On Berezin Number Inequalities for Operator Matrices

In this article, we refine certain earlier existing bounds for Berezin number of operator matrices. We also prove some new Berezin number inequalities for general n × n operator matrices.Further, we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator matrices. Finally, some interesting examples are discussed.     

A convenient synthesis of the enantiomerically pure (S)-2,4-dihydroxybutyl-4-hydroxybenzoate using hydrolytic kinetic resolution

(S)-2,4-Dihydroxybutyl-4-hydroxybenzoate was prepared in an extremely simple and practical way with high enantiomeric excess (99% ee) using Jacobsen’s Hydrolytic Kinetic Resolution technique as a key step and source of chirality.     

Solution properties of amitriptyline and its partitioning into lipid bilayers

Solution properties of a drug and its partitioning into lipid bilayers were studied for drug extraction using several different techniques, such as surface tension, zeta potential, ultra filtration and UV-Vis spectroscopy. From the surface tension study it was found that the presence of salt makes the drug molecules more surface-active. Zeta potential revealed the adsorption of the drug into the liposome bilayers to be governed mostly by electrostatic forces. The drug retention volume was expressed as a capacity factor, K, and that was normalized with respect to the amount of the immobilized phospholipids. The K-values for the positively charged drug on the liposomes decreased in the presence of phosphate buffer due to the presence of the oppositely charged ions. The above methods can thus be used to understand the mechanism of drug-membrane interaction and quantification of drug absorption into liposomes.     

Green Enzymatic Synthesis of L-Ascorbyl Fatty Acid Ester: An Antioxidant

In green chemistry, biocatalysis using microwaves is a very attractive tool for various regioselective syntheses. L-Ascorbyl fatty acid esters were synthesized by an immobilized lipase from Bulkholderia multivorans using microwaves, with a dynamically enhanced rate of reaction and appreciable yield of around 80%. Microwave radiation had no effect on enzymic inactivation, however, synergism between microwaves and biocatalyst was observed.     

Inorganic-Organic Hybrid Polymers from the Polymerisation of Methacrylate-Substituted Oxotantalum Clusters with Methylmethacrylate: A Thermomechanical and Spectroscopic Study

New inorganic-organic hybrid materials were prepared by free-radical polymerization of methyl methacrylate (MMA) with methacrylate-substituted oxotantalum cluster [Ta₄O₄(OEt)₈(OMc)₄] and their properties evaluated. The cluster was prepared by the reaction of the parent alkoxide with methacrylic acid. Samples of the hybrid materials were produced with Ta-cluster to methyl methacrylate in the ratios of 1:50 and 1:100 and were characterized by thermal and spectroscopic techniques. The glass transition temperatures of the hybrid materials are shifted to higher temperatures than pure PMMA as a result of cross-linking of the polymer by the oxotantalum clusters. The increase in T_g is also observed from the dynamic mechanical analysis (DMA). Evidence of crosslinking between the Ta-cluster and PMMA is obtained from infrared spectroscopic study. Surface studies performed by X-ray photoelectron spectroscopy (XPS) provide information about the atomic concentrations of the surface and indicate tantalum bonded to oxygen.     

Conformational changes of pyrene-labeled polyelectrolytes with pH: effect of hydrophobic modifications

Structural changes of pyrene-labeled and unlabeled poly(maleic acid/octyl vinyl ether) (PMAOVE) and poly(maleic acid/methyl vinyl ether) (PMAMVE) with changes in pH have been investigated in this study. The changes in the photophysical properties of pyrene are interpreted to investigate uncoiling or swelling of the polymeric chains with pH. The vibrational fine structure of the pyrene fluorescence (I(3)/I(1)) and the ratio between excimer and monomer fluorescence (I(e)/I(m)) of both pyrene-labeled and unlabeled PMAMVE and PMAOVE suggest that, at pH 4, the polymers are in the coiled form and PMAOVE forms hydrophobic nanodomains. An increase in pH ionizes a number of COOH groups on both PMAMVE and PMAOVE, which leads to the stretching or swelling of the polymers.     

Effects of Dielectric Barrier Discharge Plasma on Physicochemical Characteristics,Mechanical Properties and Biocompatibility of Silk/PVA Nanofibers

Plasma Chemistry and Plasma Processing - This work reports an investigation of the discharge characteristics of atmospheric dielectric barrier discharge (DBD) plasma in terms of I-V curves and...     

Cu (II) and Co (II/III) complexes of N,O‐chelated Schiff base ligands: DNA interaction,protein binding,cytotoxicity, cell death mechanism and reactive oxygen species generation studies

A series of copper (II) ( 1 and 3 ) and cobalt (II/III) ( 2 , 4 and 5 ) complexes comprising different imino‐phenolate ligands DCH , DTH and DBH ₂ (where DCH = 2,4‐dichloro‐6‐((mesitylimino)methyl)phenol, DTH = 2,4‐di‐tert‐butyl‐6‐((mesitylimino)methyl) phenol and DBH ₂ = 2,4‐dibromo‐6‐((mesitylimino)methyl)phenol) have been prepared with excellent yield and high purity. By utilizing different spectroscopic tools such as UV–visible, electrospray ionization (ESI)‐mass, Fourier‐transform infrared (FTIR) spectrometry and elemental analysis, the prepared complexes ( 1 – 5 ) were thoroughly characterized. The molecular structure of the synthesized complexes was ascertained by using single‐crystal X‐ray diffraction studies (SCXRDs). The experiment reveals that Complexes 1 – 5 bind to calf thymus DNA (CT‐DNA) through non‐intercalative way with good interacting abilities. However, 1 – 5 are excellent quenchers of the fluorescence intensity of bovine serum albumin (BSA) following the static pathway. Additionally, they had shown remarkable cytotoxic potential against MCF‐7 (mammary gland adenocarcinoma) and A549 (lung adenocarcinoma) cell lines. The IC₅₀ values associated with these complexes were much lower than the conventional drug cisplatin. Apoptosis‐induced cell death was confirmed from the DNA fragmentation studies and Hoechst 33342 staining. The 2′,7′‐dichlorofluorescein diacetate (DCFDA) assay indicates that the complex mediated reactive oxygen species (ROS) generation is accountable for governing the apoptosis mechanism via oxidative cell distress. Apart from these studies, by carrying out density functional theory (DFT) method, highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gap calculations and optimized structures of the synthesized complexes were accomplished.     

Fixed Points of Mappings Satisfying a Weakly Contractive Type Condition

In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak(k, k/) contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T_1 : X γ Y → X and T_2: X γ Y → Y be two operators which satisfy weak(k, k/) contractive type condition. Using T_1 and T_2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γ Y.We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings(T_1, T_2) satisfying weak(k, k/)contractive type condition on X γ Y and from this pair, we also obtain two self mappings S_1 and S_2 on X and Y respectively with unique fixed points.     

A Finite Element Galerkin Method for a Unidimensional Single-Phase Nonlinear Stefan Problem with Dirichlet Boundary Conditions

Based on straightening the free boundary, an H¹-Galerkin methodis proposed and analysed for a single-phase nonlinear Stefanproblem with Dirichlet boundary conditions. Optimal H¹ estimatesfor continuous-time Galerkin approximations are derived.