Magnetic Field Curves and Magnetic Equipotential Surfaces around Crossing Electrical Wires Replacing Classical Magnetic Field Lines

This article is based on a recent model specifically defining magnetic field values around electrical wires. With this model, calculations of field around parallel wires were obtained. Now, this model is extended with the new concept of magnetic equipotential surface to magnetic field curves around crossing wires. Cases of single, double, and triple wires are described. Subsequent article will be conducted for more general scenarios where wires are neither infinite nor parallel.

Accurate Formulae for the Cross-Section Data for the Radio-Halogen I-123 from Cyclotron Production

123I is the most widely used cyclotron-produced radio-halogen in medical research. In this paper, excitation function formulae for the nuclear reactions of 123I production are introduced. 124Te (p, 2n)123I and 127I (p, 5n)123Xe → 123I nuclear reactions have been studied as a function of the energy of the neutrons. Both two formulae were created using the least squares regression of the experimental cross sections data, which were obtained from the Experimental Nuclear Reaction Data EXFOR Database version of 2023. The proposed formulae were evaluated using two statistical indicators for goodness-of-fit. High agreement was observed between the empirical and experimental results for both nuclear processes.

Equivalence of crossed product of linear categories and generalized Maschke theorem

Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.

CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~＊-algebra. Then, the crossed product C~＊-algebra C~＊（G, A, α） has tracia rank zero（or has tracial rank no more than one）. In fact,we get a more general results.

Cotorsion Dimension of Weak Crossed Products

Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#;H in terms of the corresponding data for H and A.

Reversible Properties of Monoid Crossed Products

We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.

Crossed products for Hopf group-algebras

First,the group crossed product over the Hopf group-algebras is defined,and the necessary and sufficient conditions for the group crossed product to be a group algebra are given.The cleft extension theory of the Hopf group algebra is introduced,and it is proved that the crossed product of the Hopf group algebra is equivalent to the cleft extension.The necessary and sufficient conditions for the crossed product equivalence of two Hopf groups are then given.Finally,combined with the equivalence theory of the Hopf group crossed product and cleft extension,the group crossed product constructed by the general 2-cocycle as algebra is determined to be isomorphic to the group crossed product of the 2-cocycle with a convolutional invertible map of the 2-cocycle.The unit property of a general 2-cocycle is equivalent to the convolutional invertible map of the 2-cocycle,and the combination condition of the weak action is equivalent to the convolutional invertible map of the 2-cocycle and the combination condition of the weak action.Similarly,crossed product algebra constructed by the general 2-cocycle is isomorphic to the Hopfπ-crossed product algebra constructed by the 2-cocycle with a convolutional invertible map.

Diagonal crossed product of multiplier Hopf algebras

Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon＇s information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.

Homological Dimension of Crossed Products of Hopf Algebras

Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.

M_(αβ) X-ray production cross sections of Pb and B iby 9–40 keV electron impact

The experimental data of Mαβ X-ray production cross sections for Pb and Bi by 9–40 keV electron impact have been given. Thin films with thick carbon substrates are used in the experiment. The effects of target structure on the Mαβ X-ray production cross sections are corrected by using the Monte Carlo method. The corrected experimental data are compared with calculated cross sections in terms of the distorted-wave Born approximation(DWBA) theory. The measured Mαβ X-ray production cross sections for Pb and Bi are lower than the DWBA calculations. The atomic relaxation parameters used in comparing the DWBA values with experimental results affect the degree of difference.

Calculation of production cross sections of γ-rays from thermal-neutron captures

The calculation methods of production cross sections of γ-rays for thermal-neutron captures are briefly presented. The check of intensity balance is made. The examples are given to illustrate its application.

The Crossing Number of Cartesian Products of Stars with 5-vertex Graphs II

The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star K 1,n are known. In this paper, we will extent those results, and determine the crossing numbers of cartesian products of two 5-vertex graphs with star K 1,n .

