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Order N. (order + n)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

Muffin-Tin Orbital Wannier-Like Functions for Insulators and Metals

CHEMPHYSCHEM, Issue 9 2005
Eva Zurek
Abstract Herein, we outline a method that is able to generate truly minimal basis sets that accurately describe either a group of bands, a band, or even just the occupied part of a band. These basis sets are the so-called NMTOs, muffin-tin orbitals of order N. For an isolated set of bands, symmetrical orthonormalization of the NMTOs yields a set of Wannier functions that are atom-centered and localized by construction. They are not necessarily maximally localized, but may be transformed into those Wannier functions. For bands that overlap others, Wannier-like functions can be generated. It is shown that NMTOs give a chemical understanding of an extended system. In particular, orbitals for the , and , bands in an insulator, boron nitride, and a semimetal, graphite, will be considered. In addition, we illustrate that it is possible to obtain Wannier-like functions for only the occupied states in a metallic system by generating NMTOs for cesium. Finally, we visualize the pressure-induced s,d transition. [source]

Codiameters of 3-connected 3-domination critical graphs

JOURNAL OF GRAPH THEORY, Issue 1 2002
Yaojun Chen
Abstract A graph G is 3-domination critical if its domination number , is 3 and the addition of any edge decreases , by 1. Let G be a 3-connected 3-domination critical graph of order n. In this paper, we show that there is a path of length at least n,2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76,85, 2002 [source]

The proof of a conjecture of Bouabdallah and Sotteau

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2004
Min Xu
Abstract Let G be a connected graph of order n. A routing in G is a set of n(n , 1) fixed paths for all ordered pairs of vertices of G. The edge-forwarding index of G, ,(G), is the minimum of the maximum number of paths specified by a routing passing through any edge of G taken over all routings in G, and ,,,n is the minimum of ,(G) taken over all graphs of order n with maximum degree at most ,. To determine ,n,2p,1,n for 4p + 2,p/3, + 1 , n , 6p, A. Bouabdallah and D. Sotteau proposed the following conjecture in [On the edge forwarding index problem for small graphs, Networks 23 (1993), 249,255]. The set 3 × {1, 2, , , ,(4p)/3,} can be partitioned into 2p pairs plus singletons such that the set of differences of the pairs is the set 2 × {1, 2, , , p}. This article gives a proof of this conjecture and determines that ,n,2p,1,n is equal to 5 if 4p + 2,p/3, + 1 , n , 6p and to 8 if 3p + ,p/3, + 1 , n , 3p + ,(3p)/5, for any p , 2. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 292,296 2004 [source]

The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEs

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2005
A. S. Fokas
Let q(x,t) satisfy a nonlinear integrable evolution PDE whose highest spatial derivative is of order n. An initial boundary value problem on the half-line for such a PDE is at least linearly well-posed if one prescribes initial conditions, as well as N boundary conditions at x = 0, where for n even N equals n/2 and for n odd, depending on the sign of the highest derivative, N equals either n,1/2 or n+1/2. For example, for the nonlinear Schrödinger (NLS) and the sine-Gordon (sG), N = 1, while for the modified Korteweg-deVries (mKdV) N = 1 or N = 2 depending on the sign of the third derivative. Constructing the generalized Dirichlet-to-Neumann map means determining those boundary values at x = 0 that are not prescribed as boundary conditions in terms of the given initial and boundary conditions. A general methodology is presented that constructs this map in terms of the solution of a system of two nonlinear ODEs. This formulation implies that for the focusing NLS, for the sG, and for the two focusing versions of the mKdV, this map is global in time. It appears that this is the first time in the literature that such a characterization for nonlinear PDEs is explicitly described. It is also shown here that for particular choices of the boundary conditions the above map can be linearized. © 2005 Wiley Periodicals, Inc. [source]