Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

One-dimensional zig-zag type coordination polymers of Ni(II) and Cu(II) containing 1,3-benzenedicarboxylate and 1,3-diaminopropane: Structural, spectral and thermal studies

Two coordination polymers [Ni(ipt)(dap)(2)](n) (1) and [Cu(ipt)(dap)H2O](n) center dot nH(2)O (2) with an overall one-dimensional arrangement and having isophthalate (ipt) as bridging moieties and chelating 1,3-diaminopropane (dap) as structure modulating units have been prepared and characterized by crystallographic, spectroscopic and thermo-analytical studies. Both have an overall one-dimensional zig-zag nature but with a distorted octahedral NiN4O2 chromophore for 1 and a distorted square pyramidal CuN2O3 chromophore for 2. Even though the ipt units are acting as bridging units through mono-dentatively coordinating carboxylate functions in both polymers, compound 1 has the carboxylate oxygen linkages at the trans positions, while in 2 the oxygen linkages occur at the cis positions leading to a different type of zig-zag arrangement. Relevant spectral and bonding parameters also could be evaluated for the compounds using UV-Vis and EPR spectra. Thermal stability and possible structural modifications on thermal treatment of the compounds were also investigated and the relevant thermodynamic and kinetic parameters evaluated from the thermal data. (C) 2007 Elsevier B.V. All rights reserved.

ESR and optical absorption studies in copper diethyldithiocarbamate

ESR investigations at X band and optical-absorption measurements have been reported in single crystals of copper (n) diethyldithiocarbamate Cu[S 2CN(C2H5)2]2 diluted to 0.2% with the corresponding zinc complex. The measurements have been made both at room and liquid-oxygen temperatures. ESR measurements gave the following values for the parameters in spin Hamiltonian g11=2.1085, g=2.023(6), A63= 142.4×10-4 cm-1, A65 = 152.0×10-4 cm-1, B = 22.4×10-4 cm-1, Q~3×10-4 cm-1. Polarized optical absorption study has made possible a proper assignment of the absorption bands to their corresponding transitions. This has led to information regarding the ordering of the MO levels of the complex. The coefficients used in the MO description of the complex have been calculated from the observed parameters. The results show that the metal ligand BIσ bond is purely covalent and that the out-of-plane w bonding is appreciably covalent whereas the in-plane Π bonding is ionic. Further, it is noted that the metal ligand binding is more covalent with sulfur as ligand than with oxygen or nitrogen.

The Influence of Titania on Creep in Superplastic Zirconia

Detailed high-temperature compression creep experiments on a pure 3 mol% yttria-stabilized tetragonal zirconia (3YTZ) and 3YTZ doped with 4.8 wt% TiO2 revealed that both materials exhibit a similar transition in stress exponents from n similar to 1 to n similar to 2 with a decrease in stress. The stress exponent of 1 and the inverse grain size dependence p of similar to 3 are consistent with the Coble diffusion creep at high stresses; the increase in stress exponent at low stresses is attributed to an interface-controlled diffusion creep process. Measurements revealed that grain-boundary sliding contributes to >similar to 50% of the total strain in both regions with n similar to 1 and n similar to 2, indicating the operation of the same fundamental deformation process in both regions. The creep data indicate that doping with TiO2 leads to an increase in the grain-boundary diffusion coefficients. The increase observed in the dihedral angle with doping is also consistent with the increase in grain boundary diffusion coefficient and the reported enhanced ductility in such materials.

Template-Assisted Sol-Gel Synthesis of Nanocrystalline BaTiO3

Nanocrystalline perovskite barium titanate with an average particle size less than similar to 10 nm is produced using sol-gel route involving ligand-assisted templating. BaTiO3 is obtained by the controlled hydrolysis and condensation reaction of barium acetate (Ba(CH3COO)(2)) with titanium tetra chloride (TiCl4) in the reverse micelles of dodecylamine (DDA) which is used as the template. Our attempts to produce mesoporous BaTiO3 have resulted in the formation of nanocrystalline BaTiO3. The synthesis of nanostructured BaTiO3 is carried out using the ligand-assisted templating approach which proceeds through the sol-gel route. Dodecylamine is used as the template. The sol-gel process in general presents inherent advantages because the nanostructure of the desired materials can be controlled together with their porous structure. Ligand-assisted templating approach involves the formation of covalent bond between the inorganic analogue and the template. Ba(CH3COO)(2) and TiCl4 are used as barium-source and titanium-source respectively. The reaction between Ba(CH3COO)(2) and TiCl4 is found to take place deliberately on the pre-assembled species which acts as the template or occurring with in them which in turn will lead to the generation of the desired nanoscale structure (nanopores or nanoparticles).

