Home About us Contact
|
Home About us Contact | ||
|
|
||
Lower Order (lower + order)
Selected AbstractsEfficient reduction of fault current through the grounding grid of a substation supplied by an overhead lineEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 3 2006Ljubivoje M. Popovi Abstract The paper presents a directly applicable and reasonably accurate method for the evaluation of the effects of the counterpoise, the measure for the reduction of the fault current through the substation grounding grid. Under practical conditions the magnitude of the current diverted from a substation grounding grid by the counterpoise conductor is a very complex function of the self and mutual impedances of overhead and underground conductors, substation grounding impedance, transmission line towers resistance, proximity effect between the grounding grid and the counterpoise conductor, as well as on many other factors of lower order. Therefore certain idealizations and simplification of the real physical model were indispensable to develop the mathematical model presented here. The obtained expressions are mostly based on the general equations of a line represented by its lumped parameters and the general equations of uniform ladder circuits. Copyright © 2006 John Wiley & Sons, Ltd. [source] Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matricesCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2007Percy Deift We prove universality at the edge of the spectrum for unitary (, = 2), orthogonal (, = 1), and symplectic (, = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e,V(x) where V is a polynomial, V(x) = ,2mx2m + · · ·, ,2m > 0. The precise statement of our results is given in Theorem 1.1 and Corollaries 1.2 and 1.4 below. For the same class of weights, a proof of universality in the bulk of the spectrum is given in [12] for the unitary ensembles and in [9] for the orthogonal and symplectic ensembles. Our starting point in the unitary case is [12], and for the orthogonal and symplectic cases we rely on our recent work [9], which in turn depends on the earlier work of Widom [46] and Tracy and Widom [42]. As in [9], the uniform Plancherel-Rotach-type asymptotics for the orthogonal polynomials found in [12] plays a central role. The formulae in [46] express the correlation kernels for , = 1, 4 as a sum of a Christoffel-Darboux (CD) term, as in the case , = 2, together with a correction term. In the bulk scaling limit [9], the correction term is of lower order and does not contribute to the limiting form of the correlation kernel. By contrast, in the edge scaling limit considered here, the CD term and the correction term contribute to the same order: this leads to additional technical difficulties over and above [49]. © 2006 Wiley Periodicals, Inc. [source] A new numerical approach for solving high-order non-linear ordinary differential equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2003Songping Zhu Abstract There have been many numerical solution approaches to ordinary differential equations in the literature. However, very few are effective in solving non-linear ordinary differential equations (ODEs), particularly when they are of order higher than one. With modern symbolic calculation packages, such as Maple and Mathematica, being readily available to researchers, we shall present a new numerical method in this paper. Based on the repeated use of a symbolic calculation package and a second-order finite-difference scheme, our method is particularly suitable for solving high-order non-linear differential equations arising from initial-value problems. One important feature of our approach is that if the highest-order derivative in an ODE can be written explicitly in terms of all the other terms of lower orders, our method requires no iterations at all. On the other hand, if the highest-order derivative in an ODE cannot be written explicitly in terms of all the other lower-order terms, iterations are only required before the actual time marching begins. Copyright © 2003 John Wiley & Sons, Ltd. [source] Poisoning the minds of the lower ordersJOURNAL OF THE HISTORY OF THE BEHAVIORAL SCIENCES, Issue 2 2001Mark Goldie fellow in history No abstract is available for this article. [source] | ||||||||||