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1.
Graphene nanoflakes (GNFs) are predicted to possess novel magnetic, optical, and spintronic properties. They have recently been synthesized and a number of applications are being studied. Here we investigate the statistical properties of rippled GNFs (50–5,000 atoms) at $\text{ T}=300$ K. An adjacency matrix is calculated from the coordinates and we find that the free energy, enthalpy, entropy, and atomic displacement all show power law behavior. The vibrational energy versus the Wiener index also shows power law character. We distinguish between using Euclidean topographical indices and compare them to topological ones. These properties are determined from atomic coordinates using MATLAB routines. 相似文献
2.
In this note a representation of the discrete Green's function of a compact discretization of a two point boundary value problem of order n 2 is given which among other things allows a direct proff of the convergence (and divergence) properties. 相似文献
3.
A matricial computation of quadrature formulas for orthogonal rational functions on the unit circle, is presented in this paper. The nodes of these quadrature formulas are the zeros of the para-orthogonal rational functions with poles in the exterior of the unit circle and the weights are given by the corresponding Christoffel numbers. We show how these nodes can be obtained as the eigenvalues of the operator Möbius transformations of Hessenberg matrices and also as the eigenvalues of the operator Möbius transformations of five-diagonal matrices, recently obtained. We illustrate the preceding results with some numerical examples. 相似文献
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A. Bultheel 《Journal of Computational and Applied Mathematics》1984,10(3):301-328
A set of formulas is given for the relations that exist between the first and last block now or column of the inverse of a block Hankel or Toeplitz matrix. This is related to making arbitrary steps in a matrix Padé table. 相似文献
6.
Adhemar Bultheel 《Journal of Computational and Applied Mathematics》2010,235(4):927-949
We study particular sequences of rational matrix functions with poles outside the unit circle. These Schur-Nevanlinna-Potapov sequences are recursively constructed based on some complex numbers with norm less than one and some strictly contractive matrices. The main theme of this paper is a thorough analysis of the matrix functions belonging to the sequences in question. Essentially, such sequences are closely related to the theory of orthogonal rational matrix functions on the unit circle. As a further crosslink, we explain that the functions belonging to Schur-Nevanlinna-Potapov sequences can be used to describe the solution set of an interpolation problem of Nevanlinna-Pick type for matricial Schur functions. 相似文献
7.
In this paper, we study the computation of the moments associated to rational weight functions given as a power spectrum with known or unknown poles of any order in the interior of the unit disc. A recursive algebraic procedure is derived that computes the moments in a finite number of steps. We also study the associated interpolatory quadrature formulas with equidistant nodes on the unit circle. Explicit expressions are given for the positive quadrature weights in the case of a polynomial weight function. For rational weight functions with simple poles, mostly real or uniformly distributed on a circle in the open unit disc, we also obtain expressions for the quadrature weights and sufficient conditions that guarantee that they are positive. The Poisson kernel is a simple example of a rational weight function, and in the last section, we derive an asymptotic expansion of the quadrature error. 相似文献
8.
Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad 《Numerical Algorithms》1992,3(1):91-104
Leta 1,...,a p be distinct points in the finite complex plane ?, such that |a j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ0, μ π (j) , ν π (j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?* outside {a 1,...,a p,b 1,...,b p}. 相似文献
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We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416. 相似文献