Construction of conformal mappings by generalized polarization tensors

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Small Data Scattering for the One-Dimensional Nonlinear Dirac Equation with Power Nonlinearity

We study scattering problems for the one-dimensional nonlinear Dirac equation (?_t + α?_x + iβ)Φ = λ|Φ|^p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?_x + x?_t ? α/2, where {D(t)}_t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?_x + x?_t ? α/2.     

Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

相干态统计特性的弱测量结构研究

理论分析相干态位移参数估计在弱测量方法下的放大效应.引入偏振态作为附属态(Ancilla States),分别进行初选择和后选择,中间的相互作用采用了偏振相关的弱位移操作算符.通过最后检测光子数的分布来估计位移参数;在牺牲检测光子强度的情况下可以有效提高放大效应.     

Distributed and multicore QuBiLS-MIDAS software v2.0: Computing chiral,fuzzy, weighted and truncated geometrical molecular descriptors based on tensor algebra

Advances to the distributed, multi-core and fully cross-platform QuBiLS-MIDAS software v2.0 ( http://tomocomd.com/qubils-midas ) are reported in this article since the v1.0 release. The QuBiLS-MIDAS software is the only one that computes atom-pair and alignment-free geometrical MDs (3D-MDs) from several distance metrics other than the Euclidean distance, as well as alignment-free 3D-MDs that codify structural information regarding the relations among three and four atoms of a molecule. The most recent features added to the QuBiLS-MIDAS software v2.0 are related (a) to the calculation of atomic weightings from indices based on the vertex-degree invariant (e.g., Alikhanidi index); (b) to consider central chirality during the molecular encoding; (c) to use measures based on clustering methods and statistical functions to codify structural information among more than two atoms; (d) to the use of a novel method based on fuzzy membership functions to spherically truncate inter-atomic relations; and (e) to the use of weighted and fuzzy aggregation operators to compute global 3D-MDs according to the importance and/or interrelation of the atoms of a molecule during the molecular encoding. Moreover, a novel module to compute QuBiLS-MIDAS 3D-MDs from their headings was also developed. This module can be used either by the graphical user interface or by means of the software library. By using the library, both the predictive models built with the QuBiLS-MIDAS 3D-MDs and the QuBiLS-MIDAS 3D-MDs calculation can be embedded in other tools. A set of predefined QuBiLS-MIDAS 3D-MDs with high information content and low redundancy on a set comprised of 20,469 compounds is also provided to be employed in further cheminformatics tasks. This set of predefined 3D-MDs evidenced better performance than all the universe of Dragon (v5.5) and PaDEL 0D-to-3D MDs in variability studies, whereas a linear independence study proved that these QuBiLS-MIDAS 3D-MDs codify chemical information orthogonal to the Dragon 0D-to-3D MDs. This set of predefined 3D-MDs would be periodically updated as long as new results be achieved. In general, this report highlights our continued efforts to provide a better tool for a most suitable characterization of compounds, and in this way, to contribute to obtaining better outcomes in future applications.     

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method.     

n阶变系数线性差分微分方程的解

利用Mikusi'nski算符域中变系数算符概念和相应的算符系数移动算符幂级数的概念和结果,获得初值条件下n阶变系数线性差分微分方程的解.     

面向天基引力波探测的时间延迟干涉技术

时间延迟干涉技术(Time-delay?Interferometry,TDI)对中国引力波探测项目及其它天基激光精密测量任务具有重要的参考价值.在天基引力波探测任务中,需利用激光干涉仪对无拖曳检验质量块间实现十皮米量级的位移测量精度.其中,激光源频率噪声和时钟频率噪声是两项主要噪声.在欧洲主导的LISA(Laser?I...     

Canny算法的改进及其硬件的实现

传统的Canny边缘检测算法是先对图像进行平滑,然后利用二维滤波器计算图像的梯度值,从而得到梯度直方图。通过基于梯度直方图来选取双阈值,最后进行基于双阈值的非极大值抑制,得到边缘检测的图像。为了能很方便地在硬件中实现这种算法,对传统的Canny算法进行了适当的改进,利用模板来代替原算法中的卷积,从而使得该算法在FPGA(Field Programmable Gate Array)中可以完全利用原理图来实现。     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.