PEDOT-PSSA as an alternative support for Pt electrodes in PEFCs

Poly (3,4-ethylenedioxythiophene) (PEDOT) and poly (styrene sulphonic acid) (PSSA) supported platinum (Pt) electrodes for application in polymer electrolyte fuel cells (PEFCs) are reported. PEDOT-PSSA support helps Pt particles to be uniformly distributed on to the electrodes, and facilitates mixed electronic and ionic (H+-ion) conduction within the catalyst, ameliorating Pt utilization. The inherent proton conductivity of PEDOT-PSSA composite also helps reducing Nation content in PEFC electrodes. During prolonged operation of PEFCs, Pt electrodes supported onto PEDOT-PSSA composite exhibit lower corrosion in relation to Pt electrodes supported onto commercially available Vulcan XC-72R carbon. Physical properties of PEDOT-PSSA composite have been characterized by X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy and transmission electron microscopy. PEFCs with PEDOT-PSSA-supported Pt catalyst electrodes offer a peak power-density of 810 mW cm(-2) at a load current-density of 1800 mA cm(-2) with Nation content as low as 5 wt.% in the catalyst layer. Accordingly, the present study provides a novel alternative support for platinized PEFC electrodes.

PEDOT-PSSA as an alternative support for Pt electrodes in PEFCs

Poly (3,4-ethylenedioxythiophene) (PEDOT) and poly (styrene sulphonic acid) (PSSA) supported platinum (Pt) electrodes for application in polymer electrolyte fuel cells (PEFCs) are reported. PEDOT-PSSA support helps Pt particles to be uniformly distributed on to the electrodes, and facilitates mixed electronic and ionic (H+-ion) conduction within the catalyst, ameliorating Pt utilization. The inherent proton conductivity of PEDOT-PSSA composite also helps reducing Nation content in PEFC electrodes. During prolonged operation of PEFCs, Pt electrodes supported onto PEDOT-PSSA composite exhibit lower corrosion in relation to Pt electrodes supported onto commercially available Vulcan XC-72R carbon. Physical properties of PEDOT-PSSA composite have been characterized by X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy and transmission electron microscopy. PEFCs with PEDOT-PSSA-supported Pt catalyst electrodes offer a peak power-density of 810 mW cm(-2) at a load current-density of 1800 mA cm(-2) with Nation content as low as 5 wt.% in the catalyst layer. Accordingly, the present study provides a novel alternative support for platinized PEFC electrodes

Crystal structures and photocatalysis of the triclinic polymorphs of BiNbO4 and BiTaO4

The high-temperature polymorphs of two photocatalytic materials, BiNbO4 and BiTaO4 were synthesized by the ceramic method. The crystal structures of these materials were determined by single-crystal X-ray diffraction. BiNbO4 and BiTaO4 crystallize into the triclinic system P (1) over bar (No. 2), with a = 5.5376(4) angstrom, b = 7.6184(3) angstrom, c = 7.9324(36) angstrom, alpha = 102.565(3)degrees, beta = 90.143(2)degrees, gamma = 92.788 (4)degrees, V = 326.21 (5) angstrom(3). Z = 4 and a = 5.931(1) angstrom, b = 7.672(2) angstrom, c = 7.786(2) angstrom, alpha = 102.94 (3)degrees, beta = 90.04(3)degrees gamma = 93.53(3)degrees, V = 344.59(1) angstrom(3) and Z = 4, respectively. The structures along the c-axis, consist of layers of [Bi2O2] units separated by puckered sheets of (Nb/Ta)O-6 octahedra. Photocatalytic studies on the degradation of dyes indicate selectivity of BiNbO4 towards aromatics containing quinonic and azo functional groups

Vitamin A and thyroxine carrier proteins in chicken plasma Steady-state control of the plasma level of free retinol-binding protein and free thyroxine

