Approximation of fuzzy integrals using fuzzy bernstein polynomials

In this paper, we approximate the integration of continuous fuzzy real number valued function of one and two variables. To do this, we use Bernstein-type fuzzy polynomials. Moreover, we obtain the error estimates for these approximations in terms of the modulus of continuity.     

Experimental Investigation on Upgrading of Lignin‐Derived Bio‐Oils: Kinetic Analysis of Anisole Conversion on Sulfided CoMo/Al2O3 Catalyst

Kinetics of the hydroprocessing of anisole, a compound representative of lignin‐derived bio‐oils, catalyzed by a commercial sulfided CoMo/Al₂O₃, was determined at 8–20 bar pressure and 573–673 K with a once‐through flow reactor. The catalyst was sulfided in an atmosphere of H₂ + H₂S prior to the measurement of its performance. Selectivity‐conversion data were used as a basis for determining an approximate, partially quantified reaction network showing that hydrodeoxygenation (HDO), hydrogenolysis, and alkylation reactions take place simultaneously. The data indicate that these reactions can be stopped at the point where HDO is virtually completed and hydrogenation reactions (and thus H₂ consumption) are minimized. Phenol was the major product of the reactions, with direct deoxygenation of anisole to give benzene being kinetically almost insignificant under our conditions. We infer that the scission of the C_methyl–O bond is more facile than the scission of the C_aromatic–O bond, so that the HDO of anisole likely proceeds substantially through the reactive intermediate phenol to give transalkylation products such as 2‐methylphenol. The data determine rates of formation of the major primary products. The data show that if oxygen removal is the main processing goal, higher temperatures and lower pressures are favored.     

(SiH)48X12 Heterofullerenes with the Group III and V Dopants: A DFT Prediction of Geometry,Stability, and Electronic Structure

We have applied DFT calculations to devise some (SiH)₄₈X₁₂ heterofullerenes with replacing of 12 Si–H units with a series of the group III and V dopants, P, N, As, B, Al and Ga, with the configuration of one dopant per pentagonal ring. Our results indicate that binding energies of heterofullerenes with group III dopants are smaller than those of heterfullerenes with group V dopants. Density of state obtained for the systems indicate a distinct change near the valence level compared to that of Si₆₀H₆₀, and a local energy level appears after the doping. (SiH)₄₈X₁₂ heterofullerenes with the group III and V dopants are composed of positively and negatively charged dopant atoms, each of which is surrounded by opposite charged Si atoms. The electrophilicity values of (SiH)₄₈X₁₂ heterofullerenes, except for (SiH)₄₈N₁₂, are greater than that of their parent. Because of the higher electronegativity of group V elements and electron transfer from the cages to the group V dopants, electrophilicity values for the (SiH)₄₈X₁₂ heterofullerenes with the group V dopants are always smaller than those of heterofullerenes with the group III dopants.