Letter: A Solution of the Weyl–Lanczos Equations for the Schwarzschild Space-Time

The spin coefficient form of the Weyl–Lanczos equations is analysed for the Schwarzschild space-time. The solution obtained yields an alternative form of Lanczos coefficients to the one currently known for this particular metric.     

The Lanczos Potential for Weyl-Candidate Tensors Exists Only in Four Dimensions

We prove that a Lanczos potential L _abc for the Weyl candidate tensor W _abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L _abc and W _abcd, then this system's integrability conditions should be checked, and so on. When we find a non-trivial condition involving only W _abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L _abc.     

A Lanczos Potential for Plane Gravitational Waves

We exhibit explicitly a Lanczos generator for the conformal tensor associated with plane gravitational waves.     

Lanczos Spintensor and GHP Formalism

This work shows how the equations which relate the Lanczos potential K _ijr to the conformal tensor C _abpq, can be structured in a simple form when written in terms of the formalism proposed by Geroch-Held-Penrose. As working examples, we present the immediate construction of K _ijk for any spacetime with Petrov type O, N or III. Our findings are in good agreement with already published results, which indicates a relationship between the spin coefficients and the Lanczos spintensor onto the canonical tetrad.     

Scattering Coefficients for a Trapezoidal Potential

The trapezoidal potential is the result of the superposition of a rectangular barrier and a linear potential. It has interest in the field of solid-state physics as long as heterostructures are concerned. The determination and discussion of the scattering coefficients for this potential revealed unknown properties of the Airy functions.     

Gauss quadrature based finite temperature Lanczos method

The finite temperature Lanczos method (FTLM), which is an exact diagonalization method intensively used in quantum many-body calculations, is formulated in the framework of orthogonal polynomials and Gauss quadrature. The main idea is to reduce finite temperature static and dynamic quantities into weighted summations related to one- and two-dimensional Gauss quadratures. Then lower order Gauss quadrature, which is generated from Lanczos iteration, can be applied to approximate the initial weighted summation. This framework fills the conceptual gap between FTLM and kernel polynomial method, and makes it easy to apply orthogonal polynomial techniques in the FTLM calculation.     

Some potentials for the curvature tensor on three-dimensional manifolds

We study equations of Riemann–Lanczos type on three dimensional manifolds. Obstructions to global existence for global Lanczos potentials are pointed out. We check that the imposition of the original Lanczos symmetries on the potential leads to equations which do not have a determined type, leading to problems when trying to prove global existence. We show that elliptic equations can be obtained by relaxing those symmetry requirements in at least two different ways, leading to global existence of potentials under natural conditions. A second order potential for the Ricci tensor is introduced.     

Lanczos Potential for the Gödel Cosmological Model

Using a Lovelock's theorem we obtain the Lanczos spintensor for the Gödel's metric.     

Augmented Lanczos bidiagonalization by small singular value decompositions for face recognition and image compression

A new method for face recognition and image compression is presented here. In this method, Lanczos bidiagonalization is combined with sequences of small singular value decompositions. The goal of this method is to perform the truncated singular value decomposition for large matrices. It is an extension of standard Lanczos bidiagonalization, which improves its approximation capabilities and keeps the computational cost reasonable. Face recognition and image compression examples show the new method is competitive with pervious methods.     

Lanczos Potential for Arbitrary Petrov Type II Spacetimes

The Lanczos potential for an arbitrary Petrov type II spacetime has been obtained and Robinson–Trautman family of metrics has been considered as an example.     

Letter: A Potential for the Lanczos Spintensor in Kerr Geometry

We show a generator of the Lanczos spintensorfor a rotating black hole.     

Calculating pure rotational transitions of water molecule with a simple Lanczos method

We have calculated pure rotational transitions of water molecule from a kinetic energy operator (KEO) with the z-axis perpendicular to the molecular plane. We have used rotational basis functions which are linear combinations of symmetric top functions so that all matrix elements are real. The calculated spectra agree well with the observed values.     

