Measures of Multivariate Relationships for the Uniform Covariance Case

Behaviormetrika - Simple procedures for obtaining the m.l. estimates of multiple correlation, canonical correlation, partial canonical correlation and bi-partial canonical correlation have been...     

Canonical-covariant Wigner function in polar form

The two-dimensional Wigner function is examined in polar canonical coordinates, and covariance properties under the action of affine canonical transformations are derived.     

Effects of size distribution on the combustion efficiency of a liquid propellant rocket motor

Abstract

A new algorithm is presented to generate the parameters of the Schwarz canonical form. This new algorithm is simpler than the Routh algorithm in evaluating the Schwarz canonical form. The similarity transformation from a state‐space model in the phase‐variable form to that in the Schwarz canonical form is naturally established.     

Canonical Correlation Analysis of Formulation Optimization Experiments

Formulation optimization experiments are primarily composed of two groups of variables, a set of independent variables and a set of dependent variables. Simultaneous consideration of all the variables in a single analysis is desirable since it provides an opportunity to study the interrelationships of all variables, independent as well as dependent at the same time and imparts an in-depth insight into the entire system as a whole. A multivariate statistical analysis, known as canonical correlation analysis, has indeed this capability. In addition, the analysis has the capacity of extracting the maximum possible correlation, called canonical correlation, between the variables of the two sets. The larger the value of the canonical correlation (0.90 or above), the higher is the predictability of one set from the other set. The analysis produces two composite canonical functions, one for each set. They can be used to streamline the subsequent search process associated with the full-fledged optimization analysis. The analysis also has the cardinal property to rank-order the variables in each set according to their relative contributions to the canonical prediction function, and to delineate the most important variable in each set. This information can be useful in monitoring the future performance of the formulation in a time-and-cost effective manner and in selecting variables for future experiments. All the relevant features of the analysis have been depicted in this paper in the context of a mobile phase composition optimization experiment.     

Finite-Size Effects of Surface Tension in Two Segregated BECs Confined by Two Hard Walls

The finite-size effects of the surface tension in two segregated Bose–Einstein condensates limited by two hard walls are studied respectively in canonical ensemble and grand canonical ensemble by means of the Gross–Pitaevskii theory in the modified double-parabola approximation. The analytical formulae of surface tensions and their finite-size effects are found together with a new type of long-range forces acting on two walls.     

A Hamiltonian approach to fairly low and fairly long gravity waves

The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally more attractive Helmholtz-type equations. In an earlier attempt by Broer et al. [4, 6] canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal.     

Canonical duality for solving nonconvex and nonsmooth optimization problem

This paper presents an application of the canonical duality theory for solving a class of nonconvex and nonsmooth optimization problems. It is shown that by use of the canonical dual transformation, these difficult optimization problems in R ⁿ can be converted into a one-dimensional canonical dual problems, which can be solved to obtain all extremal points. Both global and local extremality conditions can be identified by the triality theory. Applications are illustrated.     

李代数在磁偏转系统三级像差计算中的应用

提出了电子光学偏转像差的李代数理论 ,将这种新型数学工具的应用领域从带电粒子束的聚焦传输系统推广到扫描偏转系统。推导出了磁偏转系统的高斯光学性质及全部三级正则像差 (包括在任意观察平面的正则位置像差和正则动量像差 ) ,所导出的结果与传统的逐次近似像差理论相同 ,为将李代数方法用于扫描探针系统的高阶像差的分析计算奠定了理论基础     

Sequential Metropolis Algorithms for Fluid Simulations

In this work, the implementation of our recently proposed sequential Metropolis algorithm in the grand canonical ensemble, a case particularly relevant for continuum fluids, is considered. By performing Monte Carlo simulations for the two-dimensional lattice gas, it is shown that our algorithm converges faster than all known grand canonical algorithms that satisfy strict detailed balance. The main advantages of the new algorithm are its simplicity, generality, and the possibility of parallel implementation.     

Properties of the linear canonical integral transformation

We provide a general expression and different classification schemes for the general two-dimensional canonical integral transformations that describe the propagation of coherent light through lossless first-order optical systems. Main theorems for these transformations, such as shift, scaling, derivation, etc., together with the canonical integral transforms of selected functions, are derived.     

