morphologies seemed to favor the reaction. In addition, the kinetics results showed in most cases a good correlation with the aeration efficiency of the gel media.

Photophysical behavior of poly(propyl ether imine) dendrimer in the presence of nitroaromatic compounds

This paper deals with a study of the photophysical property of poly(ether imine) (PETIM) dendritic macromolecule in the presence of aromatic compounds. The inherent photoluminescence property of the dendrimer undergoes quenching in the presence of guest aromatic nitro-compounds. From life-time measurements study, it is inferred that the lifetimes of luminescent species of the dendrimer are not affected with nitrophenols as guest molecules, whereas nitrobenzenes show a marginal change in the lifetimes of the species. Raman spectral characteristic of the macromolecular host-guest complex is conducted in order to identify conformational change of the dendrimer and a significant change in the stretching frequencies of methylene moieties of the dendrimer is observed for the complex with 1,3,5-trinitrobenzene, when compared to other complexes, free host and guest molecules. The photophysical behavior of electron-rich, aliphatic, neutral dendritic macromolecule in the presence of electron-deficient aromatic molecules is illustrated in the present study. (C) 2012 Elsevier B.V. All rights reserved.