Resolution of Singularities for a Class of Hilbert Modules

Let M be the completion of the polynomial ring C(z) under bar] with respect to some inner product, and for any ideal I subset of C (z) under bar], let I] be the closure of I in M. For a homogeneous ideal I, the joint kernel of the submodule I] subset of M is shown, after imposing some mild conditions on M, to be the linear span of the set of vectors {p(i)(partial derivative/partial derivative(w) over bar (1),...,partial derivative/partial derivative(w) over bar (m)) K-I] (., w)vertical bar(w=0), 1 <= i <= t}, where K-I] is the reproducing kernel for the submodule 2] and p(1),..., p(t) is some minimal ``canonical set of generators'' for the ideal I. The proof includes an algorithm for constructing this canonical set of generators, which is determined uniquely modulo linear relations, for homogeneous ideals. A short proof of the ``Rigidity Theorem'' using the sheaf model for Hilbert modules over polynomial rings is given. We describe, via the monoidal transformation, the construction of a Hermitian holomorphic line bundle for a large class of Hilbert modules of the form I]. We show that the curvature, or even its restriction to the exceptional set, of this line bundle is an invariant for the unitary equivalence class of I]. Several examples are given to illustrate the explicit computation of these invariants.

Mammalian neuronal sodium channel Blocker mu-conotoxin BuIIIB has a structured N-terminus that influences potency

Among the mu-conotoxins that block vertebrate voltage-gated sodium channels (VGSCs), some have been shown to be potent analgesics following systemic administration in mice. We have determined the solution structure of a new representative of this family, mu-BuIIIB, and established its disulfide connectivities by direct mass spectrometric collision induced dissociation fragmentation of the peptide with disulfides intact The major oxidative folding product adopts a 1-4/2-5/3-6 pattern with the following disulfide bridges: Cys5-Cys17, Cys6-Cys23, and Cys13-Cys24. The solution structure reveals that the unique N-terminal extension in mu-BuIIIB, which is also present in mu-BuIIIA and mu-BuIIIC but absent in other mu-conotoxins, forms part of a short a-helix encompassing Glu3 to Asn8. This helix is packed against the rest of the toxin and stabilized by the Cys5-Cys17 and Cys6-Cys23 disulfide bonds. As such, the side chain of Val1 is located close to the aromatic rings of Trp16 and His20, which are located on the canonical helix that displays several residues found to be essential for VGSC blockade in related mu-conotoxins. Mutations of residues 2 and 3 in the N-terminal extension enhanced the potency of mu-BuIIIB for Na(v)1.3. One analogue, D-Ala2]BuIIIB, showed a 40-fold increase, making it the most potent peptide blocker of this channel characterized to date and thus a useful new tool with which to characterize this channel. On the basis of previous results for related mu-conotoxins, the dramatic effects of mutations at the N-terminus were unanticipated and suggest that further gains in potency might be achieved by additional modifications of this region.

Linear and nonlinear optical properties of expanded porphyrins: a DMRG study

We study absorption spectra and two photon absorption coefficient of expanded porphyrins (EPs) by the density matrix renormalization group (DMRG) technique. We employ the Pariser-Parr-Pople (PPP) Hamiltonian which includes long-range electron-electron interactions. We find that, in the 4n+2 EPs, there are two prominent low-lying one-photon excitations, while in 4n EPs, there is only one such excitation. We also find that 4n+2 EPs have large two-photon absorption cross sections compared to 4n EPs. The charge density rearrangement in the one-photon excited state is mostly at the pyrrole nitrogen site and at the meso carbon sites. In the two-photon states, the charge density rearrangement occurs mostly at the aza-ring sites. In the one-photon state, the C-C bond length in aza rings shows a tendency to become uniform. In the two-photon state, the bond distortions are on C-N bonds of the pyrrole ring and the adjoining C-C bonds which connect the pyrrole ring to the aza or meso carbon sites.