Optical momentum in negative-index media

The correct form of the energy-momentum tensor in a dielectric has been the subject of a controversy spanning the last hundred years. Three principal forms for the momentum, in particular, have been identified for dispersive media. These are the Abraham, Minkowski and canonical momenta. We investigate whether any of these forms can be distinguished by considering pulses of light incident on materials with a negative refractive index and find that, for such materials, the canonical momentum has a qualitatively different behaviour to the other two.     

Geometry and dynamics of squeezing in finite systems

Squeezing and its inverse magnification form a one-parameter group of linear canonical transformations of continuous signals in paraxial optics. We search for corresponding unitary matrices to apply on signal vectors in N-point finite Hamiltonian systems. The analysis is extended to the phase space representation by means of Wigner quasi-probability distribution functions on the discrete torus and on the sphere. Together with two previous studies of the fractional Fourier and Fresnel transforms, we complete the finite counterparts of the group of linear canonical transformations.     

Gauge formulation of general relativity using conformal and spin symmetries

The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge field theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero-Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar field but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.     

A new technique to derive the Green’s type integral formula in thermoelasticity

New closed-form influence functions of a unit point heat source on elastic displacements and new Green’s type integral formula for a boundary-value problem (BVP) for a thermoelastic half-space are presented. The main difficulties in obtaining such results are observed in deriving the influence functions of a concentrated unit force onto elastic volume expansion and, also, in Green’s functions in heat conduction. For canonical Cartesian domains, these functions have been derived successfully for hundreds of BVPs and were published in a handbook. So, this paper shows the way to derive not only thermoelastic influence functions and Green’s type integral formulas for the half-space, but also for many new BVPs in thermoelasticity in other Cartesian canonical domains. Moreover, the technique proposed here may be applied in any orthogonal canonical domain provided by the lists of Green’s functions in heat conduction and influence functions for elastic volume expansion that are known.     

Phase reconstruction from intensity measurements in linear systems

The phase of a signal at a plane is reconstructed from the intensity profiles at two close parallel screens connected by a small abcd canonical transform; this applies to propagation along harmonic and repulsive fibers and in free media. We analyze the relationship between the local spatial frequency (the signal phase derivative) and the derivative of the squared modulus of the signal under a one-parameter canonical transform with respect to the parameter. We thus generalize to all linear systems the results that have been obtained separately for Fresnel and fractional Fourier transforms.     

Aspects of cauchy elastic materials

The Darboux theorem on the classification and canonical forms of first degree exterior differential forms is used to obtain a canonical representation of Cauehy elastic materials. It is shown that the balance of moment of momentum and the principle of material indifference are independent for materials whose Darboux class is greater than 1. By means of the Caratheodory's theorem on inaccessibility it is shown that any homogeneous deformation state can be reached from any other homogeneous deformation state by a path of zero work whenever the Darboux class of the material is 3 or greater.     

四边简支压电层合板灵敏度分析的精确解

为了应用弹性力学中的Hamilton 正则方程研究压电材料的灵敏度系数问题,基于压电材料的H-R(Hellinger-Reissner) 变分原理,简要地导出Hamilton正则方程算子表达式,建立了四边简支板静力学控制方程。根据灵敏度定义,在静力学控制方程的基础上联立灵敏度控制方程,得到了增维的齐次压电材料静力响应和灵敏度系数混合控制方程。应用该方程可以同时求得压电层合板的力学、电学参量及其灵敏度。该算法过程简单、运算效率和稳定性好。数值算例结果与有限差分法的结果比较表明本文方法切实有效。      

基于小波计算的平面物体射影不变性的识别

利用非均匀有理B样条从单幅图像中提取平面物体在射影变换下的几何不变特征,建立经典框架。讨沦用小波计算框架的一维和二维特征不变矩的方法以减少计算量。实验结果表明所选取的特征不变量和算法有较小的计算量,对二维平面物体的识别有很好的性能,特别是允许景物中有部分的遮挡物存在。