On the simplification of the coefficients of a parametrization

This paper deals with the problem of finding, for a given parametrization of an algebraic variety V$V$ of arbitrary dimension, another parametrization with coefficients over a smaller field. We proceed adapting, to the parametric case, a construction introduced by A. Weil for implicitly given varieties. We find that this process leads to the consideration of new varieties of a particular kind (ultraquadrics, in the terminology of this paper) in order to check, algorithmically, several interesting properties of the given variety V$V$, such as the property of being reparametrizable over the smaller field.     

Algorithmic detection of hypercircles

In the algebraically optimal reparametrization problem, one of the possible approaches deals with computing a parametric variety of Weyl and checking whether this variety is a hypercircle. Here, algorithms to detect whether a curve given parametrically is a hypercircle are provided.     

Flatness-Based Control of a Single Qubit Gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space , having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.     

Detecting real singularities of a space curve from a real rational parametrization

In this paper we give an algorithm that detects real singularities, including singularities at infinity, and counts local branches and multiplicities of real rational curves in the affine n$n$-space without knowing an implicitization. The main idea behind this is a generalization of the D$D$-resultant (see [van den Essen, A., Yu, J.-T., 1997. The D$D$-resultant, singularities and the degree of unfaithfulness. Proc. Amer. Math. Soc. 25 (3), 689–695]) to n$n$ rational functions. This allows us to find all real parameters corresponding to the real singularities between the solutions of a system of polynomials in one variable.     

A global parametrization of asymptotically stable linear systems

In this paper we construct a homeomorphism from the set of p × m transfer functions of McMillan degree n onto the open subspace of asymptotically stable linear systems. This homeomorphism yields a one-to-one correspondence between

1. (i) canonical forms for state space equivalence of minimal systems and

2. (ii) canonical forms for state space equivalence of asymptotically stable minimal systems.

Implications for the topology of various sets of asymptotically stable systems are given.     

一类三次隐式代数曲面参数化研究

在CAGD中隐式曲面和参数曲面作为曲面的两种表示形式各有其内在的优点 ,多年来如何有效地实现二者的相互转换一直是CAGD的一个热点问题 对一类GC1拼接两个二次曲面的三次混合代数曲面进行了研究 ,提出一种基于同轴平面束与代数曲面相交的几何化参数化方法 与传统参数化方法相比 ,该方法结构直观且具有可使三次代数曲面位于 [0 ,1]× [0 ,1]参数区间内 ,以及曲面的边界位于等参数线上等特点 ,利用这种参数曲面可以方便地实现机器作图和各种操作 实验结果验证了方法的有效性     

Local parametrizations of ARMAX systems with nonlinear restrictions

A necessary and sufficient condition of local identifiability is derived by using the well-known Rank Theorem. Using this condition a suitable local parametrization is defined. The topological and geometrical properties of this parametrization are investigated. The results obtained generalize the corresponding results of Deistler and Wang (1989), which deal with essentially the systems with linear restrictions. The treatment covers also the systems without a priori restrictions.     

Parametrization of all minimal square spectral factors

Two different parametrizations of minimal square spectral factors are given. These parametrizations extend recent results by Picci and Pinzoni since they characterize spectral factors without specification on the zero or pole structure.     

On the existence of maximal solution for generalized algebraic Riccati equations arising in stochastic control

Existence of maximal solution is proved for a generalized version of the well-known standard algebraic Riccati equations which arise in certain stochastic optimal control problems.     

Parametrization of all stabilizing controllers of nonlinear systems

We consider a nonlinear multiobjective optimal control problem, where a controller is to be designed such that a number of constraints are to be satisfied for all possible disturbances. We show that, under mild continuity assumptions, such a controller exists if and only if, for every weighted combination of the constraints, there exists a controller satisfying the weighted constraint.     

A New QEM for Parametrization of Raster Images

We present an image processing method that converts a raster image to a simplical two‐complex which has only a small number of vertices (base mesh) plus a parametrization that maps each pixel in the original image to a combination of the barycentric coordinates of the triangle it is finally mapped into. Such a conversion of a raster image into a base mesh plus parametrization can be useful for many applications such as segmentation, image retargeting, multi‐resolution editing with arbitrary topologies, edge preserving smoothing, compression, etc. The goal of the algorithm is to produce a base mesh such that it has a small colour distortion as well as high shape fairness, and a parametrization that is globally continuous visually and numerically. Inspired by multi‐resolution adaptive parametrization of surfaces and quadric error metric, the algorithm converts pixels in the image to a dense triangle mesh and performs error‐bounded simplification jointly considering geometry and colour. The eliminated vertices are projected to an existing face. The implementation is iterative and stops when it reaches a prescribed error threshold. The algorithm is feature‐sensitive, i.e. salient feature edges in the images are preserved where possible and it takes colour into account thereby producing a better quality triangulation.     

非局域Bell-态测量的实现

利用预先分享的最大纠缠对、局域操作和经典通信,提出了执行非局域Bell-态测量的一个完美方案。通过用部分纠缠信道取代最大纠缠信道,推广了上述方案,指出采用酉变换就能概率地施行非局域Bell-态测量,并且推广方案可视为一个提纯方案。讨论了这些协议所需的资源,并说明了这些方案在现有技术下的实验实现是可行的。此外,该协议可以用来生成一些新的最大量子纠缠态。     

An Examination of Qubit Neural Network in Controlling an Inverted Pendulum

The Qubit neuron model is a new non-standard computing scheme that has been found by simulations to have efficient processing abilities. In this paper we investigate the usefulness of the model for a non linear kinetic control application of an inverted pendulum on a cart. Simulations show that a neural network based on Qubit neurons would swing up and stabilize the pendulum, yet it also requires a shorter range over which the cart moves as compared to a conventional neural network model.     

基于Generative Component的中国古建筑参数化设计

为有效分析古建筑,利用参数化建模软件Generative Component（GC）,结合编程设计对中国古建筑主要结构和构件进行参数化分析,找出其内在结构的规律性及各构件之间的参数关系,实现古建筑的数字化、参数化描述,生成参数可修改的结构化三维模型.     

Rational general solutions of planar rational systems of autonomous ODEs

In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear reparametrizations, we can find the rational solutions of the given system of ODEs. Moreover, if the system has a rational first integral, we can decide whether it has a rational general solution and compute it in the affirmative case.     

基于PCL的折叠式夹层板结构参数化建模

折叠式夹层板具有优越的力学性能,在有限元分析中,由于夹层板结构复杂,建模工作量大.针对这些问题,基于PCL对Patran进行二次开发,通过输入夹层板尺寸和网格数量等参数实现V形折叠式夹层板结构的参数化建模.编制折叠式夹层板建模界面,实现夹层板结构有限元分析参数化,提高建模效率,为夹层板结构设计提供支撑.     

On the problem of guidance of an autonomous conflict-controlled system onto a cylinder set

The problem of guidance of a conflict-controlled system onto a cylinder set is considered. This problem is compared with the problem of guidance of a transformed system onto the base of the cylinder at the last moment. It is shown that the problems considered are equivalent. Moreover, the sequences constructed by the programmed iteration method coincide for both problems. This work is supported by the Russian Foundation for Fundamental Research, grants Nos. 06-01-00414 and 07-01-96088-p. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 117–126, September–October 2008.