Upper bounds on the coarsening rate of discrete,ill‐posed nonlinear diffusion equations

We prove a weak upper bound on the coarsening rate of the discrete‐in‐space version of an ill‐posed, nonlinear diffusion equation. The continuum version of the equation violates parabolicity and lacks a complete well‐posedness theory. In particular, numerical simulations indicate very sensitive dependence on initial data. Nevertheless, models based on its discrete‐in‐space version, which we study, are widely used in a number of applications, including population dynamics (chemotactic movement of bacteria), granular flow (formation of shear bands), and computer vision (image denoising and segmentation). Our bounds have implications for all three applications. © 2008 Wiley Periodicals, Inc.     

Novel metal complexes containing 6-methylpyridine-2-carboxylic acid as potent α-glucosidase inhibitor: synthesis,crystal structures,DFT calculations,and molecular docking

Molecular Diversity - The World Health Organization (WHO) report shows that diabetes mellitus (DM) will be one of the ten deadly diseases in the near future. The best way to prevent DM is to...     

Oxalic acid removal from wastewater using multi-walled carbon nanotubes: Kinetic and equilibrium analysis

Oxalic acid adsorption from aqueous solution is studied in this work. Multi-walled carbon nanotubes (MWCNT) were used as an adsorbent. The investigated adsorption variables are equilibrium time, initial acid concentration, and temperature. The experimental results were presented using equilibrium isotherm and kinetic models. The used equilibrium models are Langmuir, Freundlich, and Temkin adsorption isotherms. And the kinetic models are Elovich, Lagergren pseudo-first-order and pseudo-second-order kinetic models. The thermodynamics studies were carried out at three different temperatures: 278, 298, and 318 K. Langmuir isotherm was the best fitted equilibrium model for the experimental data. The all applied kinetic models fitted the data suitably.     

Complexation of metal ions with the novel azathia crown ethers carrying anthracene pendant in acetonitrile–dichloromethane

A series of crown ethers carrying an anthracene group with nitrogen–sulfur donor atom, which differ in having three, four and five sulfur atoms in the macrocycle was designed and synthesized by the reaction of the corresponding macrocyclic compound and 9-chloromethyl-anthracene. The influence of metal cations such as Al³⁺, Zn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Mn²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺ on the spectroscopic properties of the ligands was investigated in acetonitrile–dichloromethane (1:1) by means of absorption and emission spectrometry. Absorption spectra show isosbestic points in the spectrophotometric titration of Al³⁺, Zn²⁺, Fe²⁺, Fe³⁺, Cu²⁺, Hg²⁺ and Pb²⁺ the results of which disclosed the complexation compositions and complex stability constants of the novel ligands with these cations. The monoazapentathia crown ether showed sensitivity for Al³⁺ with linear range and detection limit of 2.6 × 10⁻⁶ M–2.6 × 10⁻⁵ M and 8.1 × 10⁻⁷ M, respectively.     

Spectroscopic Studies and Crystal Structure of 4-(2-Hydroxy-3-Methoxybenzylideneamino)-<Emphasis Type="Italic">N</Emphasis>-(5-Methylisoxazol-3-yl) Benzenesulfonamide

Abstract  

Schiff base 4-[(2-hydroxy-3-methoxybenzylideneamino)-N-(5-methylisoxazol-3-yl)benzene-sulfonamide has been synthesized from the reaction of 4-amino-N-(5-methylisoxazol-3-yl)benzenesulfonamide(sulfamethoxazole) with 2-hydroxy-3-methoxybenzaldehyde. It has been characterized by elemental analysis, MS, IR, ¹H NMR, ¹³C NMR, HETCOR and UV–Visible techniques. The structure of it also has been examined crystallographically. For the compound exist as dominant form of enol-imines in both the solid state and the solutions. It crystallizes in the monoclinic space group P2₁/c with a = 8.2694(7), b = 8.3453(5), c = 26.260(2) ?, β = 97.142(7) °, V = 1798.1(2) ?³, D _x  = 1.431 g cm⁻³, R ₁ = 0.0529 and wR ₂ = 0.1370 [I > 2σ(I)], respectively.     

