Puckering behavior in six new phosphoric triamides containing aliphatic six- and seven-membered ring groups and a database survey of analogous ring-containing structures

The influence of a N heteroatom on the ring conformations of six- and seven-membered aliphatic rings in six new C(O)NHP(O)-based phosphoric triamide structures (analysed by X-ray crystallography) is investigated. Additionally the influence of steric and crystal packing effects is also studied by the analysis of Hirshfeld surfaces. The results are compared to analogous structures with three- to seven- aliphatic membered rings deposited in the Cambridge Structural Database. In the newly determined structures, the six-membered rings only show the near-chair conformation with a maximum deviation of the θ puckering parameter of 4.4° from the ideal chair value of 0°/180°, while the seven-membered rings are found in different conformations such as near-chair, twist chair and twist sofa.     

Collocation method for the numerical solutions of Lane–Emden type equations using cubic Hermite spline functions

Three numerical techniques based on cubic Hermite spline functions are presented for the solution of Lane–Emden equation. Some properties of Hermite splines are presented and are utilized to reduce the solution of Lane–Emden equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of these techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

FRW cosmology from five dimensional vacuum Brans–Dicke theory

We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans–Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar field are not constants, the 5D equations, for any kind of geometry, admit a power–law relation between the scalar field and scale factor of the fifth dimension. Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant, [(w)\tilde]{\tilde{\omega}} . We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra dimensions for any kind of geometry without any priori assumption among them. For non-constant scalar fields and spatially flat geometries, solutions are found to be in the form of power–law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The power–law solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the solutions are more restricted. We illustrate that the accelerating power–law solutions, which satisfy the weak energy condition and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the condition ${\tilde{\omega} > -3/2}${\tilde{\omega} > -3/2} which prevents ghost scalar fields in the equivalent 4D vacuum Brans–Dicke equations. The results are presented in a few tables and figures.     

Numerical solution of nth‐order integro‐differential equations using trigonometric wavelets

The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro‐differential equations of nth‐order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredholm integro‐differential equations to the solution of algebraic equations. Furthermore, we get an estimation of error bound for this method. Copyright © 2011 John Wiley & Sons, Ltd.     

Different cyclic motifs in phosphoric triamides containing a C(O)NHP(O)(NH)2 skeleton and an R22(10) graph set in three new compounds: a database analysis of hydrogen‐bond strengths based on motifs

In the crystal networks of N,N′‐bis(2‐chlorobenzyl)‐N′′‐(2,6‐difluorobenzoyl)phosphoric triamide, C₂₁H₁₈Cl₂F₂N₃O₂P, (I), N‐(2,6‐difluorobenzoyl)‐N′,N′′‐bis(4‐methoxybenzyl)phosphoric triamide, C₂₃H₂₄F₂N₃O₄P, (II), and N‐(2‐chloro‐2,2‐difluoroacetyl)‐N′,N′′‐bis(4‐methylphenyl)phosphoric triamide, C₁₆H₁₇ClF₂N₃O₂P, (III), C=O...H—N_C(O)NHP(O) and P=O...H—N_amide hydrogen bonds are responsible for the aggregation of the molecules. This is the opposite result from that commonly observed for carbacylamidophosphates, which show a tendency for the phosphoryl group, rather than the carbonyl counterpart, to form hydrogen bonds with the NH group of the C(O)NHP(O) skeleton. This hydrogen‐bond pattern leads to cyclic R₂²(10) motifs in (I)–(III), different from those found for all previously reported compounds of the general formula RC(O)NHP(O)[NR¹R²]₂ with the syn orientation of P=O versus NH [R₂²(8)], and also from those commonly observed for RC(O)NHP(O)[NHR¹]₂ [a sequence of alternate R₂²(8) and R₂²(12) motifs]. In these cases, the R₂²(8) and R₂²(12) graph sets are formed through similar kinds of hydrogen bond, i.e. a pair of P=O...H—N_C(O)NHP(O) hydrogen bonds for the former and two C=O...H—N_amide hydrogen bonds for the latter. This article also reviews 102 similar structures deposited in the Cambridge Structural Database and with the International Union of Crystallography, with the aim of comparing hydrogen‐bond strengths in the above‐mentioned cyclic motifs. This analysis shows that the strongest N—H...O hydrogen bonds exist in the R₂²(8) rings of some molecules. The phosphoryl and carbonyl groups in each of compounds (I)–(III) are anti with respect to each other and the P atoms are in a tetrahedral coordination environment. In the crystal structures, adjacent molecules are linked via the above‐mentioned hydrogen bonds in a linear arrangement, parallel to [010] for (I) and (III) and parallel to [100] for (II). Formation of the N_C(O)NHP(O)—H...O=C instead of the N_C(O)NHP(O)—H...O=P hydrogen bond is reflected in the higher N_C(O)NHP(O)—H vibrational frequencies for these molecules compared with previously reported analogous compounds.     

