A Note on the Generalized and Universal Associated Legendre Equations

A class of second-order differential equations commonly arising in physics applications are considered,and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated Legendre Equations are examined and established. The hypergeometric solutions, presented in this work,will promote future investigations of their mathematical properties and applications to problems in theoretical physics.     

Wavelet neural network based on islanding detection via inverter‐based DG

In this article, a passive neurowavelet based on islanding detection technique for grid‐connected inverter‐based distributed generation has been developed. Connecting distributed generator to the distribution network has many benefits such as increasing the capacity of the grid and enhancing the power quality. However, it gives rise to many problems. This is mainly due to the fact that distribution networks are designed without any generation units at that level. Hence, integrating distributed generators into the existing distribution network is not problem‐free. Unintentional islanding is one of the encountered problems. Islanding is the situation where the distribution system containing both distributed generator and loads is separated from the main grid as a result of many reasons such as electrical faults and their subsequent switching incidents, equipment failures, or preplanned switching events like maintenance. The proposed method utilizes and combines wavelet analysis and artificial neural network to detect islanding. Discrete wavelet transform is capable of decomposing the signals into different frequency bands. It can be utilized in extracting discriminative features from the acquired voltage signals. Passive schemes have a large nondetection zone (NDZ) and concern has been raised on active method due to its degrading power quality effect. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. The simulations results, performed by MATLAB/Simulink, shows that the proposed method has a small NDZ. Also, this method is capable of detecting islanding accurately within the minimum standard time. © 2014 Wiley Periodicals, Inc. Complexity 21: 309–324, 2015     

Solvable systems of linear differential equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.     

An investigation of hydrogen-bonding effects on the nitrogen and hydrogen electric field gradient and chemical shielding tensors in the 9-methyladenine real crystalline structure: a density functional theory study

Hydrogen-bonding effects in the real crystalline structure of 9-methyladenine, 9-MA, were studied using calculated electric field gradient, EFG, and chemical shielding, CS, tensors for nitrogen and hydrogen nuclei via density functional theory. The calculations were carried out at the B3LYP and B3PW91 levels with the 6-311++G basis set via the Gaussian 98 package. Nuclear quadrupole coupling constants, C(Q), and asymmetry parameters, eta(Q), are reported for (14)N and (2)H. The chemical shielding anisotropy, Deltasigma, and chemical shielding isotropy, sigma(iso), are also reported for (15)N and (1)H. The difference between the calculated parameters of the monomer and heptameric layer-like cluster 9-MA shows how much H-bonding interactions affect the EFG and CS tensors of each nucleus. This result indicates that N(10) (imino nitrogen) has a major role in H-bonding interactions, whereas that of N(9) is negligible. There is good agreement between the present calculated parameters and reported experimental data. Although some discrepancies were observed, this could be attributed to the different conditions which were applied for calculation and the experiments.     

2-Aminophenyl diphenylphosphinite as an easily accessible ligand for heterogeneous palladium-catalyzed Suzuki-Miyaura reaction in water in the absence of any organic co-solvent

In this article, we have introduced application of 2-aminophenyl diphenylphosphinite as an easily accessible ligand for heterogeneous palladium-catalyzed Suzuki-Miyaura reaction in water in the absence of any organic co-solvent. By using 2-aminophenyl diphenylphosphinite as a ligand and Pd(OAc)₂ as the pre-catalyst, structurally different aryl halides (I, Br, Cl) were reacted efficiently with phenylboronic acid in water to produce their corresponding biphenyl products in good to excellent yields under heterogeneous conditions. The catalyst is recyclable and was recycled for seven runs for the reaction of bromobenzene with phenylboronic acid without appreciable loss of its catalytic activity.     

Quantum deficits and correlations of two superconducting charge qubits

Motivated by recent experiments [Y.A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D.V. Averin, J.S. Tsai, Nature 421 (2003) 823] that show coherent oscillations of two superconducting qubits system, we consider a system of two charge qubits coupled to a common stripline microwave resonator. We discuss the separable and entangled behavior as well as the quantum and classical information deficits. Numerical computation of these quantities is performed for several regimes. We find that for less entangled states the partner can extract much more information by means of classical communication and local operations.     

A one-pot, efficient, and odorless synthesis of symmetrical disulfides using organic halides and thiourea in the presence of manganese dioxide and wet polyethylene glycol (PEG-200)

Primary, secondary, tertiary, allylic, and benzylic halides are converted efficiently into symmetric disulfides in high yields using thiourea as the sulfur atom source. The reactions are odorless and are performed at 30-35 °C in wet PEG-200 using MnO₂ as an oxidant.     

Aluminium dodecatungstophosphate (AlPW12O40) as a highly efficient catalyst for the selective acetylation of -OH, -SH and -NH2 functional groups in the absence of solvent at room temperature

AlPW12O40 was found to be an effective catalyst for the selective acetylation of alcohols, thiols, and amines in the absence of solvent at room temperature.     

A density functional study of N NQR parameters of imidazole derivatives and extrapolation to PfHRP2–Fe-PPIX complex

In this paper, density functional theory (DFT) was used to calculate ¹⁴N nuclear quadrupole coupling constants (NQCC), χ, and asymmetry parameters, η, for a series of imidazole derivatives: imidazole, 5-methylimidazole and histidine. These calculations were carried out with the PW91P86 method via the Gaussian 98 package. A systematic theoretical investigation of the different environmental effects on (χ, η) values of amino ¹⁴N1 and imino ¹⁴N2 of imidazole ring of these compounds, reveals that the local surrounding of nitrogen atoms play an important role in determining their χ and η values. Our calculations in solution show that adding explicit solvent molecules to the polarizable continuum model (PCM) has a strong effect on (χ, η) values, thereby indicating that for long-range effects, PCM, is not sufficient to describe the whole solvent effects. We also evaluate the influence of [Fe³⁺ (S = 1/2)] on the (χ, η) values of proximal and remote nitrogens of an axial ligand and compare with those of free ligands. The results show that Fe³⁺ has a strong effect on the (χ, η) values of proximal nitrogen unlike remote nitrogen. Finally, our results predict (χ = 1.56 MHz, η = 0.690) for proximal nitrogen and (χ = 2.75 MHz, η = 0.169) for remote nitrogen in PfHRP2–Fe³⁺-PPIX complex.     

Synthesis of 5′-azido- and 5′-amino-2′,5′-dideoxynucleosides from quinazoline-2,4(1H,3H)-diones

Quinazoline-2,4(1H,3H)-diones 4 were silylated and condensed with methyl 5-azido-2,5-dideoxy-3-O-(4-methylbenzoyl)-α,β-D-erythro-pentofuranoside (3) using trimethylsilyl trifluoromethanesulfonate (TMS triflate) as the catalyst to afford the corresponding 5′-azidonucleosides 5 . 1-(5-Azido-2,5-dideoxy-α-D-erythro-pentofuranosyl)quinazoline-2,4(1H,3H)-diones 6 and the corresponding β anomers were obtained by treating 5 with sodium methoxide in methanol at room temperature. 6-Methyl-1-(5-amino-2,5-dideoxy-β-D-erythro-pentofuranosyl)quinazoline-2,4(1H,3H)-dione (8) was obtained by treatment of the corresponding azido derivative 7 with triphenylphosphine in pyridine, followed by hydrolysis with ammonium hydroxide.