An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.     

Application of Gaussian quadrature method to characterize heavy ends of hydrocarbon fluids for modeling wax precipitation

The hydrocarbon plus fractions that comprise a significant portion of naturally occurring hydrocarbon fluids create major problems when determining the thermodynamic properties and the volumetric behavior of these fluids by equations of state. These problems arise due to the difficulty of properly characterizing the plus fractions (heavy ends). Proper characterization of the heavier components is important when cubic equations of state and/or solid formation thermodynamic models are used to describe complex phase behavior of reservoir fluids. The effect of heavy fractions characterization on thermodynamic modeling of wax precipitation has been investigated using different models including Won, Pan and proposed models. In order to characterize the plus fraction (heavier part) as a series of pseudocomponents, a probability model that expresses the mole fraction as a continuous function of the molecular weight has been used. The study has been conducted using several mixtures. Two different SCN (single carbon number), C₇₊${\text{C}}_{7^{+}}$ and C₁₀₊${\text{C}}_{{10}^{+}}$ were chosen. The Chosen SCN were distributed to multi-components of five, six, and/or ten using continuous function and Gaussian quadrature method. The results showed that the fractioning is required to be able to predict wax precipitation. Distribution of C₁₀₊${\text{C}}_{{10}^{+}}$ using a proper distribution function has shown improvement in predictions of WAT and the amount of wax deposited in comparison with the characterization of C₇₊${\text{C}}_{7^{+}}$ using semi-continuous approach. In predicting of WAT and the amount of wax build up the developed model showed superiority over the others.     

Solving multi-period interdiction via generalized Bender’s decomposition

This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.     

Synthesis and Cytotoxic Evaluation of Novel 1,2,3‐Triazole‐4‐Linked (2E,6E)‐2‐Benzylidene‐6‐(4‐nitrobenzylidene)cyclohexanones

This work describes the synthesis of novel 1,2,3‐triazole‐4‐linked (2E,6E)‐2‐benzylidene‐6‐(4‐nitrobenzylidene)cyclo‐hexanones starting from cyclohexanone. 1‐(Cyclohex‐1‐en‐1‐yl)piperidine, the enamine from cyclohexanone and piperidine, reacted with 4‐nitrobenzaldehyde to obtain 2‐(4‐nitrobenzylidene)cyclohexanone. Condensation of the latter compound with (prop‐2‐yn‐1‐yloxy)benzaldehyde derivatives under acidic conditions gave (4‐nitrobenzylidene)‐[(prop‐2‐yn‐1‐yloxy)‐benzylidene]cyclohexanones. Finally, ‘click reaction’ of these derivatives and various organic azides led to the title compounds. All compounds were examined by MTT assay for cytotoxic activity in one human breast cancer cell line, MDA‐MB‐231.     

Vibrational assignment, structure and intramolecular hydrogen bond study of 3-amino-1-phenyl-2-buten-1-one

Fourier transform infrared and Fourier transform Raman spectra of 3-amino-1-phenyl-2-buten-1-one and its deuterated analogue were recorded in the regions 400-4,000 and 150-4,000 cm(-1), respectively. Furthermore, the molecular structure and vibrational frequencies of title compound were investigated by a series of density functional theoretical, DFT, and ab initio calculations at the post-Hartree-Fock (MP2) level. Although, the calculated frequencies are generally in agreement with the observed spectra but the DFT results are in much better quantitative agreement with the observed spectra than the MP2 results. The observed wavenumbers were analyzed and assigned to different normal modes of vibration of the molecule. The calculated geometrical parameters show a strong intramolecular hydrogen bond with a N...O distance of 2.621-2.668 A. This bond length is shorter than that of its parent, 4-amino-3-penten-2-one (with two methyl groups in the beta-position), which is in agreement with spectroscopic results. The topological properties of the electron density contributions for intramolecular hydrogen bond in 3-amino-1-phenyl-2-buten-1-one and 4-amino-3-penten-2-one have been analyzed in term of the Bader theory of atoms in molecules (AIM). These results also support the stronger hydrogen bond in the title compound with respect to the parent molecule.     

A molecular orbital rationalization of ligand effects in N2 activation

Molecular orbital theory has been used to study a series of [(micro-N2){ML3}2] complexes as models for dinitrogen activation, with M=Mo, Ta, W, Re and L=NH2, PH2, AsH2, SbH2 and N(BH2)2. The main aims of this study have been to provide a thorough electronic analysis of the complexes and to extend previous work involving molecular orbital analyses. Molecular orbital diagrams have been used to rationalize why for L=NH2 ligand rotation is important for the singlet state but not the triplet, to confirm the effect of ligand pi donation, and to rationalize the importance of the metal d-electron configuration. The outcomes of this study will assist with a more in-depth understanding of the electronic basis for N2 activation and allow clearer predictions to be made about the structure and multiplicity of systems involved in transition-metal catalysis.     

The vibration-rotation emission spectrum of gaseous HZnCl

Gaseous HZnCl has been synthesized for the first time in a high-temperature tube furnace with a dc discharge in a flowing mixture of pure HCl and Zn vapor. The vibration-rotation emission spectrum of HZnCl was recorded at high resolution using a Fourier transform spectrometer. The H-Zn stretching modes (nu(1)) of the H(64)Zn(35)Cl, H(66)Zn(35)Cl, H(68)Zn(35)Cl, and H(64)Zn(37)Cl species, as well as the 2nu(1)-nu(1) hot band of the most abundant isotopologue H(64)Zn(35)Cl, were observed near 1966 cm(-1). A least-squares fit was performed for each of the four observed isotopologues, and their spectroscopic constants were determined.