1. 1. The binding parameters of prealbumin-2 with retinol-binding protein and thyroxine (T4) revealed the existence of distinct and multiple sites for both retinol-binding protein and T4. 2. 2. From the analysis of binding parameters of retinol-binding protein with prealbumin-2 it is clear that under steady-state conditions about 99% of the holo-retinol-binding protein remains bound to prealbumin-2. 3. 3. Equilibrium dialysis studies on binding properties of thyroid hormones with prealbumin-2 revealed that it has a single high affinity site and three low affinity sites. 4. 4. The occurrence of three carrier proteins for thyroid hormones, thyroxine-binding globulin, prealbumin-2 and albumin has been demonstrated. However, the chicken thyroxine-binding globulin differs from human thyroxine-binding globulin by being relatively less acidic and occuring at a two-fold lower concentration. But the thyroid hormone binding parameters are comparable. 5. 5. Highly sensitive methods were developed for determination of T4 binding capacities of the various proteins and plasma level of total T4 by fractionation of carrier proteins and further quantitatively employing in electrophoresis and equilibrium dialysis. 6. 6. The thyroxine-binding proteins were found to be two types, one (viz., thyroxine-binding globulin) of great affinity but of low binding capacity, which mainly acts as reservoir of T4, and another (viz.,prealbumin-2) of low affinity but of high binding capacity, which can participate predominantly in the control of the free T4 pool.

Critical behavior of electrical resistivity in polar + nonpolar binary liquid systems

The behavior of electrical resistivity in the critical region of three polar + nonpolar binary liquid systems CS2 +(CH3CO)2O, C6H12+(CH3CO)2O, and n‐C7H16+(CH3CO)2O is studied. For the mixtures with critical composition, the two phase region shows a conductivity behavior with σ1−σ2∼ (−ϵ)β with β?0.35. In the one phase region dR/dT has a singularity ϵ−b with b?0.35. A possible theory of the impurity conduction is given, which broadly explains these results. The possibility of dR/dT being positive or negative is also discussed.

Catalytic hydrogen combustion for treatment of combustible gases from fuel cell processors

Catalytic combustion of H-2 was carried out over combustion synthesized noble metal (Pd or Pt) ion-substituted CeO2 based catalysts using a feed stream that simulated exhaust gases from a fuel cell processor The catalysts showed a high activity for H-2-combustion and complete conversion was achieved below 200 C over all the catalysts when O-2 was used in a stoichiometric amount With higher amounts of O-2 the reaction rates Increased and complete conversions were possible below 100 C The reaction was also carried out over Pd-impregnated CeO2 The conversions of H-2 with stoichiometric amount of O-2 were found to be higher over Pd-substituted compound The mechanism of the reaction over noble metal-substituted compounds was proposed on the basis of X-ray photoelectron spectroscopy studies The redox couples between Ce and metal ions were established and a dual site redox mechanism was pi posed for the reaction (C) 2010 Elsevier B V All rights reserved

Photo-activated cytotoxicity of a pyrenyl-terpyridine copper(II) complex in HeLa cells

Terpyridine copper(II) complexes Cu(L)(2)](NO3)(2) where L is (4'-phenyl)-2 2' 6' 2 `'-terpyridine (ph-tpy in 1) and 4-(1 pyrenyl)]-2 2' 6' 2'-terpyridine (py-tpy in 2) are prepared characterized and their photocytotoxic activity studied The crystal structure of complex 1 shows distorted octahedral CuN6 coordination geometry The 1 2 electrolytic and one-electron paramagnetic complexes show a visible band near 650 nm in DMF-H2O The complexes show emission band at 352 nm for 1 and 425 nm for 2 when excited at 283 and 346 nm respectively The Cu(II)-Cu(I) redox couple is observed near -0 2 V versus SCE in DMF-0 1 m TBAP The complexes are avid partial-intercalative binders to calf thymus DNA giving binding constant (K-b) values of similar to 10(6) M-1 Complex 2 with its photoactive pyrenyl moiety exhibits significant photocleavage of pUC19 DNA in red light via singlet oxygen pathway Complex 2 also exhibits significant photo-activated cytotoxicity in HeLa cancer cells in visible light giving IC50 value of 11 9 mu M while being non-toxic in dark with an IC50 value of 130 5 mu M (C) 2010 Elsevier Ltd All rights reserved

Crystal structures, spectral and magnetic properties of (µ-hydroxo)(µ-acetato)dicopper(II) complexes containing chelating amines