Invariant Velocities for Two-Dimensional Minkowski Space-Time

It is shown that in two-dimensional space-time only the velocities parallel to the velocities of moving reference frames may be invariant with respect to Lorentz transformations.     

基于预条件LANCZOS算法快速实现三维地电场正演计算

针对三维地电场正演计算过程中形成的超大规模稀疏线性方程组,采用不完全Cholesky分解方法进行预条件处理,经过条件数改善后形成的新线性方程组的系数矩阵变为一个近似的单位矩阵,再应用Lanczos算法将会提高数值计算的稳定性,加快迭代收敛的速度,通常在迭代次数远小于系数矩阵阶数时就能得到较好精确解的近似值,为下一步的电阻率三维反演计算打下了非常好的基础.     

六角密堆结构钇的解析型键序作用势

为了构建拟合势需要的数据库,采用密度泛函理论方法计算了六角密堆结构钇(hcp-Y)的晶格参数、弹性常数、内聚能、结构能差以及相关的点、面缺陷性质. 基于解析型键序作用势,构建了hcp-Y的多体作用势模型. hcp-Y势模型是通过拟合Y的晶格参数、弹性常数、体弹模量、内聚能、空位形成能和不同相之间的结构能差而构建.分析发现,所得到的势模型能够很好地描述hcp-Y的自填隙原子形成能、空位形成能、双空位键能以及其它体性质,同时,构建的势模型用来研究Y的热动力学性质的相关结果也比较理想.     

Improved Lanczos algorithms for blackbox MRS data quantitation

Magnetic resonance spectroscopy (MRS) has been shown to be a potentially important medical diagnostic tool. The success of MRS depends on the quantitative data analysis, i.e., the interpretation of the signal in terms of relevant physical parameters, such as frequencies, decay constants, and amplitudes. A variety of time-domain algorithms to extract parameters have been developed. On the one hand, there are so-called blackbox methods. Minimal user interaction and limited incorporation of prior knowledge are inherent to this type of method. On the other hand, interactive methods exist that are iterative, require user involvement, and allow inclusion of prior knowledge. We focus on blackbox methods. The computationally most intensive part of these blackbox methods is the computation of the singular value decomposition (SVD) of a Hankel matrix. Our goal is to reduce the needed computational time without affecting the accuracy of the parameters of interest. To this end, algorithms based on the Lanczos method are suitable because the main computation at each step, a matrix-vector product, can be efficiently performed by means of the fast Fourier transform exploiting the structure of the involved matrix. We compare the performance in terms of accuracy and efficiency of four algorithms: the classical SVD algorithm based on the QR decomposition, the Lanczos algorithm, the Lanczos algorithm with partial reorthogonalization, and the implicitly restarted Lanczos algorithm. Extensive simulation studies show that the latter two algorithms perform best.     

Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space–times

We investigate the possibility of existence of a symmetric potential H_ABA′B′=H_{(AB)(A′B′)} for a symmetric (3,1)-spinor L_ABCA′, e.g., a Lanczos potential of the Weyl spinor, as defined by the equation L_ABCA′=_(A^B′H_BC)A′B′. We prove that in all Einstein space–times such a symmetric potential H_ABA′B′ exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space–times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell’s equations in a curved space–time.     

关于最弱受约束电子势模型理论中势函数物理意义的讨论

从屏蔽、贯穿和极化作用考虑,对最弱受约束电子势模型理论（简称WBEPM理论）的势函数进行了讨论。通过一系推导、论证,得出WBEPM理论的有效势的物理意义为：势函数中的第一项表示最弱受约束电子在有效核电荷＋Z′e中心场中的势能;第二项代表最弱受约束电子对非最弱受约束电子和核组成的“实”的极化作用所引起的偶极子场中的势能。     

Ordered and Periodic Chaos of the Bounded One-Dimensional Multibarrier Potential

Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets result upon passing through the multibarrier potential.