Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

Three-dimensional integrable models and associated tangle invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry

Calibration of the relationship between height and phase is of uttermost importance to perform accurate 3D measurements in phase measurement profilometry. This work reports a different approach to this problem by first looking at the analytical expression for this relationship and determining the regime spanned by the fringe analysis method. The conclusions thus ascertained, amply justify confronting the analytical expression with a simple normalization procedure of the experimental data, with a remarkable matching between both results. In light of this, a linear calibration procedure with just one plane is proposed and verified experimentally.     

Furtivity and Masking Problems in Time-Dependent Electromagnetic Obstacle Scattering

In this paper, we consider furtivity and masking problems in time-dependent three-dimensional electromagnetic obstacle scattering. That is, we propose a criterion based on a merit function to minimize or to mask the electromagnetic field scattered by a bounded obstacle when hit by an incoming electromagnetic field and, with respect to this criterion, we drive the optimal strategy. These problems are natural generalizations to the context of electromagnetic scattering of the furtivity problem in time-dependent acoustic obstacle scattering presented in Ref. 1. We propose mathematical models of the furtivity and masking time-dependent three-dimensional electromagnetic scattering problems that consist in optimal control problems for systems of partial differential equations derived from the Maxwell equations. These control problems are approached using the Pontryagin maximum principle. We formulate the first-order optimality conditions for the control problems considered as exterior problems defined outside the obstacle for systems of partial differential equations. Moreover, the first-order optimality conditions derived are solved numerically with a highly parallelizable numerical method based on a perturbative series of the type considered in Refs. 2–3. Finally, we assess and validate the mathematical models and the numerical method proposed analyzing the numerical results obtained with a parallel implementation of the numerical method in several experiments on test problems. Impressive speedup factors are obtained executing the algorithms on a parallel machine when the number of processors used in the computation ranges between 1 and 100. Some virtual reality applications and some animations relative to the numerical experiments can be found in the website http://www.econ.unian.it/recchioni/w10/.     

A 3D-BPP approach for optimising stowage plans and terminal productivity

This paper addresses the problem of determining stowage plans for containers in a ship, that is the so-called master bay plan problem (MBPP).     

三线性直接分解法分析高维灰色体系

对于由多个两维测量数据组成的三维阵，本文提出一种新三线性直接分解方法。采用高维ＰＣＡ分解，从三维阵中直接提取抽象光谱和抽象浓度，再结合ＱＺ算法，唯一地确定混合物中各组分光谱的浓度。该方法可以排除其它未知组分的干扰，适用于高维灰色体系定性定量分析和多点校准。用模拟数据讨论了光谱分离度对该方法的影响，应用于混合维生素Ｂ１、Ｂ２和Ｂ６的荧光分析，求得的光谱和浓度与实验值吻合很好。     

三维有序大孔杂化材料SiW11O39^8——SiO2和γ—SiW10O36^8——SiO2的制备与表征

通过溶胶 -凝胶和聚苯乙烯模板等方法制备了含缺位 Keggin阴离子 Si W1 1 O8- 3 9和 γ-Si W1 0 O8- 3 6的三维有序大孔杂化氧化硅复合材料 ,并通过紫外漫反射光谱 ( UV/ DRS)、傅里叶变换红外光谱 ( FTIR)、固体核磁共振波谱 ( MAS NMR)等手段对其结构进行了表征 .结果表明 ,杂化材料中的 Keggin阴离子仍保留其基本骨架结构 ,但其与氧化硅基体之间存在化学作用 .杂化材料的孔道结构用扫描和透射电子显微镜 ( SEM和TEM)进行表征 ,其平均孔径为 ( 335± 5 0 ) nm.对杂化材料孔壁的微孔性通过氮气吸附进行了测定 .此类材料对水溶液中羟基丁二酸的降解反应具有活性 ,光催化过程中未发现 Keggin阴离子自载体中脱落的现象 .     

Hydrothermal Synthesis, Crystal Structure, and Characterization of a Novel Terbium（Ⅲ） Coordination Polymer Bridged by 5-Sulfoisophthalate Trivalent Anions

Introduction Recently, several efforts have been made for thestudy of coordination polymers assembled from lantha-nide ions and aromatic polycarboxylate ligands becauseof their intriguing structural diversity and potentialapplications in several fields, s…     

Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups

In this paper, the author computes canonical connections and KobayashiNomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.