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.

Coordination self-assembly of tetranuclear Pt(II) macrocycles with an organometallic backbone for sensing of acyclic dicarboxylic acids

Coordination self-assembly of a series of tetranuclear Pt(II) macrocycles containing an organometallic backbone incorporating ethynyl functionality is presented. The 1 : 1 combination of a linear acceptor 1,4-bistrans-Pt(PEt3)(2)(NO3)(ethynyl)]benzene (1) with three different dipyridyl donor `clips' (L-a-L-c) afforded three 2 + 2] self-assembled Pt-4(II) macrocycles (2a-2c) in quantitative yields, respectively L-a = 1,3-bis-(3-pyridyl)isothalamide; L-b = 1,3-bis(3-pyridyl)ethynylbenzene; L-c = 1,8-bis(4-pyridyl)ethynylanthracene]. These macrocycles were characterized by multinuclear NMR (H-1 and P-31); ESI-MS spectroscopy and the molecular structures of 2a and 2b were established by single crystal X-ray diffraction analysis. These macrocycles (2a-2c) are fluorescent in nature. The amide functionalized macrocycle 2a is used as a receptor to check the binding affinity of aliphatic acyclic dicarboxylic acids. Such binding affinity is examined using fluorescence and UV-Vis spectroscopic methods. A solution state fluorescence study showed that macrocycle 2a selectively binds (K-SV = 1.4 x 10(4) M-1) maleic acid by subsequent enhancement in emission intensity. Other aliphatic dicarboxylic acids such as fumaric, succinic, adipic, mesaconic and itaconic acids caused no change in the emission spectra; thereby demonstrating its potential use as a macrocyclic receptor in distinction of maleic acid from other aliphatic dicarboxylic acids.

Structure, tensile properties and cytotoxicity assessment of sebacic acid based biodegradable polyesters with ricinoleic acid

A new family of ricinoleic acid based polyesters was synthesized using catalyst free melt-condensation polymerization with sebacic acid, citric acid, mannitol and ricinoleic acid as precursors. The use of FT-IR and NMR characterisation techniques confirms the presence of ester linkages in the as-synthesized polymers. Depending on the precursor combination, their relative amount and the degree of curing, a broad range of elastic modulus (22-327 MPa) and tensile strength (0.7-12.7 MPa) can be obtained in the newly synthesized biopolymers. The polymers show rubbery behaviour at a physiological temperature (37 degrees C) and the contact angles of the synthesized polymers fall in the range of 42 degrees to 71 degrees, making them ideal substrates to study delivery of drugs through polymer scaffolds. The cytocompatibility assessment of the cured polymers confirmed good cell attachment and growth of smooth muscle cells (C2C12 myoblast cells). Importantly, oriented cell growth was observed after culturing myoblast cells for 3 days. The in vitro degradation in PBS indicates that the mild cured polymers follow a first order reaction kinetics and have degradation rate constants in the range of 0.009-0.038 h(-1), depending on the relative proportions of monomers. Overall, the results of our study indicate that the physical properties can be tailored by varying the composition of the monomers and curing conditions in the newly developed polyesters. Hence, they may be used as potential substrates for tissue engineering scaffolds and for localized drug delivery.

Employing denaturation for rapid electrochemical detection of myoglobin using TiO2 nanotubes

An alternative antibody-free strategy for the rapid electrochemical detection of cardiac myoglobin has been demonstrated here using hydrothermally synthesized TiO2 nanotubes (Ti-NT). The denaturant induced unfolding of myoglobin led to easy access of the deeply buried electroactive heme center and thus the efficient reversible electron transfer from protein to electrode surface. The sensing performance of the Ti-NT modified electrodes were compared vis a vis commercially available titania and GCEs. The tubular morphology of the Ti-NT led to facile transfer of electrons to the electrode surface, which eventually provided a linear current response (obtained from cyclic voltammetry) over a wide range of Mb concentration. The sensitivity of the Ti-NT based sensor was remarkable and was equal to 18 mu A mg(-1) ml (detection limit = 50 nM). This coupled with the rapid analysis time of a few tens of minutes (compared to a few days for ELISA) demonstrates its potential usefulness for the early detection of acute myocardial infarction (AMI).

