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71.
We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms
can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling,
we also allow for a second neighbor coupling. It is shown, how to apply the 2π
k method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate
our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit
along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily
on the strength of the second neighbor interaction. 相似文献
72.
We consider a mathematical problem modelling some characteristics of near field optical microscope.We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem.Some numerical examples to show the feasibility of the method are presented. 相似文献
73.
Huanan Wang Yi Zuo Qin Zou Lin Cheng Di Huang Li Wang Yubao Li 《Journal of polymer science. Part A, Polymer chemistry》2009,47(3):658-669
Based on a biomimetic conception, nano‐hydroxyapatite (n‐HA)/polyamide66 (PA66) composite scaffolds were prepared with anisotropic properties both in morphology and mechanical behavior. A novel improved thermally induced phase separation (TIPS) technique was developed to generate orientation‐structured scaffolds for tissue engineering. The physiochemical, morphological, and mechanical properties of the resultant scaffolds were evaluated. According to the results, the improved TIPS method exhibited good processability and reproducibility and enabled the composite scaffolds to have a high content of inorganic fillers. The morphological study proved that the n‐HA/PA66 scaffolds exhibited unidirectional microtubular architecture with high porosity (ca. 80–85%) and an optimal pore size ranging from 200 to 500 μm. Besides, the effect of n‐HA content on the morphology of the scaffolds was studied, and the results indicated that the obtained scaffolds presented an improvement in anisotropic morphology with increase of n‐HA content. The anisotropy was also evaluated in the mechanical properties of the scaffolds, that is, the longitudinal compressive strength and modulus were ~1.5 times of the transverse ones. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 658–669, 2009 相似文献
74.
A unification of some factorization results regarding products of positive-definite matrices, commutators, and products of involutions is presented. This topic was first presented by Sourour for fields with, in the latter two classes, sufficiently many elements in terms of the order of the matrix being factored. The current presentation is valid for matrices over any field with at least four elements, and is independent of the order of the matrix being factored. 相似文献
75.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》2005,133(1):155-162
In this paper, relationships among the concepts, majorization, range inclusion, and factorization, are studied in a general setting for bounded linear operators. Some applications of these concepts are given.
76.
There have been a few recent numerical implementations of the stress‐jump condition at the interface of conjugate flows, which couple the governing equations for flows in the porous and homogenous fluid domains. These previous demonstration cases were for two‐dimensional, planar flows with simple geometries, for example, flow over a porous layer or flow through a porous plug. The present study implements the interfacial stress‐jump condition for a non‐planar flow with three velocity components, which is more realistic in terms of practical flow applications. The steady, laminar, Newtonian flow in a stirred micro‐bioreactor with a porous scaffold inside was investigated. It is shown how to implement the interfacial jump condition on the radial, axial, and swirling velocity components. To avoid a full three‐dimensional simulation, the flow is assumed to be independent of the azimuthal direction, which makes it an axisymmetric flow with a swirling velocity. The present interface treatment is suitable for non‐flat surfaces, which is achieved by applying the finite volume method based on body‐fitted and multi‐block grids. The numerical simulations show that a vortex breakdown bubble, attached to the free surface, occurs above a certain Reynolds number. The presence of the porous scaffold delays the onset of vortex breakdown and confines it to a region above the scaffold. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
77.
Carlos Gomez Humberto Prado Sergei Trofimchuk 《Journal of Mathematical Analysis and Applications》2014
This paper is concerned with a scalar nonlinear convolution equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the convolution equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the convolution equation. Finally, we apply our theoretical results to several well-studied classes of evolution equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these equations can possess simultaneously stationary, expansion and extinction waves. 相似文献
78.
A fast algorithm for solving systems of linear equations with banded Toeplitz matrices is studied. An important step in the algorithm is a novel method for the spectral factorization of the generating function associated with the Toeplitz matrix. The spectral factorization is extracted from the right deflating subspaces corresponding to the eigenvalues inside and outside the open unit disk of a companion matrix pencil constructed from the coefficients of the generating function. The factorization is followed by the Woodbury inversion formula and solution of several banded triangular systems. Stability of the algorithm is discussed and its performance is demonstrated by numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
79.
G. R. Everest A. J. van der Poorten 《Proceedings of the American Mathematical Society》1997,125(5):1293-1298
We study factorisation in the ring of exponential polynomials and provide a proof of Ritt's factorisation theorem in modern notation and so generalised as to deal with polynomial coefficients as well as with several variables. We do this in the more general context of a group ring of a divisible torsion-free ordered abelian group over a unique factorisation domain.
80.