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.     

Integrability of subdifferentials of directionally Lipschitz functions

Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of subdifferentials of such functions over arbitrary Banach space.

     

Modeling Media with Oriented Structures

Heterogeneity is typically the result of space variability of soil parameters at different scales. Soil anisotropy may be defined as the spatial persistence in some direction only, across coarse-grid elements, of heterogeneous structures with different characteristic lengths in different directions. One can account for the effect of these structures by upscaling soil properties. Analyzing flow in a strongly anisotropic structured soil at different scales evidences how transverse dispersion reduces to a subscale process, leading to mixing within the conductive structures.     

Simple and efficient cleavage reaction of the boc group in heterocyclic compounds

Dedicated to the memory of Pr. Ladjama Daif A series of chiral cyclosulfamides have been synthesized by alkaline cyclisation starting from N‐benzoylamino acids (Ala, Val, Leu, Phe) derivatives and chlorosulfonyl isocyanate. A simplified and regioselective deprotection of the cyclic compounds (cyclosulfamides) containing the tert‐butyloxycarbonyl group (Boc) has been achieved in good yield by fusion under reduced pressure.     

Novel ethero atoms containing polyesters based on 2,6‐naphthalendicarboxylic acid: A comparative study with poly(butylene naphthalate)

Poly(butylene naphthalate) (PBN), poly(diethylene naphthalate) (PDEN), and poly(thiodiethylene naphthalate) (PTDEN) were synthesized and characterized in terms of chemical structure and molecular weight. The polyesters were examined by TGA, DSC, and DMTA. All the polymers showed a good thermal stability, even though depending on chemical structure. At room temperature they appeared as semicrystalline materials; the effect of the introduction along the PBN polymer chain of ether oxygen atoms or sulfur ones was a lowering in the T_g value, a decrement of T_m, and a decrease of the crystallization rate. Changing in chemical structure also affects the main α absorption associated with the glass transition which moves to lower temperature and whose energetic requirements decrease. The results were explained as due to the presence of highly flexible C? S? C or C? O? C bonds in the polymeric chain. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1694–1703, 2007     

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.     

Surface characterization of recycled tire rubber to be used in cement paste matrix

The surface modification of tire rubber after treatment with saturated NaOH aqueous solution was investigated by HATR infrared analysis, potentiometric titration, and contact angle measurements. Infrared analysis of the powdered treated rubber showed a decrease in absorption at 1540, 1450, and 1395 cm(-1). This decrease is attributed to the removal of zinc stearate, an additive present in tire formulations that often migrates and diffuses to the surface, resulting in poor adhesion between the rubber and other materials. The potentiometric titration of the suspension of powdered rubber in 0.1 M NaCl showed that more hydrochloric acid was consumed by the untreated rubber, most likely a result of the hyrdrolysis of the zinc stearate to the organic acid. Contact angles of flat tire pieces showed an homogeneity enhancement of the treated rubber surface. The decrease of the zinc stearate on the treated rubber surface explains the improvement in the adhesion of this material to the cement matrix, observed in a previous research. The promising results of this study are a starting point for future research on incorporating rubber particles into cementitious materials as a means of successfully utilizing the vast amounts of tire waste currently in landfills.     

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.