Physical,chemical and biological studies on transition metal complexes of chelating tridentate ligand

Summary The interaction of 1-benzoin-4-phenylthiosemicarbazone (H₂ BPS) with some transition metal ions has been investigated. The ligand can function as a tridentate chelating agent, giving M(HBPS)₂ and M(BPS). Potentiometric studies proved that the mechanism of chelation is based on hydrogen ion liberation. Spectral studies in solution show that the ligand could be used for the microdetermination of Cu^IIions. On the basis of magnetic and spectral data, an octahedral structure is proposed for the Co^II and Ni^II complexes and a square-planar structure for the Cu^II complex. The corrosion inhibition of aluminium in Cl₃CCO₂H using H₂BPS is studied. The electrical conductivity of H₂BPS and of its complexes have been measured. The ligand shows an activation energy in the range of semiconducting materials. The antimicrobial activity of all compounds has also been demonstrated.     

In vitro surface biocompatibility of high-content silicon-substituted calcium phosphate ceramics

The present work investigates surface biocompatibility of silicon-substituted calcium phosphate ceramics. Different silicon-substituted calcium phosphate ceramic bodies were prepared from co-precipitated powders by sintering at 1300°C. The in vitro bioactivity of the ceramics was assessed in simulated body fluid (SBF) at 37°C for periods up to 4 weeks. The changes in the surface morphology and composition were determined by scanning electron microscopy (SEM) coupled with electron probe microanalysis and energy dispersive spectrometer (EDX). Inductively coupled plasma optical emission spectroscopy (ICP-OES) was used to observe the change in ionic concentration of SBF after removal of the samples. The bioactivity of the ceramics increased with an increasing silicate ion substitution in a systematic way. The surface of ceramics with 2.23% silicon substitution was partially covered with apatite layer after one week, while ceramics with 8.1% silicon substitution were completely covered with apatite in the first week. The porous microstructure of high-concentration Si-substituted ceramics helps the dissolution of surface ions and the leaching process. This allows SBF to reach supersaturation in a short time and accelerate the deposition of apatite layer.      

Novel Pyrano[2,3‐d]thiazole and Thiazolo[4,5‐b]pyridine Derivatives: One‐pot Three‐component Synthesis and Biological Evaluation as Anticancer Agents,c‐Met,and Pim‐1 Kinase Inhibitors

Preparation of pyrano[2,3‐d]thiazole and thiazolo[4,5‐b]pyridine derivatives through multicomponent reactions (MCRs) was achieved by the reaction of 2‐(2‐amino‐4,5,6,7‐tetrahydrobenzo[b]thiophen‐3‐yl)thiazol‐4(5H)‐one with various active methylene reagents such as ethyl cyanoacetate or malononitrile in basic conditions containing diverse aromatic aldehyde. Furthermore, this study aims to evaluate the in vitro cytotoxic activity of the synthetic compounds against six cancer cell lines, and all the prepared compounds revealed valuable activity compared with the CHS‐828, which is the 2‐[6‐(4‐chlorophenoxy)hexyl]‐1‐cyano‐3‐pyridin‐4‐ylguanidine as the standard drug. Some of the pyrano[2,3‐d]thiazole and thiazolo[4,5‐b]pyridine derivatives showed the highest antitumor activity towards the six cancer cell lines. Moreover, (c‐Met) enzymatic activity of the most potent compounds showed that compounds 3b 2‐(2‐amino‐4,5,6,7 tetrahydrobenzo[b]thiophen‐3‐yl)‐5‐hydroxy‐7‐(2‐hydroxy‐phenyl)‐7H‐pyrano[2,3‐d]thiazole‐6 carbonitrile and 5e 2‐(2‐amino‐4,5,6,7‐tetrahydrobenzo[b]thiophen‐3‐yl)‐5‐hydroxy‐7‐phenyl‐4,7‐dihydrothiazolo[4,5‐b]pyridine‐6‐carbonitrile were with higher activities than foretinib. Three compounds were selected to examine their Pim‐1 kinase where compounds 3b and 7b showed the highest inhibitions.     

The embedding conjecture for quasi-ordinary hypersurfaces

This paper has two objectives: we first generalize the theory of Abhyankar-Moh to quasi-ordinary polynomials, then we use the notion of approximate roots and that of generalized Newton polygons in order to prove the embedding conjecture for this class of polynomials. This conjecture-made by S.S. Abhyankar and A. Sathaye-says that if a hypersurface of the affine space is isomorphic to a coordinate, then it is equivalent to it.     

Exponential Attractor for a Nonlinear Boussinesq Equation

This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H0^2（0, 1） × L^2（0, 1）. The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H0^3（0, 1） × H0^1（0, 1）.     

A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients

We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order μ ∈ (0, 1) with variable coefficients. For the spatial discretization, we apply the standard continuous Galerkin method of total degree ≤ 1 on each spatial mesh elements. Well-posedness of the fully discrete scheme and error analysis will be shown. For a time interval (0, T) and a spatial domain Ω, our analysis suggest that the error in \(L^{2}\left ((0,T),L^{2}({\Omega })\right )\)-norm is \(O(k^{2-\frac {\mu }{2}}+h^{2})\) (that is, short by order \(\frac {\mu }{2}\) from being optimal in time) where k denotes the maximum time step, and h is the maximum diameter of the elements of the (quasi-uniform) spatial mesh. However, our numerical experiments indicate optimal O(k² + h²) error bound in the stronger \(L^{\infty }\left ((0,T),L^{2}({\Omega })\right )\)-norm. Variable time steps are used to compensate the singularity of the continuous solution near t = 0.     

On a perturbed anisotropic equation with a critical exponent

Abstract We study a perturbed anisotropic equation without using the knowledge of the limiting problem. This provides a different method from that introduced by Brézis and Nirenberg [4]. Our arguments use some tools recently developed in [5, 6]. Keywords: Anisotropic critical exponent, Critical level, Compactness, Nehari manifold Mathematics Subject Classification (2000): 35J25, 35J60, 35J65     

Statistical learning control of uncertain systems: theory and algorithms

It has recently become clear that many control problems are too difficult to admit analytic solutions. New results have also emerged to show that the computational complexity of some “solved” control problems is prohibitive. Many of these control problems can be reduced to decidability problems or to optimization questions. Even though such questions may be too difficult to answer analytically, or may not be answered exactly given a reasonable amount of computational resources, researchers have shown that we can “approximately” answer these questions “most of the time”, and have “high confidence” in the correctness of the answers.     

Long-Time Behavior for Second Order Lattice Dynamical Systems

Many researchers examined the existence of global attractors for various types of first and second order lattice dynamical systems. Here we prove the existence of a global attractor for a new type of second order lattice dynamical systems in the Hilbert space l ²×l ². For specific choices of the linear operators this system can be regraded as a spatial discretization of a continuous damped nonlinear Boussinesq equation on ℝ ^m ,m≥1.