Molecular structures and antiproliferative activity of side-chain saturated and homologated analogs of 2-chloro-3-(n-alkylamino)-1,4-napthoquinone

Side chain homologated derivatives of 2-chloro-3-(n-alkylamino)-1,4-naphthoquinone {n-alkyl: pentyl; L-5, hexyl; L-6, heptyl; L-7 and octyl; L-8} have been synthesized and characterized by elemental analysis, FT-IR, H-1 NMR, UV-visible spectroscopy and LC-MS. Compounds, L-4, n-alkyl: butyl; L-4}, L-6 and L-8 have been characterized by single crystal X-ray diffraction studies. The single crystal X-ray structures reveal that L-4 and L-8 crystallizes in P2(1) space group, while L-6 in P2(1)/c space group. Molecules of L-4 and L-8 from polymeric chains through C-H center dot center dot center dot O and N-H center dot center dot center dot O close contacts. L-6 is a dimer formed by N-H center dot center dot center dot O interaction. Slipped pi-pi stacking interactions are observed between quinonoid and benzenoid rings of L-4 and L-8. Orientations of alkyl group in L-4 and L-8 is on same side of the chain and polymeric chains run opposite to one another to form zip like structure to the alkyl groups. Antiproliferative activities of L-1 to L-8{n-alkyl: methyl; L-1, ethyl; L-2, propyl; L-3 and butyl; L-4} were studied in cancer cells of colon (COLO205), brain (U87MG) and pancreas (MIAPaCa2) where L-1, L-2 and L-3 were active in MIAPaCa2 (L-1 = 1-2 > L-3) and COLO205 (L-2 = L-3 > L-1) and inactive in U87MG. From antiproliferative studies with compounds L-1 to L-8 it can be concluded that homologation of 2-chloro-3-(n-alkylamino)-1,4-napthoquinone with saturated methyl groups yielded tissue specific compounds such as L-2 (for MIAPaCa2) and L-3 (for COLO205) with optimal activity. (c) 2013 Elsevier B.V. All rights reserved.

Variable field ion traps

This paper presents a technique to vary the electric field within a cylindrical ion trap (CIT) mass spectrometer while it is in operation. In this technique, the electrodes of the CIT are split into number of mini-electrodes and different voltages are applied to these split-electrodes to achieve the desired field. In our study we have investigated two geometries of the split-electrode CIT. In the first, we retain the flat endcap electrodes of the CIT but split the ring electrode into five mini-rings. In the second configuration, we split the ring electrode of the CIT into three mini-rings and also divide the endcaps into two mini-discs. By applying different potentials to the mini-rings and mini-discs of these geometries we have shown that the field within the trap can be optimized to desired values. In our study, two different types of fields were targeted. In the first, potentials were adjusted to obtain a linear electric field and, in the second, a controlled higher order even multipole field was obtained by adjusting the potential. We have shown that the different potentials required can be derived from a single RF generator by connecting appropriate capacitor terminations to split electrodes. The field within the trap can be modified by changing the values of the external capacitors. (C) 2013 Elsevier B.V. All rights reserved.

Vortex reconnections between coreless vortices in binary condensates

Vortex reconnections plays an important role in the turbulent flows associated with the superfluids. To understand the dynamics, we examine the reconnections of vortex rings in the superfluids of dilute atomic gases confined in trapping potentials using Gross-Petaevskii equation. Further more we study the reconnection dynamics of coreless vortex rings, where one of the species can act as a tracer.

