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.     

Electron escape time from single quantum wells

A theoretical model for electrons escaping a quantum well under the influence of an applied electric field is developed. Both the thermionic emission and tunneling components of the currents are calculated, taking into account the proper partitioning between the two currents. The group velocity for a nonuniform electron distribution within the quantum well, which is a function of position and energy, and the continuous energy dependence of the quantum well density of states is considered. A comparison between this model and previously reported experimental results are made which demonstrates excellent agreement     

Numerical calculations of temperature distribution of double layer metallic surface treated by laser beams

A mathematical model of laser beam treatment of double layer alloys (Ni/Fe, Al/Fe and Cr/Fe systems) describing the effect of laser beam on different physical and geometrical parameters of coated layer system has been adapted. The numerical solutions of the non-homogeneous heat-transport differential equation could estimate the temperature of the treated region.The suggested model allows investigation of the temperature distribution as a function of treated surface and laser parameters. The physical parameters of the treated materials were taken as functions of temperature due to the change in the temperature of the treated double layer materials.     

Bias dependence of high-frequency noise in heterojunction bipolar transistors

Hawkins' isothermal model developed to study noise in bipolar junction transistors (BJTs) is modified to investigate bias-dependent noise in heterojunction bipolar transistors (HBTs) by incorporating thermal effects. It is shown that the inclusion of thermal effects into the high-frequency noise model of HBTs is necessary as the temperature of the device may become very different from the ambient temperature, especially at high bias current. Calculation of the noise figure by including the thermal effect shows that the isothermal calculation may underestimate the noise figure at high bias current. It is observed that noise at low bias is ideality factor n dependent whereas high bias noise is insensitive to the variation of n. Moreover, the common base current gain plays a major role in the calculation of the minimum noise figure. The excellent fit obtained between the theoretical calculation and the measured data are attributed to the inclusion of the bias-dependent junction heating as well as C/sub De/ and C/sub bc/ into the present calculation.     

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.     

A comparison between reliability analyses based primarily on disjointness or statistical independence: The case of the generalized indra network

A switching expression is readily convertible to a reliability expression if (a) all ORed terms are disjoint, and (b) all ANDed sums are statistically independent. The usual approach of system reliability analysis makes a primary use of (a) and a secondary use of (b). An alternative approach reverses the roles of (a) and (b). Symbolic reliability expressions for the source-to-terminal reliability of a generalized Indra network (GIN) with nonidentical components are derived by the two approaches. For this particular case, the second approach leads to a shorter, more elegant derivation and simpler novel results. Typical plots of the GIN reliability functions are presented and their properties are discussed.     

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     

New pyranosyl cembranoid diterpenes from Sarcophyton trocheliophorum

During our continual searching programme for novel bioactive metabolites from Sarcophyton trocheliophorum, collected from Red Sea, we describe herein the isolation and structural elucidation of further two new pyrane-based cembranoid diterpenes: 9-hydroxy-7,8-dehydro-sarcotrocheliol (1) and 8,9-expoy-sarcotrocheliol acetate (2), along with the well-known sarcotrocheliol acetate (3), (+)-sarcophine (4), (+)-sarcophytoxide (5) and (-)-sarcophytoxide (6). The chemical structures of compounds 1 and 2 were determined on the basis of 1D and 2D NMR (¹H, ¹³C, ¹H–¹H COSY, HMQC, HMBC and NOE), mass spectra (ESI and HR-ESIMS) and by comparison with related structures. The antimicrobial activities of the reported compounds 1–6 were investigated. According to the molecular docking study of compounds 1–6 using 3D structure of α,β tubulin in complex with taxol (PDB code 1JFF) and epothilone A (PDB code 1TVK), sarcophine (4) displayed the highest affinity towards both crystal structures, followed by 5 and 6, meanwhile pyrane-based cembranoid diterpenes (1–3) showed less affinity.