Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.     

On reparametrization and the Gibbs sampler

Gibbs samplers derived under different parametrizations of the target density can have radically different rates of convergence. In this article, we specify conditions under which reparametrization leaves the convergence rate of a Gibbs chain unchanged. An example illustrates how these results can be exploited in convergence rate analyses.     

Canonical basis linearity regions arising from quiver representations

In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author [Math. Z. 237 (2001) 639] arising from representations of quivers. We prove that some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large cone by linear functions arising from these monomial bases for a quantized enveloping algebra.     

Optimal control methods applied on the ionization processes of alkali dimers

We present two novel optimization methods by employing shaped fs-laser pulses in a closed feedback loop. The first describes control pulse cleaning where extraneous features were removed by applying genetic pressure on certain pulse components. The second reports parametric optimization with intuitive parameters such as subpulse distances, chirps, phase differences, and spectral peak patterns. These methods were conducted on the ionization process of alkali dimers produced in a molecular beam and improved the performances of the optimized pulses compared with short pulses at the same pulse energy. Moreover, we attempt to analyze the obtained pulse shapes regarding the underlying optimized processes. Further investigations concerning isotope selective fragmentation and optimal control of excitation processes of ultracold rubidium dimers in a magneto-optical trap (MOT) are also shown.     

A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation

In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.     

基于三维荧光光谱的沥青老化行为研究

沥青在服役过程中暴露在自然环境里,受到光、热、氧等的作用,易出现老化从而引起的多种病害,如裂缝、龟裂和坑槽等,严重影响沥青混凝土路面的服役寿命。为了提高沥青混凝土路面的耐久性能,揭示沥青在老化过程中的成分与结构的变化规律,基于荧光光谱技术,从沥青的荧光猝灭现象出发,利用实验室内的紫外老化与热氧老化,针对两种不同沥青进行了老化实验,并研究了沥青在老化前后的性能和组分变化;借助荧光分光光度计采集了沥青的三维荧光光谱,并分析了沥青荧光光谱谱图的特征,获取了沥青荧光光谱的峰值强度坐标,计算了老化前后峰值坐标的偏移向量。实验结果表明,沥青避免出现荧光猝灭的理想浓度是0.1 g·L-1;沥青老化后其软化点增加,针入度与延度减小;其四组分中饱和分基本不变,芳香分减小,胶质与沥青质增加。结合三维荧光光谱发现,沥青的荧光强度峰值坐标出现了“蓝移”,且沥青组成中的芳香分的含量决定了荧光光谱峰值的偏移程度;通过向量计算表明,峰值坐标偏移的向量的模大于36时,沥青已经严重老化。通过对沥青三维荧光光谱特征值的分析,可以有效评价沥青的老化过程,对提高沥青的耐久性具有重要意义。     

Analysis of parametric functionals in semiempirical approaches using simulation techniques

In this work a comparative study of energy functional components of a parametric Hamiltonian (H_pa) and those obtained from an analytical method is presented. Error cancellations in approximations occur between electronic and nuclear repulsion energies and between attractive and repulsive electronic components of the energy. Parametric functionals associated with the correlation energy are discussed. Some modifications to the studied H_pa, mainly in the way of simulating electron repulsion integrals, are tested. Simulation techniques based on binding energy functionals were utilized to parameterize the modified H_pa. Preliminary results indicate that important improvements of the total, electronic, and core–core repulsion energies with respect to analytical values can be obtained by modifying the way the electron repulsion integrals in H_pa are simulated.     

The boundary Carathéodory-Fejér interpolation problem

We give a new solvability criterion for the boundary Carathéodory-Fejér problem: given a point x∈R and, a finite set of target values, to construct a function f in the Pick class such that the first few derivatives of f take on the prescribed target values at x. We also derive a linear fractional parametrization of the set of solutions of the interpolation problem with real target values. The proofs are based on a reduction method due to Julia and Nevanlinna.     

Minimal Gröbner bases and the predictable leading monomial property

We focus on Gröbner bases for modules of univariate polynomial vectors over a ring. We identify a useful property, the “predictable leading monomial (PLM) property” that is shared by minimal Gröbner bases of modules in F[x]^q, no matter what positional term order is used. The PLM property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property (= row reducedness), a terminology introduced by Forney in the 70’s. Because of the presence of zero divisors, minimal Gröbner bases over a finite ring of the type Z_p^r (where p is a prime integer and r is an integer >1) do not necessarily have the PLM property. In this paper we show how to derive, from an ordered minimal Gröbner basis, a so-called “minimal Gröbner p-basis” that does have a PLM property. We demonstrate that minimal Gröbner p-bases lend themselves particularly well to derive minimal realization parametrizations over Z_p^r. Applications are in coding and sequences over Z_p^r.