Composite cyclodextrin-calcium carbonate porous microparticles and modified multilayer capsules: novel carriers for encapsulation of hydrophobic drugs

Novel composite cyclodextrin (CD)-CaCO3 spherical porous microparticles have been synthesized through Ca2+-CD complex formation, which influences the crystal growth of CaCO3. The CDs are entrapped and distributed uniformly in the matrix of CaCO3 microparticles during crystallization. The hydrophobic fluorescent molecules coumarin and Nile red (NR) are efficiently encapsulated into these composite CD-CaCO3 porous particles through supramolecular inclusion complexation between entrapped CDs and hydrophobic molecules. Thermogravimetric (TGA) and infrared spectroscopy (IR) analysis of composite CD-CaCO3 particles reveals the presence of large CDs and their strong interaction with calcium carbonate nanoparticles. The resulting composite CD-CaCO3 microparticles are utilized as sacrificial templates for preparation of CD-modified layer-by-layer (LbL) capsules. After dissolution of the carbonate core, CDs are retained in the interior of the capsules in a network fashion and assist in the encapsulation of hydrophobic molecules. The efficient encapsulation of the hydrophobic fluorescent dye, coumarin, was successfully demonstrated using CD-modified capsules. In vitro release of the encapsulated coumarin from the CD-CaCO3 and CD-modified capsules has been demonstrated.

Biotin-conjugated tumour-targeting photocytotoxic iron(III) complexes

Iron(III) complexes FeL(B)] (1-4) of a tetradentate phenolate-based ligand (H3L) and biotin-conjugated dipyridophenazine bases (B), viz. 7-aminodipyrido 3,2-a: 2',3'-c]-phenazine (dppza in 1), (N-dipyrido3,2-a: 2',3'-c]-phenazino) amidobiotin (dppzNB in 2), dipyrido 3,2-a: 2',3'-c]-phenazine-11-carboxylic acid (dppzc in 3) and 2-((2-biotinamido) ethyl) amidodipyrido 3,2-a: 2',3'-c]-phenazine (dppzCB in 4) are prepared, characterized and their interaction with streptavidin and DNA and their photocytotoxicity and cellular uptake in various cells studied. The high-spin iron(III) complexes display Fe(III)/Fe(II) redox couple near -0.7V versus saturated calomel electrode in dimethyl sulfoxide-0.1M tetrabutylammonium perchlorate. The complexes show non-specific interaction with DNA as determined from the binding studies. Complexes with appended biotin moiety show similar binding to streptavidin as that of free biotin, suggesting biotin conjugation to dppz does not cause any loss in its binding affinity to streptavidin. The photocytotoxicity of the complexes is tested in HepG2, HeLa and HEK293 cell lines. Complex 2 shows higher photocytotoxicity in HepG2 cells than in HeLa or HEK293, forming reactive oxygen species. This effect is attributed to the presence of overexpressed sodium-dependent multi-vitamin transporters in HepG2 cells. Microscopic studies in HepG2 cells show internalization of the biotin complexes 2 and 4 essentially occurring by receptor-mediated endocytosis, which is similar to that of native biotin and biotin fluorescein isothiocyanate conjugate.

Albumin-mediated incorporation of water-insoluble therapeutics in layer-by-layer assembled thin films and microcapsules

The present study demonstrates a method to deliver hydrophobic drugs by incorporation into thin films and microcapsules fabricated via a layer-by-layer assembly approach. The hydrophobic molecule binding properties of albumin have been exploited for solubilization of a water-insoluble molecule, pyrene (model drug), by preparation of non-covalent conjugates with bovine serum albumin (BSA). Conjugation with BSA renders a highly negative zeta potential to the previously uncharged pyrene which favors the assembly formation by electrostatic interaction with a positively charged polyelectrolyte, chitosan (at acidic pH). The growth of the assembly was followed by monitoring pyrene absorbance with successive layer deposition. The thin film assembly was demonstrated to be capable of releasing its hydrophobic cargo under physiological conditions. We demonstrated the applicability of this approach by encapsulating a water-insoluble drug, curcumin. These assemblies were further loaded with the anti-cancer drug Doxorubicin. Biocompatible calcium carbonate microparticles were used for capsule preparation. The porous nature of the microparticles allows for the pre-encapsulation of therapeutic macromolecules like protein. The fabrication of protein encapsulated stable microcapsules with hydrophobic molecules incorporated into the shell of the microcapsules has been demonstrated. The microcapsules were further capable of loading hydrophilic molecules like Rhodamine B. Thus, using the approach described, a multi-agent carrier for hydrophobic and hydrophilic drugs as well as therapeutic macromolecules can be envisioned.

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.