High-Resolution Solid State C-13 NMR Studies of Bent-Core Mesogens of Benzene and Thiophene

Bent-core mesogens are an important class of thermotropic liquid crystals as they exhibit unusual properties as well as morphologies distinctly different from rodlike mesogens. Two bent-core mesogens with differing center rings namely benzene and thiophene are considered and investigated using high-resolution oriented solid state C-13 NMR method in their liquid crystalline phases. The mesogens exhibit different phase sequences with the benzene-based mesogen showing a B-1 phase, while the one based on thiophene showing nematic and smectic C phases. The 2-dimensional separated local field (2D-SLF) NMR method was used to obtain the C-13-H-1 dipolar couplings of carbons in the center ring as well as in the side-wing phenyl rings. Couplings, characteristic of the type of the center ring, that also provide orientational information on the molecule in the magnetic field were observed. Together with the dipolar couplings of the side-wing phenyl ring carbons from which the local order parameters of the different subunits of the core could be extracted, the bent angle of the mesogenic molecule could be obtained. Accordingly, for the benzene mesogen in its B-1 phase at 145 degrees C, the center ring methine C-13-H-1 dipolar couplings were found to be significantly larger (9.5-10.2 kHz) compared to those of the side-wing rings (1.6-2.1 kHz). From the local order parameter values of the center (0.68) as well as the side-wing rings (0.50), a bent-angle of 130.3 degrees for this mesogen was obtained. Interestingly, for the thiophene mesogen in its smectic C phase at 210 degrees C, the C-13-H-1 dipolar coupling of the center ring methine carbon (2.11 kHz) is smaller than those of the side-wing phenyl ring carbons (2.75-3.00 kHz) which is a consequence of the different structures of the thiophene and the benzene rings. These values correspond to local order parameters of 0.85 for the center thiophene ring and 0.76 for the first side-wing phenyl ring and a bent-angle of 149.2 degrees. Thus, the significant differences in the dipolar couplings and the order parameter values between different parts in the rigid core of the mesogens are a direct consequence of the nature of the center ring and the bent structure of the molecule. The present investigation thus highlights the ability of the C-13 2D-SLF technique to provide the geometry of the bent-core mesogens in a straightforward manner through the measurement of the C-13-H-1 dipolar couplings.

Designing stuffed hetero-fullerene nano-clusters: C26B46N12 and C14B58N12Li12

The stuffed fullerene-like nano clusters based on the approximately spherical B-84, (B-12@B-12@B-60, fragment of the beta-rhombohedral boron), are proposed using Wade's Rules and the criterion of overlap matching. Thus the fifty additional electrons required to make the B-84 skeleton electron sufficient, are provided by replacing 26 boron atoms by carbon atoms and 12 boron atoms by nitrogen atoms giving rise to C26B46N12. This particular combination has the added advantage of the fullerene surface made from C2B3N five-membered rings having less strain arising from the pyramidalization of the sp(2) hybridised trigonal planar carbon or nitrogen; the natural angle needed to have an optimum overlap is not far from the 31.7 degrees required for icosahedral symmetry. The advantage from overlap-matching can be further increased by capping the two pentagonal faces of the cluster by a Li atom each, keeping the electron count the same by replacing 12 carbon atoms with 12 boron atoms. DFT based computational results support these formulations.

Effect of High-Pressure Torsion on Texture, Microstructure, and Raman Spectroscopy: Case Study of Fe- and Te-Substituted CoSb3

Fe0.05Co0.95Sb2.875Te0.125, a double-element-substituted skutterudite, was prepared by induction melting, annealing, and hot pressing (HP). The hot-pressed sample was subjected to high-pressure torsion (HPT) with 4 GPa pressure at 673 K. X-ray diffraction was performed before and after HPT processing of the sample; the skutterudite phase was observed as a main phase, but an additional impurity phase (CoSb2) was observed in the HPT-processed sample. Surface morphology was determined by high-resolution scanning electron microscopy. In the HP sample, coarse grains with sizes in the range of approximately 100 nm to 300 nm were obtained. They changed to fine grains with a reduction in grain size to 75 nm to 125 nm after HPT due to severe plastic deformation. Crystallographic texture, as measured by x-ray diffraction, indicated strengthening of (112), (102) poles and weakening of the (123) pole of the HPT-processed sample. Raman-active vibrational modes showed a peak position shift towards the lower energy side, indicating softening of the modes after HPT. The distortion of the rectangular Sb-Sb rings leads to broadening of Sb-Sb vibrational modes due to local strain fluctuation. In the HPT process, a significant effect on the shorter Sb-Sb bond was observed as compared with the longer Sb-Sb bond.

