Existence of positive solution for a sixth–order differential system with variable parameters

This paper investigates the existence of positive solutions for a sixth-order differential system with three variable parameters. Using a fixed point theorem and an operator spectral theorem we give some new existence results.     

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.     

High temperature enthalpy increment and thermodynamic functions of U2Ti

This study investigated thermodynamic properties of uranium–titanium alloy to determine its suitability for storage of hydrogen isotopes. The enthalpy increments of U₂Ti were measured using a high temperature inverse drop calorimeter in the temperature range of 299–1,169 K. Temperature dependence of the molar enthalpy increment and molar heat capacity is expressed in the form $ H^\circ_{\text{m}} (T) - H^\circ_{\text{m}} (298.15\,{\text{K}})({\text{J }}\,{\text{mol}}^{ - 1} ) = 23.236(T/{\text{K}}) + 53.292 \times 10^{ - 3} (T/{\text{K}})^{2} - 21.294 \times 10^{5} ({\text{K}}/T) - 4523 $ and $ C^\circ_{\text{p,m}} ({\text{J}}\,{\text{K}}^{ - 1} \,{\text{g}}^{ - 1} ) = 23.236 + 10.6584 \times 10^{ - 2} (T/{\text{K}}) + 21.294 \times 10^{5} ({\text{K}}/T)^{2} (300 \le T/{\text{K}} \le 900) $ , respectively. A set of self consistent thermodynamic functions such as entropy, Gibbs energy function, heat capacity, and Gibbs energy and enthalpy values for U₂Ti have been computed using data obtained in this study and required data from the literature.     

Regiospecific Functionalization of Cyclic Allenes with Catecholeorane

Reaction of diborane¹ and disiamylborane² with cyclic allenes, resulted in the formation of a mixture of products resulting from the addition of boron at the central carbon as well as terminal carbon. Fish has reported that addition of 4, 4, 6-trimethyl-1, 3, 2-dioxaborinane to 1, 3-disubstituted allenes takes place at the central carbon atom preferentially when the hydroboration was done at 130° for 35–50 h in a sealed tube.³ The reactivity and stability of catecholborane at high temperatures which is known to provide greater stearic     

Synthesis of Metal‐Free Phthalocyanines in Functionalized Ammonium Ionic Liquids

A convenient, fast, efficient, and ecofriendly synthesis of metal‐free phthalocyanines from various substituted phthalonitriles in different hydroxyalkylammonium ionic liquids in the presence of 1,8‐diazabicyclo‐[5,4,0]‐undec‐7‐ene (DBU) is reported in moderate yields. The effect of concentration of DBU and temperature on the synthesis of phthalocyanine in N‐(2‐hydroxyethyl)‐N,N‐dimethylbutylammonium bromide ionic liquid has been examined, and the ionic liquid has been recovered and reused conveniently.     

A silicon-position dependent 6-endo-trig cyclization during Tsuji–Trost alkylation

Two silylated cyclohexenes products have been prepared by using a Tsuji–Trost palladium-catalyzed cyclization. It involves the generation of a cationic π-allylic palladium complex bearing a triethylsilyl group on C-3, which cyclizes via a 6-endo-trig process to afford the cyclohexene derivatives. It is also demonstrated that the position of the silyl group on the starting allylic substrate strongly influenced the reaction. It could favor either the production of the expected cyclohexenyl ring or a diene by an elimination that occurs on the silyl-substituted C-2 π-allylic palladium complex.     

DIFFUSION MEASUREMENTS IN MICROEMULSIONS

We have carried out diffusion coefficient measurements in both aqueous micelles and microemulsions using the techniques of palaeography and quasielastic light scattering (QLS) The former method involves the determination of the diffusion coefficient of an electroactive oil soluble probe at a polarizable microelectrode. For high water content microemulsions, both methods yield the same diffusion coefficients, which can be identified as the self diffusion coefficient For cetyltrimethylammonium bromide (CTAB) micelles, both methods yield the same result at the salt (NaBr) concentration at which the QLS measurements are independent of CTAB concentration. In more concentrated microemulsions, QLS data gave diffusion coefficients in agreement with polarography only for a sodium cetyl sulfate (SCS) system at 65-75 wt % water. For the SCS microemulsions at 60% water, and CTAB microemulsion at 60-75% water, the QLS data yielded rapid, nonexponential decays. However, consistent polarographic diffusion coefficients could still be obtained, By using probes of varying chain length (oil solubility), it has been demonstrated that these CTAB and SCS microemulsions containing butanol and pentanol cosurfactants respectively, are not cosolubilized systems but do contain distinct hydrophilic and hydropobic regions.