Spectral asymptotics and basis properties of fourth order differential operators with regular boundary conditions

In this paper, we consider the problem where λ is a spectral parameter; q(x) ∈ L₁(0,1) is complex‐valued function; α_s, s = 1,2,3, are arbitrary complex constants that satisfy α₂ = α₁ + α₃ and σ = 0,1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established. It is proved that all the eigenvalues, except for finite number, are simple and the system of root functions of this spectral problem forms a basis in the space L_p(0,1), 1 < p < ∞ , when ; moreover, this basis is unconditional for p = 2. We note that the considered problem was previously investigated in the condition of α₂ ≠ α₁ + α₃. Copyright © 2013 John Wiley & Sons, Ltd.     

Thermal Decomposition Kinetics of Some Metal Complexes of 2,3-Hydroxyimino-4-phenyl-6-phenyazo-1-thia-4,5-diazacyclohexa-5-diene

The Ni(II), Cu(II) Co(II) and Zn(II) complexes of 2,3‐hydroxyimino‐4‐phenyl‐6‐phenyazo‐1‐thia‐4,5‐diaza‐ cyclohexa‐5‐diene (H₂L) were synthesized. Thermal behavior of these complexes was studied in dynamic nitrogen atmosphere by TA (thermogravimetric analysis), DTA (differential thermal analysis) and DTG (differential thermal gravimetry) techniques. The reaction order, the activation energies, the entropies, the enthalpies, the free energies, and the pre‐exponential factors of the thermal decomposition reactions were calculated from the thermogravimetric curves. The kinetic analysis of the thermogravimetric data was performed by using several methods such as MacCallum‐Tanner (MT), van Krevelen (vK), Madhusudanan‐Krishnan‐Ninan (MKN), Wanjun‐Yuwen‐Hen‐Cunxin (WYHC), Horowitz‐Metzger (HM) and Coats‐Redfern method (CR) based on the single heating rate. Most appropriate methods were determined for each decomposition step according to the least‐square linear regression. The Ni(II), Cu(II) Co(II) and Zn(II) complexes displayed one‐ or two‐stage decomposition pattern when heating in a dynamic nitrogen atmosphere and metal oxides remained as end products of the complexes. The characterization of the end products of the decomposition was performed by X‐ray diffraction.     

Monomer/polymer Schiff base copper(II) complexes for catalytic oxidative polymerization of 2,2′‐dihydroxybiphenyl

Catalytic oxidative polymerization of 2,2′‐dihydroxybiphenyl (DHBP) was performed by using both the Schiff base monomer‐Cu(II) complex and Schiff base polymer‐Cu(II) complex compounds as catalysts and hydrogen peroxide as oxidant, respectively. The dependence of monomer conversion and molecular weight distribution on various reaction parameters, including time, temperature, solvent as well as the amount of catalyst and oxidant were investigated. The structure of the poly‐2,2′‐dihydroxybiphenyl (PDHBP) was confirmed by UV‐vis, IR, ¹H and ¹³C NMR spectroscopy techniques. The electrochemical and thermal properties of PDHBP were also studied. DSC data revealed that PDHBP was amorphous. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2977–2984, 2009     

Comparison of Exact and Perturbative Results for Two Metrics

We compare the exact and perturbative results in two metrics and show that the spurious effects due to the perturbation method do not survive for physically relevant quantities such as the vacuum expectation value of the stress-energy tensor.     

A two‐grid stabilization method for solving the steady‐state Navier‐Stokes equations

We formulate a subgrid eddy viscosity method for solving the steady‐state incompressible flow problem. The eddy viscosity does not act on the large flow structures. Optimal error estimates are obtained for velocity and pressure. The numerical illustrations agree completely with the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Characterisation of α-chitin extracted from a lichenised fungus species Xanthoria parietina

Lichens are symbiotic associations formed mainly by ascomycete fungi and green algae or cyanobacteria. The presence of chitin in the fungal cell wall has been revealed by previous studies. Considering the presence of fungi in the lichens, this work determines the presence of chitin in a cosmopolitan lichen species Xanthoria parietina. In this study, chitin was derived from a lichen species for the first time and its physicochemical properties were determined by Fourier transform infrared spectroscopy, thermogravimetric analysis, X-ray diffraction, scanning electron microscopy and elemental analysis. The dry weight chitin content of X. parietina was 4.23%, and this chitin was in the α-form. The crystalline index value of the lichen chitin was calculated as 70.1%. The chitin from X. parietina had a smooth surface.     

