Polynomial numerical hulls of matrix polynomials,II

In this article, we study some algebraic and geometrical properties of polynomial numerical hulls of matrix polynomials and joint polynomial numerical hulls of a finite family of matrices (possibly the coefficients of a matrix polynomial). Also, we study polynomial numerical hulls of basic A-factor block circulant matrices. These are block companion matrices of particular simple monic matrix polynomials. By studying the polynomial numerical hulls of the Kronecker product of two matrices, we characterize the polynomial numerical hulls of unitary basic A-factor block circulant matrices.     

Some relations between rank of a graph and its complement

Let G be a graph of order n and rank(G) denotes the rank of its adjacency matrix. Clearly, . In this paper we characterize all graphs G such that or n + 2. Also for every integer n ? 5 and any k, 0 ? k ? n, we construct a graph G of order n, such that .     

Monte Carlo method via a numerical algorithm to solve a parabolic problem

This paper is intended to provide a numerical algorithm consisted of the combined use of the finite difference method and Monte Carlo method to solve a one-dimensional parabolic partial differential equation. The numerical algorithm is based on the discretize governing equations by finite difference method. Due to the application of the finite difference method, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system. Numerical tests are performed in order to show the efficiency and accuracy of the present work.     

Ionic liquid-based dispersive liquid–liquid microextraction for determination of trace amounts of iron in water, rock and human blood serum samples

A green and sensitive dispersive liquid-phase microextraction procedure based on room-temperature ionic liquid (1-hexyl-3-methylimidazolium hexafluorophosphate) for preconcentration and determination of total iron in real samples prior to flame atomic absorption spectrometry was developed. 2-Mercaptopyridine-N-oxide (pyrithione) and ethanol were used as complexing agent and dispersive solvent in the proposed method, respectively. The factors influencing the extraction were optimized. Under optimum conditions, the enhancement factor of 15 was obtained from only 11.35 mL of aqueous phase. The linear dynamic range and the detection limit were 10.0–700 and 2.4 μg L^?1, respectively. The relative standard deviation (RSD) for ten replicate measurements of 500 μg L^?1 of iron is 3.1 %. The developed method has been successfully applied for the determination of iron in water samples, human blood serum and rock certified reference material with high efficiency.     

Efficient One-Pot Synthesis of Polyhydroquinoline Derivatives Using Silica Sulfuric Acid as a Heterogeneous and Reusable Catalyst Under Conventional Heating and Energy-Saving Microwave Irradiation

An efficient Hantzsch four-component condensation reaction for the synthesis of polyhydroquinoline derivatives was reported under two conditions: solvent-free conventional heating and energy-saving microwave irradiation. The process is simple and environmentally benign, and the use of a heterogeneous and reusable catalyst, high yields, and short reaction times are the key features of this protocol.     

Simultaneous kinetic-spectrophotometric determination of sulfide and sulfite and genetic algorithim variable selection using partial least squares calibration

Simultaneous multicomponent analysis is usually carried out using multivariate calibration models, such as the partial least squares (PLS) one, that utilize the full spectrum. It has been shown by both experimental and theoretical considerations that better results can by obtained by proper selection of the spectral range to be included in calculations. A genetic algorithm (GA) is one of the most popular methods for selecting variables for PLS calibration of mixtures with almost identical spectra without loss of predictive capability. In this work, a simple and precise method for rapid and accurate simultaneous determination of sulfide and sulfite ions based on the addition reaction of these ions with new fuchsin at pH 8 and 25°C using PLS regression and GA for variable selection is proposed. The concentrations of sulfide ions varied between 0.05–2.50 and 0.15–2.00 μg/mL, respectively. A series of model solutions containing different concentrations of sulfide and sulfite were used to check the predictive ability of GA-PLS models. The root mean square error of prediction with PLS on the whole data set was 0.19 μg/mL for sulfide and 0.09 μg/mL for sulfite. After the application of GA, these values reduced to 0.04 and 0.03 μg/mL, respectively. The text was submitted by the authors in English.     

Efficient one-pot synthesis of novel 6′,9′-dihydro-2H,7′H-spiro[pyrimidine-5,8′-[1,3]dioxolo[4,5-f]quinoline]-2,4,6(1H,3H)-trione derivatives under mild and “green” reaction conditions

In this paper, an efficient method is introduced for the synthesis of 7′,9′-disubstituted 6′,9′-dihydro-2H,7′H-spiro[pyrimidine-5,8′-[1,3]dioxolo[4,5-f]quinoline]-2,4,6(1H,3H)-trione derivatives under mild and “green” reaction conditions. The method is based on one-pot multicomponent reaction of an aldehyde, barbituric acid, and benzo[d][1,3]dioxol-5-amine in ethanol as a green and environmentally friendly solvent. The reaction has given the products in the highest isolated yield in the presence of acetic acid as catalyst under reflux conditions. Various aldehydes, bearing electron-donating or -withdrawing functionalities have been used under the optimized conditions and successfully gave the desired products (13 examples) in high isolated yields.     

π-Stacking effects on acid capacity of p-aminobenzoic acid

Structural Chemistry - Acidity changes of p-aminobenzoic acid (pABA) after π-stacking with substituted benzenes (SB) have been investigated using quantum mechanical calculations at the...     

Presentation of a new index for estimation of aromaticity in halo‐ and cyanobenzenes: The role of potential energy in aromaticity

A linear correlation has been obtained between average values of Hamiltonian kinetic energy ( ) and potential energy ( ) calculated at the bond critical points using atoms in molecules method. This relation was used to introduce a new index ( ) for estimation of aromaticity in halo‐ and cyanobenzenes. Potential energy has different terms such as attraction between nuclei and electrons, also repulsion of electrons which affect the inertia and mobility of electrons, respectively. Therefore, contribution of potential energy in this relation must be controlled. Contribution of potential energy in aromaticity has been managed using a fitting parameter. This parameter was obtained by fitting the aromaticity stabilization energy data with values of aromaticity calculated by index for halo‐ and cyanobenzenes. The contribution of potential energy in index is complete when molecule is nonaromatic and is negligible when molecule is antiaromatic. Indeed, molecule is aromatic when contribution of potential energy in index lies between above limits. © 2013 Wiley Periodicals, Inc.     

The O···H intramolecular hydrogen bond in 4‐X‐2‐hydroxybenzaldehydes: The relationships between geometrical parameters,estimated binding energies,and NMR data

The relationships among geometrical parameters, estimated binding energies, and nuclear magnetic resonance data in –C?O···H? O? intramolecular H‐bond of some substituted 2‐hydroxybenzaldehyde have theoretically been studied by B3LYP and MP2 methods with 6‐311++G** and AUG‐cc‐PVTZ basis sets. All substituents increase estimated hydrogen bond energies E_HBs (with the exception of NO₂ and C₂H₅), which are in good correlation with geometrical parameters, topological properties of electron density calculated at O···H bond critical points and ring critical points by using atoms in molecules method, the results of natural bond orbital analysis, and calculated nuclear magnetic resonance data. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010