5,029 research outputs found
The complexity of recognizing linear systems with certain integrality properties
Let A be a 0 - 1 matrix with precisely two 1's in each column and let 1 be the all-one vector. We show that the problems of deciding whether the linear system Ax ≥ 1,x ≥ 0 (1) defines an integral polyhedron, (2) is totally dual integral (TDI), and (3) box-totally dual integral (box-TDI) are all co-NP-complete, thereby confirming the conjecture on NP-hardness of recognizing TDI systems made by Edmonds and Giles in 1984. © 2007 Springer-Verlag.preprin
The circumference of a graph with no K3, t-minor
It was shown by Chen and Yu that every 3-connected planar graph G contains a cycle of length at least | G |log 3 2, where | G | denotes the number of vertices of G. Thomas made a conjecture in a more general setting: there exists a function β (t) > 0 for t ≥ 3, such that every 3-connected graph G with no K3, t-minor, t ≥ 3, contains a cycle of length at least | G |β (t). We prove that this conjecture is true with β (t) = log8 t t + 1 2. We also show that every 2-connected graph with no K2, t-minor, t ≥ 3, contains a cycle of length at least | G | / tt - 1. © 2006 Elsevier Inc. All rights reserved.preprin
On the soliton width in the incommensurate phase of spin-Peierls systems
We study using bosonization techniques the effects of frustration due to
competing interactions and of the interchain elastic couplings on the soliton
width and soliton structure in spin-Peierls systems. We compare the predictions
of this study with numerical results obtained by exact diagonalization of
finite chains. We conclude that frustration produces in general a reduction of
the soliton width while the interchain elastic coupling increases it. We
discuss these results in connection with recent measurements of the soliton
width in the incommensurate phase of CuGeO_3.Comment: 4 pages, latex, 2 figures embedded in the tex
Propagation Modes of 3D Scour below a Submarine Pipeline in Oblique Steady Currents and Waves
This paper presents experimental results on 3D scour propagation along a pipeline under oblique-incidence currents and waves. Different modes of 3D scour propagation were discovered after the local scour was initiated below the pipeline. These modes include scour propagation throughout the whole pipeline, onset of scour at multiple locations due to piping, termination of scour propagation induced by backfill and no scour propagation. The critical conditions for these scour propagation modes were determined in terms of flow incident angle, embedment depth and Shields parameter (or KC number)
Molecular-field approach to the spin-Peierls transition in CuGeO_3
We present a theory for the spin-Peierls transition in CuGeO_3. We map the
elementary excitations of the dimerized chain (solitons) on an effective Ising
model. Inter-chain coupling (or phonons) then introduce a linear binding
potential between a pair of soliton and anti-soliton, leading to a finite
transition temperature. We evaluate, as a function of temperature, the order
parameter, the singlet-triplet gap, the specific heat, and the susceptibility
and compare with experimental data on CuGeO_3. We find that CuGeO_3 is close to
a first-order phase transition. We point out, that the famous scaling law
\sim\delta^{2/3} of the triplet gap is a simple consequence of the linear
binding potential between pairs of solitons and anti-solitons in dimerized spin
chains.Comment: 7.1 pages, figures include
Multifractal analysis of complex networks
Complex networks have recently attracted much attention in diverse areas of
science and technology. Many networks such as the WWW and biological networks
are known to display spatial heterogeneity which can be characterized by their
fractal dimensions. Multifractal analysis is a useful way to systematically
describe the spatial heterogeneity of both theoretical and experimental fractal
patterns. In this paper, we introduce a new box covering algorithm for
multifractal analysis of complex networks. This algorithm is used to calculate
the generalized fractal dimensions of some theoretical networks, namely
scale-free networks, small world networks and random networks, and one kind of
real networks, namely protein-protein interaction networks of different
species. Our numerical results indicate the existence of multifractality in
scale-free networks and protein-protein interaction networks, while the
multifractal behavior is not clear-cut for small world networks and random
networks. The possible variation of due to changes in the parameters of
the theoretical network models is also discussed.Comment: 18 pages, 7 figures, 4 table
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