Synthesis,Spectroscopic Studies and Structure of 2-[(Benzo[<Emphasis Type="Italic">d</Emphasis>]thiazol-2-ylamino)methyl]phenol

Abstract  

Schiff base (E)-2-[(benzo[d]thiazol-2-ylimino)methyl]phenol (1) has been synthesized from the reaction of 2-hydroxy-benzaldehyde with 2-aminobenzothiazole. The 2-[(benzo[d]thiazol-2-ylamino)methyl]phenol (2) was prepared reduction of the Schiff base 1 with sodium borohydride. The compounds 1 and 2 have been characterized by elemental analysis, FT-IR, ¹H-NMR, ¹³C-NMR and UV–visible spectroscopic techniques. The structure of the compound 2 has also been examined crystallographically. The compound 2 crystallizes in the monoclinic space group P2/c. The unit cell parameters were found as a = 10.017(1), b = 11.725(1), c = 10.341(1) ?, V = 1208.1(1) ?³, D _x = 1.409 g cm⁻³ and Z = 4. The crystal structure was solved by direct methods and refined by the full-matrix least squares method and found as R ₁ = 0.0308 and wR ₂ = 0.0818 for 2032 for the observed reflections [I > 2σ(I)].     

Effect of Ge4+ and Mg2+ doping on superconductivity,fluctuation induced conductivity and interplanar coupling of TlSr2CaCu2O7−δ superconductors

Substitution of Ge⁴⁺ in place of Cu in Tl_0.85Cr_0.15Sr₂CaCu_2?xGe_xO_7?δ (x = 0–0.6) showed initial increase in zero critical temperature value, T_{c zero} from 98 K (x = 0) to 100 K (x = 0.1) and in the range of 85–86 K for x = 0.2–0.3. The slow decrease in T_{c zero} is unexpected as tetravalent Ge⁴⁺ substitution is expected to strongly reduce hole concentration in the samples and suppress T_{c zero}. Excess conductivity analyses of resistance versus temperature data based on Asmalazov–Larkin (AL) theory revealed that the substitution induced 2D-to-3D transition of fluctuation induced conductivity with the highest transition temperature, T_2D–3D observed at x = 0.1. FTIR spectroscopy analysis indicates Ge⁴⁺ substitution cause reduction in CuO₂/GeO₂ interplanar distance while our calculation based on Lawrence–Doniach model revealed highest superconducting coherence length, ξ_c(0) and interplanar coupling, J at x = 0.3. On the other hand, substitution of divalent Mg²⁺ for Ca²⁺ in (Tl_0.5Pb_0.5)(Sr_1.8Yb_0.2)(Ca_1?yMg_y)Cu₂O₇ (y = 0–1.0), which is not expected to directly vary hole concentration, surprisingly caused T_{c zero} to increase from 89.6 K (y = 0) to an optimum value of 95.9 K (y = 0.6) before decreasing with further increase in y. Excess conductivity analyses showed 2D-to-3D transition of fluctuation induced conductivity for all samples where the highest T_2D–3D was at y = 0.4. Similar calculation revealed highest values of ξ_c(0) and J also at y = 0.4. FTIR analysis of the samples indicates inequivalent Cu(1)O(2)Pb/Tl lengths and possible tilting of CuO₂ plane as a result of Mg²⁺ substitution. The increased ξ_c(0) and J as a result of the Ge⁴⁺ and Mg²⁺ substitutions are suggested to contributed to sustenance of superconductivity above 80 K in the samples.     

On the solvability of initial boundary value problems for nonlinear time-dependent Schrödinger equations

In this paper, we study the initial boundary value problems for a nonlinear time-dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin’s method.     

Upper Maximal Graphs of Posets

We introduce and study a class of simple graphs, the upper-maximal graphs (UM-graphs), associated to finite posets. The vertices of the UM-graph of a given poset P are the elements of P, and edges are formed by those vertices x and y whenever any maximal element of P that is greater than x is also greater than y or vise versa. We show that the class of UM-graphs constitutes a subclass of comparability graphs. We further provide a characterization of chordal UM-graphs, and compare UM-graphs with known bound graphs of posets.