Depalladation of Neutral Monoalkyne- and Dialkyne-Inserted Palladacycles and Alkyne Insertion/Depalladation Reactions of Cationic Palladacycles Derived from N,N `,N `'-Triarylguanidines as Facile Routes for Guanidine-Containing Heterocycles/Carbocycles: Synthetic, Structural, and Mechanistic Aspects

Depalladation of the monoalkyne-inserted cyclopalldated guanidines (kappa 2(C,N)Pd(2,6-Me2C5H3N)Br] (I and II) in PhCl under reflux conditions and that of the dialkyne-inserted cyclopalladated guanidine kappa(2)(C,N):eta(2)(C=C)PdBr] (III) in pyridine under reflux conditions afforded a guanidine-containing indole (1), imidaziondole (2), and benzazepine (3) in 80%, 67%, and 76%, yields, respectively. trans-L2PdBr2] species (L = 2,6-Me2C5H3N, C5H5N) were also isolated in the aforementioned reactions in 35%, 42%, and 40% yields. Further , the reaction of the cyclopalladated guanidine kappa(2)(C,N)Pd(mu-Br)](2) (IV) with AgBF4 in a CH2Cl2/MeCN mixture afforded the cationic pincer type cyclopalladated guanidine kappa(3)(C,N,O)Pd(MeCN)]BF4] (4) in 85% yield and this palladacycle upon crystallization in MeCN and the reaction of kappa(2)(C,N)Pd(mu-Br)](2) (V) with AgBf(4) in a CH2Cl2/MeCN mixture afforded the cationic palladacycles {kappa(2)(C,N)Pd(MeCN)(2)]BF4](5 and 6) in 89% and 91% yields, respectively. The separate reactions of 4 with 2 equiv of methyl phenylpropiolate (MPP) or diphenylacetylene (DPA) and the reaction of 5 with 2 equiv of MPP in PhCl at 110 degrees C afforded the guanidine-containing quinazolinium tetrafluoroborate 7 in 25-32% yields. The reaction of 6 with 2 equiv of DPA under otherwise identical conditions afforded the unsymmetrically substituted guanidinium tetrafluoroborate 8, containing a highly substituted naphthalene unit, in 82% yield. Compounds 1-8 were characterized by analytical and spectroscopic techniques, and all compounds except 4 were characterized by single-crystal X-ray diffraction. The Molecular structure of 2 and 3 are nove, as the framework in the former arises due to the formation of two C-N bonds upon depalladation while the butadienyl unit in the latter revealed cis,cis stereochemistry, a-feature unprecedented in alkyne insertion chemistry. Plausible pathways for the formation of heterocycles/carbocycles are proposed. the influence of substitutents on the aryl rings fo the cyclopalladated guanidine moiety and those on alkynes upon the nature of the products in addressed. Heterocycles 1 and 7 revealed the presence of two rotamers in about a 1.00:0.43 ratio in CDCl3 and in about a 1.00:0.14 ratio in CD3OD, respectively, as detected by H-1 NMR spectroscopy while in CD3CN and DMSO-d(6) (1) and CD3CN and CDCl3 (7), these heterocycles revealed the presence of a single rotamer. These spectral features are attributed to the restricted C-N single-bond rotation of the CN3 unit of the guanidine moiety, which possibly arises from steric constraint due to the formation of a N-H center dot center dot center dot Cl hydrogen bond with CDCl3 (1) and N-H center dot center dot center dot O and O-D center dot center dot center dot O hydrogen bonds with CD3OD (7).

