TWO-VARIABLE JACOBI POLYNOMIALS FOR SOLVING SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Two-variable Jacobi polynomials, as a two-dimensional basis, are applied to solve a class of temporal fractional partial differential equations. The fractional derivative operators are in the Caputo sense. The operational matrices of the integration of integer and fractional orders are presented. Using these matrices together with the Tau Jacobi method converts the main problem into the corresponding system of algebraic equations. An error bound is obtained in a two-dimensional Jacobi-weighted Sobolev space. Finally, the efficiency of the proposed method is demonstrated by implementing the algorithm to several illustrative examples. Results will be compared with those obtained from some existing methods.     

When a line graph associated to annihilating-ideal graph of a lattice is planar or projective

Let (L,∧, ∨) be a finite lattice with a least element 0. AG(L) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L, and two distinct vertices I and J are adjacent if and only if I ∧ J = 0. We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by L(AG(L)), is a planar or projective graph.     

Efficient Ce(NO3)3 x 6H2O-catalyzed solvent-free synthesis of 3,4-dihydropyrimidin-2(1H)-ones

Cerium(III) nitrate hexahydrate efficiently catalyzes the three-component Biginelli reaction under solvent-free conditions of an aldehyde, a beta-keto ester or beta-diketone and urea or thiourea to afford the corresponding 3,4-dihydropyrimidin-2(1H)-ones or -thiones in excellent yields.     

Simultaneous in-situ measurements of gas temperature and pyrolysis of biomass smoldering via X-ray computed tomography

In-situ X-ray computed tomography (XCT) imaging is employed to investigate the smoldering dynamics of biomass at the sub-millimeter scale. This technique provides simultaneous and spatially-resolved information about the gas temperature and the biomass density, thereby enabling tracking of the pyrolysis and char oxidation fronts. To achieve well-controlled heating and flow conditioning, oak biomass samples are instrumented above a diffusion flame inside a tube, with total oxygen concentrations of 6% and 11% per volume. Experiments are performed on a laboratory XCT system. The flow is diluted with Kr to increase X-ray attenuation in the gas phase thus allowing for simultaneous 3D measurements of sample density and surrounding temperature. XCT scans are acquired every 90 s at a spatial resolution of 135 µm. The high spatial resolution enables the volumetric visualization of the smoldering process that is associated with pyrolysis and char oxidation. These measurements show how the grain structure affects flame stabilization and induces fingering of the pyrolysis front, while crack formation accelerates the char oxidation locally. Evaluations of the sample mass via XCT are compared with load cell measurements, showing good agreement. A low-order model is developed to evaluate the propagation speeds of pyrolysis and oxidation fronts from the X-ray data over time, and comparisons are made with the surface recess speed.     

Three-Component Reaction of 5,5-Dimethylcyclohexan-1,3-dione,Aromatic Aldehydes,and Acetonitrile in the Presence of Chlorosulfonic Acid Forming N-[(2-Hydroxy-4,4-dimethyl-6-oxocyclohexene-1-yl)-aryl-methyl]-acetamides

A three-component reaction between 5,5-dimethylcyclohexan-1,3-dione (dimedone), aromatic aldehydes, and acetonitrile in the presence of chlorosulfonic acid afforded N-[(2-hydroxy-4,4-dimethyl-6-oxocyclohexene-1-yl)-aryl-methyl]-acetamides in good yields. The temperature-dependent ¹H NMR of one of the products has been investigated.     

Zn[(L)proline]2: An Efficient Catalyst for the Synthesis of Biologically Active Pyrano[2,3-d]pyrimidine Derivatives

Biologically active pyrano[2,3-d]pyrimidine derivatives were efficiently synthesized in excellent yields by a three-component, one-pot condensation reaction of malononitrile, benzaldehydes, and barbituric acid using a catalytic amount of Zn[(L)proline].     

Performance of gold- and silver-coated magnetic nanoparticles as carriers for horseradish peroxidase

Noble metal nanoparticles have a great potential for biological studies. In the present work, gold-coated magnetic nanoparticles (GMNPs) and silver-coated magnetic nanoparticles (SMNPs) were synthesized at different conditions and used as carrier for the immobilization of horseradish peroxidase (HRP). UV/Vis spectroscopy and scanning electron micrograph were used for nanoparticles characterization. Also surface conductivity of MNPs, GMNPs and SMNPs was investigated by LCR meter to be 34.5, 78 and 57.4 μS, respectively. The change in secondary structure, enzymatic activity, direct electrochemistry and HRP bioactivity were studied in the presence of either GMNPs or SMNPs. The attached HRP on GMNPs and SMNPs showed quasi-reversible cyclic voltammograms with the formal potential of ?305 and ?269 and peak separation of 230 and 302 mV, respectively. In addition, HRP/GMNPs/Au and HRP/SMNPs/Au electrodes responded to hydrogen peroxide in the linear concentration range from 0.72 to 25.92 and 1.62 to 19.62 μM, respectively.     

Nitration of Aromatic Compounds Catalyzed by Divanadium-Substituted Molybdophosphoric Acid, H5[PMo10V2O40]

The nitration of aromatic compounds was carried out in the presence of divanadium-substituted molybdophosphoric acid, H₅PMo₁₀V₂O₄₀, as catalyst and a mixture of nitric acid and acetic anhydride as nitrating agent. In the presence of this heteropolyacid the ortho- and para-nitro compounds were obtained in good to excellent yields under mild reaction conditions.