Vertical uplift resistance of two closely spaced horizontal strip anchors embedded in cohesive-frictional weightless medium

The vertical uplift resistance of two closely spaced horizontal strip plate anchors has been investigated by using lower and upper bound theorems of the limit analysis in combination with finite elements and linear optimization. The interference effect on uplift resistance of the two anchors is evaluated in terms of a nondimensional efficiency factor (eta(c)). The variation of eta(c) with changes in the clear spacing (S) between the two anchors has been established for different combinations of embedment ratio (H/B) and angle of internal friction of the soil (phi). An interference of the anchors leads to a continuous reduction in uplift resistance with a decrease in spacing between the anchors. The uplift resistance becomes a minimum when the two anchors are placed next to each other without any gap. The critical spacing (S-cr) between the two anchors required to eliminate the interference effect increases with an increase in the values of both H/B and phi. The value of S-cr was found to lie approximately in the range 0.65B-1.5B with H/B = 1 and 11B-14B with H/B = 7 for phi varying from 0 degrees to 30 degrees.

Optical, photo-acoustic and electrical switching studies of amorphous GeS2 thin films

This paper reports optical, photo-acoustic and electrical switching investigations of GeS2 amorphous thin films of different thicknesses, deposited on glass substrates in vacuum. The Tauc parameter (B (1/2)) and Urbach energy (E (U)) have been determined from the transmittance spectra, to understand the changes in structural disorder; it is found that B (1/2) increases whereas E (U) decreases as the thickness of the films increases. Based on the results, it is suggested that bond re-arrangement, i.e. transformation from homopolar bonds to heteropolar bonds, takes place with increase in thickness. The thermal diffusivity values of GeS2 thin films also show the presence of a chemically ordered network in the GeS2 thin films. Further, it is found that these films exhibit memory-type electrical switching. The observed variation in the switching voltages has been understood on the basis of increase in chemical order.

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.

Effect of compositional variations on the optical properties of SbxSe60-xS40 thin films

Thin films of SbxSe60-xS40( x= 10, 20, 30, and 40) were deposited by thermal evaporation from the prepared bulk materials on glass substrates held at room temperature. The film compositions were confirmed by using energy dispersive X-ray spectroscopy. X-ray diffraction studies revealed that all the as- deposited films have amorphous structure. The optical constants ( n, k, E-g, E-e, B-1/2) of the films were determined from optical transmittance data, in the spectral range 500-1200 nm, using the Swanepoel method. An analysis of the optical absorption spectra revealed an Urbach's tail in the low absorption region, while in the high absorption region an indirect band gap characterizes the films with different compositions. It was found that the optical band gap energy decreases as the Sb content increases. Finally, in terms of the chemical bond approach, degree of disorderness has been applied to interpret the decrease in the optical gap with increasing Sb content in SbxSe60-xS40 thin films. The changes in X-ray photo electron spectra and Raman shift in the films show compositional dependence. (C) 2015 Elsevier B.V. All rights reserved.

Review on Tin (II) Sulfide (SnS) Material: Synthesis, Properties, and Applications

Tin (II) sulphide (SnS), a direct band gap semiconductor compound, has recently received great attention due to its unique properties. Because of low cost, absence of toxicity, and good abundance in nature, it is becoming a candidate for future multifunctional devices particularly for light conversion applications. Although the current efficiencies are low, the cost-per-Watt is becoming competitive. At room temperature, SnS exhibits stable low-symmetric, double-layered orthorhombic crystal structure, having a = 0.4329, b = 1.1192, and c = 0.3984nm as lattice parameters. These layer-structured materials are of interest in various device applications due to the arrangement of structural lattice with cations and anions. The layers of cations are separated only by van der Waals forces that provide intrinsically chemically inert surface without dangling bonds and surface density of states. As a result, there is no Fermi level pinning at the surface of the semiconductor. This fact leads to considerably high chemical and environmental stability. Further, the electrical and optical properties of SnS can be easily tailored by modifying the growth conditions or doping with suitable dopants without disturbing its crystal structure.In the last few decades, SnS has been synthesized and studied in the form of single-crystals and thin-films. Most of the SnS single-crystals have been synthesized by Bridgeman technique, whereas thin films have been developed using different physical as well as chemical deposition techniques. The synthesis or development of SnS structures in different forms including single-crystals and thin films, and their unique properties are reviewed here. The observed physical and chemical properties of SnS emphasize that this material could has novel applications in optoelectronics including solar cell devices, sensors, batteries, and also in biomedical sciences. These aspects are also discussed.