Hydrophobic hydration driven self-assembly of curcumin in water: Similarities to nucleation and growth under large metastability, and an analysis of water dynamics at heterogeneous surfaces

As the beneficial effects of curcumin have often been reported to be limited to its small concentrations, we have undertaken a study to find the aggregation properties of curcumin in water by varying the number of monomers. Our molecular dynamics simulation results show that the equilibrated structure is always an aggregated state with remarkable structural rearrangements as we vary the number of curcumin monomers from 4 to 16 monomers. We find that the curcumin monomers form clusters in a very definite pattern where they tend to aggregate both in parallel and anti-parallel orientation of the phenyl rings, often seen in the formation of beta-sheet in proteins. A considerable enhancement in the population of parallel alignments is observed with increasing the system size from 12 to 16 curcumin monomers. Due to the prevalence of such parallel alignment for large system size, a more closely packed cluster is formed with maximum number of hydrophobic contacts. We also follow the pathway of cluster growth, in particular the transition from the initial segregated to the final aggregated state. We find the existence of a metastable structural intermediate involving a number of intermediate-sized clusters dispersed in the solution. We have constructed a free energy landscape of aggregation where the metatsable state has been identified. The course of aggregation bears similarity to nucleation and growth in highly metastable state. The final aggregated form remains stable with the total exclusion of water from its sequestered hydrophobic core. We also investigate water structure near the cluster surface along with their orientation. We find that water molecules form a distorted tetrahedral geometry in the 1st solvation layer of the cluster, interacting rather strongly with the hydrophilic groups at the surface of the curcumin. The dynamics of such quasi-bound water molecules near the surface of curcumin cluster is considerably slower than the bulk signifying a restricted motion as often found in protein hydration layer. (C) 2014 AIP Publishing LLC.

STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES

It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation.

pentahexoctite: A new two-dimensional allotrope of carbon

The ability of carbon to exist in many forms across dimensions has spawned search in exploring newer allotropes consisting of either, different networks of polygons or rings. While research on various 3D phases of carbon has been extensive, 2D allotropes formed from stable rings are yet to be unearthed. Here, we report a new sp(2) hybridized two-dimensional allotrope consisting of continuous 5-6-8 rings of carbon atoms, named as ``pentahexoctite''. The absence of unstable modes in the phonon spectra ensures the stability of the planar sheet. Furthermore, this sheet has mechanical strength comparable to graphene. Electronically, the sheet is metallic with direction-dependent flat and dispersive bands at the Fermi level ensuring highly anisotropic transport properties. This sheet serves as a precursor for stable 1D nanotubes with chirality-dependent electronic and mechanical properties. With these unique properties, this sheet becomes another exciting addition to the family of robust novel 2D allotropes of carbon.

MEMS Tunable Optical Filter Based on Multi-Ring Resonator

We propose a novel MEMS tunable optical filter with a flat-top pass band based on multi-ring resonator in an electrostatically actuated microcantilever for communication application. The filter is basically structured on a microcantilever beam and built in optical integrated ring resonator which is placed in one end of the beam to gain maximum stress on the resonator. Thus, when a DC voltage is applied, the beam will bend, that induces a stress and strain in the ring, which brings a change in refractive index and perimeter of the rings leading to change in the output spectrum shift, providing the tenability as high as 0.68nm/mu N. and it is capable of tuning up to 1.7nm.

Solution processable diketopyrrolopyrrole (DPP) cored small molecules with BODIPY end groups as novel donors for organic solar cells

Two novel triads based on a diketopyrrolopyrrole (DPP) central core and two 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) units attached by thiophene rings have been synthesised having high molar extinction coefficients. These triads were characterised and used as donor materials in small molecule, solution processable organic solar cells. Both triads were blended with PC71BM as an acceptor in different ratios by wt% and their photovoltaic properties were studied. For both the triads a modest photovoltaic performance was observed, having an efficiency of 0.65%. Moreover, in order to understand the ground and excited state properties and vertical absorption profile of DPP and BODIPY units within the triads, theoretical DFT and TDDFT calculations were performed.