A mixed integral equation in the quasi-static displacement problem

In this work, we solve the Fredholm-Volterra integral equation (FVIE) when the kernel takes a potential function form under given conditions. We represent this kernel in the Weber-Sonin integral form.     

Projectivity of Countable Direct Products

We show that if the direct product of countably many copies of a noetherian ring R is pure in a direct sum of finitely generated modules, then R satisfies the descending chain condition on two-sided ideals. This extends a recent result of Buchweitz and Flenner.     

Dinuclear gold (I)-di-N-heterocyclic carbene complexes: syntheses,structure, density functional theory calculation and photoluminescence study

The synthesis and characterizations for a series of dinuclear gold (I)-di-NHC complexes, 1–8 through the trans-metalation method of their respective silver (I)-di-NHC complexes, i–viii are reported (where NHC = N-heterocyclic carbene). The successful complexation of a series of unusual non-symmetrical and symmetrical di-NHC ligands, 3,3'-(ethane-1,2-diyl)-1-alkylbenzimidazolium-1'-butylbenzimidazolium (with alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, benzyl) with the gold (I) ions are suggested by elemental analysis, Fourier transform-infrared, ¹H- and ¹³C-NMR data. The ¹³C-NMR spectra of 1–8 show a singlet sharp peak in the range of 190.00–192.00 ppm, indicating the presence of a carbene carbon that bonded to the gold (I) ion. From single crystal X-ray diffraction data, the structure of complex 6 with the formula of [di-NHC-Au (I)]₂·2PF₆ is obtained [where NHC = 3,3'-(ethane-1,2-diyl)-1-hexylbenzimidazolium-1'-butylbenzimidazolium]. The photophysical study in solid state of 6 displays an intense photoluminescence with a strong emission maxima, λ_em = 480 nm, upon excitation at 340 nm at room temperature. Interestingly, the emission maximum at 77 K shows a structural character with a strong peak at 410 nm, a medium at 433 nm and a weak at 387 nm, accompanied by a tail band to about 500 nm.     

Structural characterization,thermal, DFT,cytotoxicity, and antimetastatic properties of cocaine complexes with La(III), Er(III), and Yb(III)

Research on Chemical Intermediates - Reaction of cocaine (Cn) with Ln(III) chloride salts [where Ln?=?La(III), Er(III), and Yb(III)] afforded complexes of the [Ln(Cn)Cl(OH2)3].2Cl type...     

Existence and nonexistence results for reaction-diffusion equations in product of cones

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.     

Effect of annealing on the electrical properties and refractive index of HgI2 single crystals

The effect of annealing on the electrical properties and the refractive index of red mercuric iodide (HgI₂) single crystals is investigated. The ac-impedance and phase angle were measured in the frequency range from 100 Hz to 10 kHz at different annealing temperatures. The ac-conductivity, dielectric constants, loss tangent and the refractive index as a function of frequency are determined. The results are discussed in terms of structural changes taking place as a result of the heat treatment of the HgI₂ single crystals.     

Dirichlet and Neumann boundary conditions for the pressure poisson equation of incompressible flow

In a recent paper Gresho and Sani showed that Dirichlet and Neumann boundary conditions for the pressure Poisson equation give the same solution. The purpose of this paper is to confirm this (for one case at least) by numerically solving the pressure equation with Dirichlet and Neumann boundary conditions for the inviscid stagnation point flow problem. The Dirichlet boundary condition is obtained by integrating the tangential component of the momentum equation along the boundary. The Neumann boundary condition is obtained by applying the normal component of the momentum equation at the boundary. In this work solutions for the Neumann problem exist only if a compatibility condition is satisfied. A consistent finite difference procedure which satisfies this condition on non-staggered grids is used for the solution of the pressure equation with Neumann conditions. Two test cases are computed. In the first case the velocity field is given from the analytical solution and the pressure is recovered from the solution of the associated Poisson equation. The computed results are identical for both Dirichlet and Neumann boundary conditions. However, the Dirichlet problem converges faster than the Neumann case. In the second test case the velocity field is computed from the momentum equations, which are solved iteratively with the pressure Poisson equation. In this case the Neumann problem converges faster than the Dirichlet problem.     

Isolation of a Reactive Tricoordinate α‐Oxo Gold Carbene Complex

The [(P,P)Au=C(Ph)CO₂Et]⁺ complex 3 [where (P,P) is an o‐carboranyl diphosphine ligand] was prepared by diazo decomposition at ?40 °C. It is the first α‐oxo gold carbene complex to be characterized. Its crystallographic structure was determined and DFT calculations have been performed, unraveling the key influence of the chelating (P,P) ligand. The gold center is tricoordinate and the electrophilicity of the carbene center is decreased. Complex 3 mimics transient α‐oxo gold carbenes in a series of catalytic transformations, and provides support for the critical role of electrophilicity in the chemoselectivity of phenol functionalization (O?H vs. C?H insertion).     

Method Development and Quantitative Elemental Analysis of Mentha Longifolia L. Leaves from Saudi Arabia by Total Reflection X-Ray Fluorescence

A method has been developed for the quantitative elemental analysis of Mentha longifolia L. leaves collected from different cities in Saudi Arabia using total reflection X-ray fluorescence. Using a microwave digestion system, 100?mg of each sample was completely digested using 3?mL of nitric acid and 2?mL of hydrogen peroxide. The stabilization of the digested samples on the silicon reflectors was studied using a silicone solution and polyvinyl alcohol. 5?µL of either silicone solution or polyvinyl alcohol (1% m/v) was pipetted and dried on the silicon reflector prior to the deposition of the digested samples. It was recognized that there is some enhancement on the intensity of the peak area with the silicone solution at photon energies less than 11?keV. However, the obtained results confirm the ability of using silicone solution or polyvinyl alcohol (1% m/v) as the stabilizer prior to the deposition of the sample droplet on the quartz reflector. However, the silicone solution was more applicable. Based on the developed method, 15 elements were quantified, namely, P, S, Cl, K, Ca, Ti, Cr, Mn, Fe, Cu, Zn, Br, Rb, Sr, and Ba. Based on the present quantitative analysis results, M. longifolia samples collected from Al-Madina city had the highest concentration of P, Cl, K, Ti, Fe, Ni, and Cu. The lowest concentrations of P, S, Cl, K, Mn, Ni, and Br were found in Taif-Shafa.