Implicit constitutive relations in thermoelasticity

In this paper, after a brief discussion on the implicit constitutive relations used in thermoelasticity, based on Fox’s [1] work, we derive a general implicit relation for the heat flux vector. In the section following that we use the methodology suggested by Rajagopal [2] and [69] whereby we derive a class of implicit constitutive relations for q and we show that by selecting appropriate functions appearing in the formulation, we can obtain as special cases the Fourier heat conduction and the Maxwell-Cattaneo-Fox model. We do not discuss the implications of the second law of thermodynamics.     

A facile synthesis of novel pyrrolizidines under classical and ultrasonic conditions

Novel pyrrolizidines (1) were synthesized from 1,3-dipolar cycloaddition of azomethine ylides and dipolarophiles (4). The reactions were highly diastereoselective and regioselective and were carried out under reflux and ultrasonic condition at room temperature. In general, milder conditions and moderate improvements in rates and reaction times were observed when ultrasonic condition was used. The products were obtained in high yields, and their structures were determined by (1)H and (13)C NMR spectral data and X-ray diffraction.     

Ultrasonic degradation of Rhodamine B in the presence of hydrogen peroxide and some metal oxide

In this research, degradation of Rodamine B in the presence of (hydrogen peroxide), (hydrogen peroxide + ultrasound), (hydrogen peroxide + aluminum oxide), (hydrogen peroxide + aluminum oxide + ultrasound with different ultrasound power), (hydrogen peroxide + iron oxide) and (hydrogen peroxide + iron oxide + ultrasound with different ultrasound power) were investigated at 25 °C. The apparent rate constants for the examined systems were calculated by pseudo-first-order kinetics. The results indicate that the rate of degradation was accelerated by ultrasound. The rate of degradation was increased by increasing power ultrasound. The efficiency of the (hydrogen peroxide + iron oxide + ultrasound) system for degradation of Rodamine B was higher than the others examined.     

Oxygen Quenching of nπ* Triplet Phenyl Ketones: Local Excitation and Local Deactivation

We have studied the charge‐transfer‐induced deactivation of nπ* excited triplet states of benzophenone derivatives by O₂(³Σ), and the charge‐transfer‐induced deactivation of O₂(¹Δ_g) by ground‐state benzophenone derivatives in CH₂Cl₂ and CCl₄. The rate constants for both processes are described by Marcus electron‐transfer theory, and are compared with the respective data for a series of biphenyl and naphthalene derivatives, the triplet states of which have ππ* configuration. The results demonstrate that deactivation of the locally excited nπ* triplets occurs by local charge‐transfer and non‐charge‐transfer interactions of the oxygen molecule with the ketone carbonyl group. Relatively large intramolecular reorganization energies show that this quenching process involves large geometry changes in the benzophenone molecule, which are related to favorable Franck‐Condon factors for the deactivation of ketone‐oxygen complexes to the ground‐state molecules. This leads to large rate constants in the triplet channel, which are responsible for the low efficiencies of O₂(¹Δ_g) formation observed with nπ* excited ketones. Compared with the deactivation of ππ* triplets, the non‐charge‐transfer process is largely enhanced, and charge‐transfer interactions are less important. The deactivation of singlet oxygen by ground‐state benzophenone derivatives proceeds via interactions of O₂(¹Δ_g) with the Ph rings.