On a class of new and practical performance indexes for approximation of fold bifurcations of nonlinear power flow equations

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse point) is one of the key problems in power system operations and planning and such an index indicates the severity of a power system with regard to voltage collapse. There exist many interesting methods and ideas to compute this index. However, some successful methods are not yet mathematically justified while other mathematically sound methods are often proposed directly based on the bifurcation theory and they require the initial stationary state to be too close to the unknown turning point to make the underlying methods practical.This paper first gives a survey of several popular methods for estimating the fold bifurcation point including the continuation methods, bifurcation methods and the test function methods (Seydel's direct solution methods, the tangent vector methods and the reduced Jacobian method) and discuss their relative advantages and problems. Test functions are usually based on scaling of the determinant of the Jacobian matrix and it is generally not clear how to determine the behaviour of such functions. As the underlying nonlinear equations are of a particular type, this allows us to do a new analysis of the determinants of the Jacobian and its submatrices in this paper. Following the analysis, we demonstrate how to construct a class of test functions with a predictable analytical behaviour so that a suitable index can be produced. Finally, examples of two test functions from this class are proposed. For several standard IEEE test systems, promising numerical results have been achieved.     

Exact solutions of solid-liquid phase-change heat transfer when subjected to convective boundary conditions

A closed-form expression is presented to find the location of solid-liquid interface motion in convection-dominated solidification and melting problems. In this regard, the solutions are expressed in terms of the generalized representations of error functions,E (u, v) andF (u, v), which are useful to heat-conduction problems with convective-type boundary conditions. It is demonstrated that for constant surface temperature, the interface solution reduces to the classical Neumann solution.     

Barium(II)–2,4‐dinitrophenolate–18‐crown‐6 at 183 K

The title compound, bis(2,4‐dinitrophenolato‐κ²O,O′)(1,4,7,10,13,16‐hexaoxadecane‐κ⁶O)barium(II), [Ba(C₆H₃N₂O₅)₂(C₁₂H₂₄O₆)], is a 1:1 complex of barium(II)–2,4‐di­nitro­phenolate and 1,4,7,10,13,16‐hexaoxa­cyclo­octa­decane (18‐crown‐6). Its structure is located on a crystallographic inversion centre. The temperature dependence of the crystal structure has been studied. The monoclinic β angle of the P2₁/­n space group increases with increasing temperature. The packing structure of the complex is stabilized by intermolecular C—H?O interactions.     

Numerical comparison of methods for solving second-order ordinary initial value problems

In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C²-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented.     

1‐Acetyl‐3′‐(4‐bromophenyl)‐3′‐chlorospiro[3H‐indole‐3,2′‐oxetan]‐2(1H)‐one

In the title compound, C₁₈H₁₃BrClNO₃, the heterocyclic ring of the indole is distorted from planarity towards an envelope conformation. The orientations of the indole, oxetane, chloro and bromo­phenyl substituents are conditioned by the sp³ states of the spiro‐junction and the Cl‐attached C atoms.     

Effect of some organic solvents and acids on the laser-induced atomic fluorescence of tin in air-hydrogen flames

The effects of some organic solvents and acids on the atomic fluorescence of tin in air-hydrogen flames have been examined. Ketones and alcohols greatly reduced the florescence sensitivity in fuel rich air-hydrogen flame whereas organic acids generally enhanced the fluorescence signal. The depressive effect of organic solvents was found to be highly dependent on the fuel to oxidant ratio in the flame. An attempt has been made to explain these effects, on the basis of possible reactions occurring in the flame.On leave from Institute of Chemistry, University of the Punjab, Lahore 54590, PakistanOn leave from Department of Analytical Chemistry, University of Zaragoza, Zaragoza, Spain     

Di‐2‐pyridyl ketone N4,N4‐(butane‐1,4‐diyl)thiosemicarbazone

The title compound, C₁₆H₁₇N₅S, is in the thione form and crystallizes with two independent mol­ecules in the asymmetric unit. In both mol­ecules, the penta­methyl­ene­imine five‐membered ring adopts an envelope conformation, and in one of the molecules this ring shows positional disorder. The thione S and hydrazine N atoms are in the Z configuration with respect to the C—N bond.     

Bis[1,1′‐bis(diphenylphosphino)ferrocenium] hexadecachlorotetraantimony(III) ethanol solvate

In the title compound, [Fe(C₁₇H₁₄P)₂]₂[Sb₄Cl₁₆]·C₂H₆O, the Fe atoms lie on inversion centres and the pairs of cyclopentadienyl rings are consequently in a fully staggered conformation. The centrosymmetric anionic clusters formed by [Sb₄Cl₁₆]^4? are surrounded by the cations and are held together by weak C—H?Cl interactions. These formations stack along the a axis to form columns, and the columns are interconnected by another weak C—H?Cl interaction along the b axis.     

Thermal studies of some aryloxides of titanium(IV)

Thermal behaviour of aryloxides of titanium(IV) of composition TiCl_n(OAr)_4?n (wheren=0→3 and OAr=OC₆Bu^t-4, OC₆H₄OMe-4 and OC₆H₂-Bu ₂ ^t -2,6?Me-4) has been studied by DTA and TG analysis. Multiple decomposition steps have been indicated by thermal weight losses which are both exothermic and endothermic as shown by DTA curves. Based upon the total % loss in weight; during entire decomposition titanium dioxide has been found to be the final residue in each case.     

不同温度下氨基酸在α-咖啡碱水溶液中的体积、粘度及折光率特性

Measurements of density(ρ), viscosity(η), and refractive index(n), were carried out on α-amino acids, DL-solution at 298.15, 303.15, 308.15, and 313.15 K. These measurements have been carried out to evaluate some important parameters, viz., apparent molar volume (φv), partial molar volume (φv0), transfer volume (φ0v (tr)), viscosity A and B coefficients of Jones-Dole equation, free energies of activation per mole of solvent (△μ0#1) and solute (△μ0#2),enthalpies (△H*) and entropies (△S*) of activation of viscous flow, variation of B with temperature ((a)B/(a)T)P, and molar refractive index (RD). These parameters have been interpreted in terms of solute-solute and solute-solvent interactions and structure making/breaking ability of solutes in the given solution.