Painlevé analysis,conservation laws,and symmetry of perturbed nonlinear equations

We consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generator. When the perturbed KdV equation is subjected to Painlevé analysisa la Weiss, it is found that the resonance position changes compared to the unperturbed one. We prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter to be small. We determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation we determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painlevé analysis does not produce a positive answer for the perturbed NLS equation. So here we have two contrasting examples of perturbed nonlinear equations: one passes the Painlevé test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painlevé test, though its Lax pair is found in another way.     

Aspects of thermal conductivity relative to heat flow

Summary The various techniques and methodologies of thermal conductivity measurement have been conventionally based on the determination of the rate of directional heat flow through a material having a unit temperature differential between its opposing faces. The constancy of this rate depends on the material density, its thermal resistance and the heat flow path itself. The last of these variables contributes most significantly to the true value of steady-state axial and radial heat dissipation depending on the magnitude of transient thermal diffusivity along these directions. The purpose of this paper is to exemplify the above features by defined parameters of heat flow measurement by existing methodologies. No new method is proposed here. Importantly, the relationship between the rate of heat transfer, total heat transferred and thermal conductivity at a given temperature under steady-state conditions for a fixed heat flow path will be illustrated.     

An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Highly efficient recycling of a "sandwich" type polyoxometalate oxidation catalyst using solvent resistant nanofiltration

A "sandwich" type polyoxometalate catalyst ([MeN(n-C8H17)3]12[WZn3(ZnW9O34)2]) was very efficiently recycled by nanofiltration with almost quantitative retention, using an alpha-alumina supported mesoporous gamma-alumina membrane.     

Ternary iron(II) complex with an emissive imidazopyridine arm from Schiff base cyclizations and its oxidative DNA cleavage activity

The ternary iron(II) complex [Fe(L')(L")](PF6)3(1) as a synthetic model for the bleomycins, where L' and L" are formed from metal-mediated cyclizations of N,N'-(2-hydroxypropane-1,3-diyl)bis(pyridine-2-aldimine)(L), is synthesized and structurally characterized by X-ray crystallography. In the six-coordinate iron(ii) complex, ligands L' and L" show tetradentate and bidentate chelating modes of bonding. Ligand L' is formed from an intramolecular attack of the alcoholic OH group of L to one imine moiety leading to the formation of a stereochemically constrained five-membered ring. Ligand L" which is formed from an intermolecular reaction involving one imine moiety of L and pyridine-2-carbaldehyde has an emissive cationic imidazopyridine pendant arm. The complex binds to double-stranded DNA in the minor groove giving a Kapp value of 4.1 x 10(5) M(-1) and displays oxidative cleavage of supercoiled DNA in the presence of H2O2 following a hydroxyl radical pathway. The complex also shows photo-induced DNA cleavage activity on UV light exposure involving formation of singlet oxygen as the reactive species.     

Synthesis and properties of a new member of the calixnaphthalene family: a C(2)-symmetrical endo-calix[4]naphthalene

The synthesis of a new endo-calix[4]naphthalene is described. The reaction sequence involves the cyclocondensation of a key bisnaphthylmethane intermediate (8) with formaldehyde. This key intermediate (8) is formed using a modified Suzuki-Miyaura Pd-catalyzed cross-coupling reaction between bromomethylnaphthyl (6) and naphthylboronic acid (7), both of which can be derived from 2-hydroxynaphthoic acid.     

Supramolecular peptide helix from a novel double turn forming peptide containing a β-amino acid

A single-crystal X-ray diffraction study of the terminally protected tetrapeptide Boc-β-Ala-Aib-Leu-Aib-OMe 1 (Aib: α-aminoisobutyric acid; β-Ala: β-Alanine) reveals that it adopts a new type of double turn structure which self-associates to form a unique supramolecular helix through intermolecular hydrogen bonds. Scanning electron microscopic studies show that peptide 1 exhibits amyloid-like fibrillar morphology in the solid state.     

Free energy of mixing of cross-linked polymer blends

Free energy of mixing of cross-linked polymer blends is derived, as a modification to the Flory-Huggins-de Gennes free energy functional for linear polymer blends. The latter arrives from the assumption of mean-field, short-range thermal interactions among ideal Gaussian chains. However, upon cross-linking a linear chain, the chain no longer remains Gaussian; new chain architectures belying the threadlike image of linear chains emerge. Fractal dimensions of these nonlinear chain clusters convene and command new entropic interactions. Topological constraints by cross-links introduce long-range nonequilibrium elastic forces. Relatively shorter range steric repulsions between fractal network surfaces may arrive if cross-linking is carried out inside the blend's thermodynamically unstable region. Modified free energy has been used to highlight experiments on phase instability of cross-linked polymer blends.     

Radiationless transitions in trivalent lanthanide ions embedded in solids

Radiationless transitions in lanthanide ions embedded in glassy and crystalline hosts have been briefly reviewed. The correlations of multiphonon relaxation rates with energy gaps, vibrational frequencies, temperatures and electronic symmetries have been discussed. The essence of various theories, such as Nth order methods, non-adiabatic Hamiltonian method, dynamic coupling model has also been presented.