The reaction of [Cu2(O2CMe)4(H2O)2] with N, N, N′, N′-tetramethylethane- 1,2-diamine (tmen) in ethanol yielded the dicopper(II) complex [Cu2(OH)(O2CMe)(tmen)2][ClO4]21. A similar reaction with N, N- dimethylethane- 1,2-diamine (dmen) afforded a crystalline product 2 in which two dicopper(II) complexes, [Cu2(OH)(O2CMe)(dmen)2][ClO4]22a and [Cu2(OH)(O2CMe)(H2O)2(dmen)2][ClO4]22b, are cocrystallized in a 1 : 1 molar ratio along with 2NaClO4. The crystal structures of 1 and 2 have been determined. The complexes have an asymmetrically dibridged [Cu2(µ-OH)(µ-O2CMe)]2+ core. The co-ordination geometry of the metal is square planar (CuO2N2). The copper atoms in 2b have a square-pyramidal CuO3N2 co-ordination sphere. The Cu Cu distances and Cu–O–Cu angles in 1, 2a and 2b are 3.339(2), 3.368(3), 3.395(7)Å, 120.1(2), 116.4(1) and 123.6(2)°, respectively. Complex 1 exhibits an axial ESR spectrum in a methanol glass giving g∥= 2.26 (A∥= 164 × 10–4 cm–1) and g⊥= 2.04. The ESR spectra obtained from the bulk material of the dmen product are indicative of the presence of two dimers, viz. complex 2a(g∥= 2.25, A∥= 165 × 10–4 cm–1; g⊥= 2.03) and 2b(g∥= 2.19, A∥= 184 × 10–4 cm–1; g⊥= 2.0). Variable-temperature magnetic susceptibility measurements on these complexes show an intramolecular antiferromagnetic coupling in the dimeric core. The fitting parameters are J=–27.8 cm–1, g= 2.1 for complex 1 and J=–10.1 cm–1, g= 2.0 for 2. The magnetostructural properties of the complexes are discussed. There is a linear correlation of the –2J values with the Cu Cu distances among dibridged complexes having square-planar copper(II) centres.

Palladium(II) chloride complexes of bis(pyrazolyl)cyclotriphosphazenes

Reactions of the bis(3,5-dimethylpyrazolyl)cyclotriphosphazene derivatives gem-N3P3(MeNCH(2)CH(2)O)(2)(dmp)(2) (1) and nongeminal cis-N3P3(OPh)(4)(dmp)(2) (2) with PdCl2 afford complexes of the type [PdCl2.(L)] (L = 1 or 2). In these complexes, the phosphazenes act as bidentate NN-donor ligands with the two pyrazolyl pyridinic nitrogen atoms bonded to the metal, thus forming a six- and an eight-membered chelate ring, respectively. The structures of 2 and [PdCl2.(2)] (4) have been confirmed by single-crystal X-ray diffraction. Crystal data for 2: a = 16.759(2) Angstrom, b = 10.788(3) Angstrom, c = 19.635(9) Angstrom, beta = 101.61(3)degrees, P2(1/c), Z = 4, R = 0.038 for 4688 reflections with F > 5 sigma(F). Crystal data for 4: a = 9.701(3) Angstrom, b = 24.853(4) Angstrom, c = 15.794(4) Angstrom, beta = 101.46(2)degrees, P2(1/n), Z = 4, R = 0.030 for 5416 reflections with F > 5 sigma(F).

Synthesis, structure and redox properties of (?-oxo)bis(?-carboxylato)diruthenium(III) complexes containing three different terminal ligands

Blue coloured, unstable, essentially diamagnetic and non-electrolytic diruthenium(III) complexes of the formation [Ru2O(O2CR)4(en)2(PPh3)2] were prepared by reacting [Ru2O(O2CR)4(PPh3)2] with 1,2-diaminoethane (en) in CH2Cl2 (R = C6H4-p-X; X = H, Me and OMe). The molecular structure of the complexes is proposed as [{(?1-O2CR)(?1-en)(PPH3)Ru}2(?-O)(?-O2CR)2] based on the 1H NMR spectral data. The electronic spectra of the complexes display a band near 569 nm with a shoulder at 630 nm. In CH2Cl2-0.1 M [Bun4N]ClO4, the complexes exhibit redox couples Ru2III,III/Ru2III,IV and Ru2III,IV/Ru2IV,IV near 0.1 and 1.2 V (vs SCE), respectively. The potentials are the lowest among diruthenium(III) complexes with a similar core structure.