Opening Enediyne Scissors Wider: pH‐Dependent DNA Photocleavage by meta‐Diyne Lysine Conjugates

Photochemical activation of meta‐diynes incapable of Bergman and C1–C5 cyclizations still leads to efficient double‐strand DNA cleavage. Spatial proximity of the two arylethynyl groups is not required for efficient DNA photocleavage by the enediyne‐lysine conjugates. Efficiency of the cleavage is a function of the external pH and DNA damage is strongly enhanced at pH < 7. The pH‐dependence of the DNA photocleavage activity stems from the protonation states of lysine amino groups, the internal electron donors responsible for intramolecular PET quenching and deactivation of the photoreactive excited states. DNA‐binding analysis suggests intercalative DNA binding for phenyl substituted conjugate and groove binding for TFP‐substituted conjugate. Additional insights in the possible mechanism for DNA damage from the ROS (Reactive Oxygen Species) scavenger experiments found that generation of singlet oxygen is partially involved in the DNA damage.     

Theoretical study of substituent and solvent effects on the thermodynamics for <Emphasis Type="Italic">cis</Emphasis>/<Emphasis Type="Italic">trans</Emphasis> isomerization and intramolecular rearrangements of 2,2′-diphenoquinones

Enthalpies (Δ_isom H _(g)^o), Gibbs free energies (Δ_isom G _(g)^o), and equilibrium constants (log K _isom) for the trans → cis isomerization of various 3,3′-, 4,4′-, and 5,5′- disubstituted 2,2′-diphenoquinones with a range of electron withdrawing and releasing moieties (methyl, fluoro, chloro, bromo, trifluoromethyl, and amino) were calculated in the gas phase and in the solvent phase (n-hexane, benzene, n-octanol, acetonitrile, and water). In the gas phase, the trans isomer of the parent and all substituted 2,2′-diphenoquinones is predicted to be more thermodynamically stable than the cis configuration, with log K _isom ranging from −2.8 to −7.0. For all compounds, increasing solvent polarity/proticity progressively favors shifting the cis/trans equilibrium towards greater contributions of the cis configuration and substantially increases the log K _isom by up to 5.1 units relative to the gas phase. In polar protic and polar aprotic solvents, the estimated log K _isom ranges as low as −0.4, indicating significant populations of the cis isomers should be present. The findings support the polar solvent phase mechanistic predictions for a cis configuration of 2,2′-diphenoquinones participating in the thermal transformation of trans-2,2′-diphenoquinones to oxepino[2,3-b]benzofurans. With limited exceptions for some amino derivatives, the cis-2,2′-diphenoquinone to oxepino[2,3-b]benzofuran isomerization is expected to be thermodynamically favorable for all substituents/phases under consideration. The cis-2,2′-diphenoquinone to oxepino[2,3-b]benzofuran rearrangement is predicted to become less thermodynamically favored with increasing solvent polarity/proticity.     

Comparison of epithelial and fibroblastic cell behavior on nano/micro-topographic PCL membranes produced by crystallinity control

In this study, the relationship between the cellular morphology and the material surface topography was investigated. Poly(ε-caprolactone) (PCL) membranes were prepared in a wide range of surface wettabilities by means of crystallinity-controlled solvent casting process. Membrane surfaces were characterized by atomic force microscope (AFM), scanning electron microscope (SEM), and static/dynamic water contact angle measurements. It was found that solvent evaporation and non-solvent (methanol) addition to the solvent (THF) are the most decisive parameters to change the surface topography. The non-solvent addition and the decrease in solvent evaporation temperature from room temperature to -20 °C caused increased polymeric chain mobility and crystallization time. Such changes in crystallization parameters led to the formation of micro/nano-sized features on the membrane. Cell culture studies indicated that in contrast to Madin Darby kidney (MDBK) epithelial cells, L929 mouse fibroblast preferred rough and porous surfaces.     

Optimal residuals and the Dahlquist test problem

Numerical Algorithms - We show how to compute the optimal relative backward error for the numerical solution of the Dahlquist test problem by one-step methods. This is an example of a general...