A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...     

On position-space renormalization group approach to percolation

In a position-space renormalization group (PSRG) approach to percolation one calculates the probabilityR(p,b) that a finite lattice of linear sizeb percolates, wherep is the occupation probability of a site or bond. A sequence of percolation thresholdsp _c (b) is then estimated fromR(p _c ,b)=p _c (b) and extrapolated to the limitb to obtainp _c =p _c (). Recently, it was shown that for a certain spanning rule and boundary condition,R(p _c ,)=R _c is universal, and sincep _c is not universal, the validity of PSRG approaches was questioned. We suggest that the equationR(p _c ,b)=, where isany number in (0,1), provides a sequence ofp _c (b)'s thatalways converges top _c asb. Thus, there is anenvelope from any point inside of which one can converge top _c . However, the convergence is optimal if =R _c . By calculating the fractal dimension of the sample-spanning cluster atp _c , we show that the same is true aboutany critical exponent of percolation that is calculated by a PSRG method. Thus PSRG methods are still a useful tool for investigating percolation properties of disordered systems.     

Pathwise rate- stability for input-output processes

An input-output processZ = {Z(t), t 0} is said to be-rate stable ifZ(t) = o((t)) for some non-negative function(t). We prove that the processZ is -rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for-rate-stability can be verified from input data. For example, using input information, we establish-rate stability of the workload for multiserver queues, an ATM multiplexer, and-rate stability of queue-length processes for infinite server queues.     

Evaluation of the quality of colour changes of complexometric indicators in the titration of copper (II) with EDTA by tristimulus colorimetry

The quality of colour changes of the indicators hematoxylin, 4(2-pyridylazo)resorcinol (PAR), xylenol orange, pyrocatechol violet, chromazurolS and eriochrome cyanineR in the complexometric titration of copper(II) with ethylenediaminetetraacetic acid (EDTA) were studied with the help of tristimulus colorimetry, utilising a comparative study of the parameters SCD (specific colour discrimination), CIE La^*b^* 1976 and LABHNU 1977. Hematoxylin was found to be the best indicator among those studied. A screened indicator, viz. PAR + malachite green (52), was developed to enhance the quality of colour transition at the end-point and the accuracy of the titrimetric determination.     

A photochemical method for patterning the immobilization of ligands and cells to self-assembled monolayers

This work describes a chemically well defined method for patterning ligands to self-assembled monolayers (SAMs) of alkanethiolates on gold. This method begins with monolayers presenting a nitroveratryloxycarbonyl (NVOC)-protected hydroquinone which is photochemically irradiated to reveal a hydroquinone group. The resulting hydroquinone is then oxidized to the corresponding benzoquinone, providing a site for the Diels-Alder mediated immobilization of ligands. The rate constant for the photochemical deprotection is 0.032 s(-1) (with an intensity of approximately 100 mW/cm(2) between 355 and 375 nm), corresponding to a half-life of 21 s. The hydroquinone is oxidized to the benzoquinone using either electrochemical or chemical oxidation and then functionalized by reaction with a cyclopentadiene-tagged ligand. Two methods for patterning the immobilization of ligands are described. In the first, the substrate is illuminated through a mask to generate a pattern of hydroquinone groups, which are elaborated with ligands. In the second method, an optical microscope fit with a programmable translational stage is used to write patterns of deprotection which are then again elaborated with ligands. This technique is characterized by the use of well-defined chemical reactions to control the regions and densities of ligand immobilization and will be important for a range of applications that require patterned ligands for biospecific interactions.     

Complexation of Fluvastatin Sodium with β-Cyclodextrin: NMR Spectroscopic Study in Solution

¹H NMR spectroscopic study of fluvastatin sodium (FLU), β-Cyclodextrin (β-CD) and their mixtures confirmed the formation of FLU/β-CD inclusion complex in solution. The stoichiometry of the complex was determined to be 1:1 and the overall binding constant (K _s) was calculated to be 340 M⁻¹. Two dimensional COSY, ROESY and DEPTO experiments were performed for the unambiguous assignment of aromatic proton resonances and it was found that two isomeric forms of FLU are present in solution. It was confirmed with the help of ROESY spectral data that only F-substituted aromatic ring penetrates the β-CD cavity and there is chiral differentiation by the β-CD as one of the isomer binds more strongly, which is indicated by the intensity of correlation peaks. The mode of penetration of the guest into the β-CD cavity was also established and structure of the complex has been proposed.     

Spectroscopic Study on Interaction of β-Cyclodextrin with Triprolidine Hydrochloride

The complexation of triprolidine hydrochloride （TRP） and β-cyclodextrin （β-CD） in deuterium oxide was investigated by 400 MHz 1^H NMR spectroscopy. The 800 MHz 2D ROESY data revealed that two 1 ：1 and one 2 ： 1 β-CD-TRP inclusion complexes were formed. Both aromatic moieties （p-tolyl and pyridyl ring） has entered into the β-CD cavity, confirming the existence of two different equilibria for 1 ： 1 inclusion complexes in which p-tolyl ring of the guest is more tightly held by the host cavity. The ROE intermolecular interactions provided the plausible structures of these 1 ： 1 and 2 ： 1 stoichiometric inclusion complexes of β-CD-triprolidine hydrochloride in solu- tion.     

9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans

Reaction between some naphtho[2,1-b]pyrans and 1,1-diphenylethene affords 9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans.