Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

基于YOLOv5的交通标志识别

交通标志识别是自动驾驶技术中的关键一部分.针对交通标志在道路场景中目标较小且识别精度较低的问题,提出一种改进的YOLOv5算法.首先在YOLOv5模型中引入全局注意力机制(GAM),提高网络捕获不同尺度交通标志特征的能力;其次将YOLOv5算法中使用的GIoU损失函数更换为更具回归特性的CIoU损失函数来优化模型,提高对交通标志的识别精度.最后在Tsinghua-Tencent 100K数据集上进行训练,实验结果表明,改进后的YOLOv5算法对交通标志识别的平均精度均值为93.00%,相比于原算法提升了5.72%,具有更好的识别性能.     

联合空间与角度的符号相干系数平面波成像北大核心CSCD

超声平面波成像是近年来一种应用较广泛的超快速超声成像方法,多角度相干平面波复合(Coherent Plane Wave Compounding,CPWC)成像在不过多损失速率的情况下,提升成像质量。但普通的CPWC方法只是简单复合多个角度延时叠加(Delay and Sum,DAS)后的数据,并未考虑到单个角度内以及多个角度之间数据的相关性。文章提出了一种联合空间与角度的符号相干系数(Angular Spatial Sign Coherence Factor,asSCF)平面波成像方法,将空间符号相干因子和角度符号相干因子创新性地融合到波束合成的过程中,充分考虑信号之间的相关性,旨在提升多角度复合成像质量。进行了仿真实验、仿体实验以及在体组织实验,对asSCF-CPWC方法、单一的符号相干系数法以及传统CPWC方法成像进行对比,结果发现asSCF-CPWC方法具有更好的横向分辨能力和成像对比度。     

Array SSL VPN如何保障番禺有线办公网的安全运行

企业办公自动化系统的应用十分广泛,随着互联网的高速发展,WEB应用成为主流,OA系统在互联网上的延伸成为大趋势,本文阐述在WEB应用中如何保障数据和系统安全的手段和方法。     

略论平面广告的互动设计形式

数字式信息传播在现代人类生活中发挥着越来越大的作用,网络、手机、互动电视等新兴媒体成为人们信息获取的重要来源,这些结合了视、听等多感官刺激的媒体不仅满足了人们在获取信息时的感官多样性、多层次需要,更预示着现代人类对互动的思维方式的渴望。这种渴求也使得是否互动成为当代广告成功的关键。如何将互动这个"动"的概念融合到"静"的平面广告中,成为平面广告研究的重要课题。     

记忆与延续——浅析苏州博物馆与宁波博物馆建筑设计

博物馆建筑,是一个城市文化的象征,如何使博物馆具有文化感,体现传统的审美文化,又具有新的设计元素,引导人类审美意识,苏州博物馆与宁波博物馆做了比较好的探索。     

Ten commandments for good default expression simplification

This article provides goals for the design and improvement of default computer algebra expression simplification. These goals can also help users recognize and partially circumvent some limitations of their current computer algebra systems. Although motivated by computer algebra, many of the goals are also applicable to manual simplification, indicating what transformations are necessary and sufficient for good simplification when no particular canonical result form is required.After motivating the ten goals, the article then explains how the Altran partially factored form for rational expressions was extended for Derive and for the computer algebra in Texas Instruments products to help fulfill these goals. In contrast to the distributed Altran representation, this recursive partially factored semi-fraction form:

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does not unnecessarily force common denominators,

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discovers and preserves significantly more factors,

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can represent general expressions, and

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can produce an entire spectrum from fully factored over a common denominator through complete multivariate partial fractions, including a dense subset of all intermediate forms.

     

A local construction of the Smith normal form of a matrix polynomial

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular row and column operations to the original matrix. The performance of the algorithm in exact arithmetic is reported for several test cases.     

On semantic,pragmatic, and dialectic triangles

A model is built of semantic triangle characterized by its universal nature: it is suitable not only for the elements of the real world but also for any elements of the Universe. Various possibilities of the development of the given model are shown, including a dialectic triangle.     

An explicit duality for quasi-homogeneous ideals

Given r≥n$r\ge n$ quasi-homogeneous polynomials in n$n$ variables, the existence of a certain duality is shown and made explicit in terms of generalized Morley forms. This result, that can be seen as a generalization of [Corollary 3.6.14, Jouanolou, J.-P., 1996. Résultant anisotrope, compléments et applications. Electron. J. Combin. 3 (2), Research Paper 2, approx. 91 pp. (electronic), the Foata Festschrift] where this duality is proved in the case r=n$r=n$, was observed by the author at the same time. We will actually closely follow the proof of the above-cited corollary in this paper.