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.     

Variational spiked oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian –d ²/dr² +r ² +/r ^5/2,>0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).     

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.     

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.     

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.     

Retention, kinetics and thermodynamics profile of cadmium adsorption from iodide medium onto polyurethane foam and its separation from zinc bulk

The sorption behaviour of 2.5 × 10⁻⁵ M solution of Cd(II) on polyurethane foam (PUF) from iodide medium have been investigated. The conditions were optimized from aqueous solutions of different pH (1-10) and of acids of varied concentration (0.01-1.0 M). The maximum concentration of KI was found to be 0.24 M and equilibration time was established to be 20 min. The data successfully followed the Freundlich and Dubinin-Radushkevich (D-R) isotherms at low metal ion concentration while Langmuir isotherm followed at higher metal ion concentration. The Freundlich parameter 1/n = 0.66 ± 0.02 have been evaluated whereas D-R isotherm yields the sorption free energy E = 10.5 ± 0.1 kJ mol⁻¹ indicating ion exchange type chemisorption. The monolayer coverage (XL) constant of Langmuir isotherm was found to be 23.7 ± 0.4 mg g⁻¹. The numerical values of thermodynamics parameters enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) indicated the endothermic and spontaneous nature of sorption. The Scatchard plot analysis was tested to evaluate the binding sites of the PUF and stability constants of sorption were determined. On the basis of these parameters, the sorption mechanism was discussed. Among the foreign ions tested, Pb(II), Hg(II), cyanide and nitrite should be absent. The clean separation of Cd(II) from Zn(II) ions in the ratio 1:250, respectively, was achieved by column chromatography.     

Unsteady incompressible flow of magnetized aluminium oxide and titanium oxide nanoparticles with blood base fluid

In this investigation, a mixed convective nanoparticles fluid flow over an inclined plate is deliberated. The effects of slip boundary wall and magnetic field are also considered. The dimensionless governing system for the considered problem is attained by implementing recent definitions of fractional derivatives (FD). The generalized solution is obtained through the Laplace Transformation Scheme (LTS) for the momentum and thermal expressions. To improve the novelty and to demonstrate some more physical perception of the stated research work, some remarkable special cases of velocity distribution through CF and AB-fractional derivative concept are addressed, whose daily life implication is well known in the existing literature. Moreover, to evaluate the physical interest of the stated problem, the outcomes of the obtained system graphical illustrations are made by utilizing MATHEMATICA. As a result, we concluded that the aluminium oxide $A{l}_2{O}_3$ nanoparticles show more decaying behavior as compared to titanium oxide $Ti{O}_2$ nanoparticles for temperature and velocity profile. Furthermore, both fields i.e., momentum and thermal distributions are increased with the help of rising estimations parameter. Current results report novel applications in enhancement of heat transfer, thermal engineering, chemical processes, engineering and electronics devices, solar systems, extrusion processes, fission reactions etc.