Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.     

Synthesis of New Poly(biphenylene oxide) with Pendent Trifluoromethyl Group

A new AB type of monomer 4′-fluoro-3,5-dimethyl-3′-trifluoromethyl-biphenyl-4-ol has been synthesized that leads to a new poly(arylene ether) by self polycondensation reaction. The monomer and the polymer have been well characterized by elemental analyses, FT-IR and NMR spectroscopy. Both FT-IR and NMR spectra of the polymers did not show any terminal phenoxy group indicating high conversion. The polymer showed glass transition at 278°C and very good thermal stability in synthetic air. GPC results indicate high molar mass development; Mw = 53200 and MWD = 2.29.     

GPU‐accelerated direct numerical simulations of decaying compressible turbulence employing a GKM‐based solver

Gas Kinetic Method‐based flow solvers have become popular in recent years owing to their robustness in simulating high Mach number compressible flows. We evaluate the performance of the newly developed analytical gas kinetic method (AGKM) by Xuan et al. in performing direct numerical simulation of canonical compressible turbulent flow on graphical processing unit (GPU)s. We find that for a range of turbulent Mach numbers, AGKM results shows excellent agreement with high order accurate results obtained with traditional Navier–Stokes solvers in terms of key turbulence statistics. Further, AGKM is found to be more efficient as compared with the traditional gas kinetic method for GPU implementation. We present a brief overview of the optimizations performed on NVIDIA K20 GPU and show that GPU optimizations boost the speedup up‐to 40x as compared with single core CPU computations. Hence, AGKM can be used as an efficient method for performing fast and accurate direct numerical simulations of compressible turbulent flows on simple GPU‐based workstations. Copyright © 2016 John Wiley & Sons, Ltd.     

Preparation of 1,3-Dienes,its Application to the Synthesis of (Z,E)-9,11-Tetradecadienyl Acetate and (E,E)-10,12-Hexa-decadienal: Sex Pheromones of Cotton Pests

E-2-Penten-4-yn-1-ol (3) has been utilized as a source for 1,3-diene systems by employing lithium amide induced alkylation, and curpous iodide catalysed Grignard coupling reaction as key steps. Its application for the synthesis of (Z,E)-9,11-tetradecadienyl acetate and (E,E)-10,12-hexadecadienal is described.     

Microwave Thermolysis VII: Oxidative Coupling of Thiol Acetates and Esters Using “Clayan” in Dry Media

Disulfide bond formation by the oxidative cleavage of thiol acetates and thiol esters using “Clayan”s under microwave irradiation is described. The non-metallic and inexpensive nature of the reagent are the important features of the procedure.     

Total synthesis of attenols A and B

A concise approach for the total synthesis of attenols A and B is described involving MacMillan’s α-aminooxylation, Evan’s asymmetric alkylation, Brown’s allylation, and spiro-ketalization as key steps. This approach has successfully demonstrated the α-aminooxylation protocol for the construction of the anti-1,3-diol unit.     

Investigating Two-Photon-Induced Fluorescence in Rhodamine-6G in Presence of Cetyl-Trimethyl-Ammonium-Bromide

We investigate the effect of cetyl-trimethyl-ammonium-bromides (CTAB) concentration on the fluorescence of Rhodamine-6G in water. This spectroscopic study of Rhodamine-6G in presence of CTAB was performed using two-photon-induced-fluorescence at 780 nm wavelength using high repetition rate femtosecond laser pulses. We report an increment of ～10 % in the fluorescence in accordance with ～12 % enhancement in the absorption intensity of the dye molecule around the critical micellar concentration. We discuss the possible mechanism for the enhancement in the two-photon fluorescence intensity and the importance of critical micellar concentration.     

A proposal for experimental detection of amplitude nth-power squeezing

Recently, in several theoretical investigations, amplitude nth-power squeezing has been studied with n = 2, 3, 4, 5. In the present paper, we give a proposal for experimental detection of amplitude nth-power squeezing using ordinary homodyning with coherent light for arbitrary power n and discuss in detail its theory. The proposed scheme requires only repeated measurements of the factorial moments of number of photons in the light obtained after homodyning, with various shifts of phase of coherent light, and involves no approximations, whatsoever. This has advantage over the method proposed by Shchukin and Vogel [Phys. Rev. A 72 (2005) 043808] in that our method requires only one beam splitter and only one photodetector, and also lesser number of repetitions of experiment with phase-shifted coherent light.     

Synthesis,characterization, and antimicrobial activity of new benzofuran derivatives

Russian Journal of General Chemistry - A novel series of (5-substituted-1-benzofuran-2-yl)(2,4-substituted phenyl)methanones (4a–4i) have been prepared by the Knoevenagel condensation of...