基于向量叉乘标签分配的遥感图像目标检测算法

近年来遥感图像目标检测受到了广泛的关注,主流的遥感图像目标检测器通过预设锚框与真实框之间的交并比(IoU)进行正负样本的划分。为了解决基于IoU的标签分配方法在遥感图像小而密集目标中存在复检和漏检的问题,本文提出了一种基于向量叉乘标签分配的遥感图像目标检测算法YOLOXR。首先,提出了一种标签粗分配策略,通过向量叉乘的方法判断特征图的像素点是否在旋转目标内或者目标中心点附近的旋转正方形框内,从而确定其是否为候选正样本。其次,为了降低边缘低质量候选正样本对标签分配的影响,提出了旋转中心度量方法,通过向量叉乘判断像素点距离中心点的远近程度进而赋予不同的权重。最后,基于最优传输的方法(sim OTA)选取真实框和样本点的最优匹配对,使得总体代价最小,进而为旋转目标分配合适的标签。此外,为了解决旋转IoU损失不可导以及Smooth L1损失难以权衡旋转框各个参数的问题,通过计算真实框和预测框二维高斯分布的Kullback-Leibler散度(KLD)来替代IoU。在公开的遥感图像目标检测数据DOTA、HRSC 2016和UCAS-AOD上的大量实验表明,所提方法优于目前绝大多数旋转目标检测算法。

Improved Cross Entropy Algorithm for Steelmaking Continuous Casting Production Scheduling with Minimum Power Consumption

A matrix encoding scheme for the steelmaking continuous casting( SCC) production scheduling( SCCPS) problem and the corresponding decoding method are proposed. Based on it,a cross entropy( CE) method is adopted and an improved cross entropy( ICE) algorithm is proposed to solve the SCCPS problem to minimize total power consumption. To describe the distribution of the solution space of the CE method,a probability model is built and used to generate individuals by sampling and a probability updating mechanism is introduced to trace the promising samples. For the ICE algorithm,some samples are generated by the heuristic rules for the shortest makespan due to the relation between the makespan and the total power consumption,which can reduce the search space greatly. The optimal sample in each iteration is retained through a retention mechanism to ensure that the historical optimal sample is not lost so as to improve the efficiency and global convergence. A local search procedure is carried out on a part of better samples so as to improve the local exploitation capability of the ICE algorithm and get a better result. The parameter setting is investigated by the Taguchi method of design-of-experiment. A number of simulation experiments are implemented to validate the effectiveness of the ICE algorithm in solving the SCCPS problem and also the superiority of the ICE algorithm is verified through the comparison with the standard cross entropy( SCE) algorithm.

赝矢量的几何本质

本文借助于微分几何中的外积运算、微分形式、Hodge星算子等基本概念,探究了赝矢量的几何本质是微分2-形式,又借助Hodge星算子,给予微分2-形式可以被称为赝矢量的合理解释.通过将叉积运算替换为外积运算,清晰地解释了赝矢量、真矢量及其混合运算规则的逻辑关系,举例说明赝矢量及其运算在力学和电动力学等领域中的应用.特别是,应用赝矢量的运算规则给出了向心加速度是真矢量的合理解释.

利用向量叉积计算与二叉树追踪快速搜索封闭区域

目的自动填充等值线图的难点是自动搜索出值域相同的各个封闭区域,常用的扫描线填充和区域填充方式存在计算量大、效率不高等问题。方法针对此问题,提出利用多边形特征点的向量叉积计算结果与多边形的绘制顺逆方向之间的相关性,判定等值图中断层多边形的走向,基于构成封闭等值区域的等值线及其属性值具有的规律性性质,即等值线属性值是等值或等间距,追踪区域时利用填充边界或断层上的等值线端点创建追踪二叉树。追踪相邻的两个等值线端点所在的封闭区域时,将其中一个端点作为二叉树的根节点,沿边界查找左右相邻的下一条等值线端点,并将找到的端点作为左右子节点,从而实现封闭区域的快速追踪;通过封闭区域面积排序确定不同区域之间相互包含关系,据此构建拓扑相邻关系树,实现封闭区域的顺序覆盖填充,设计出更加简单、快速区分不同封闭区域的区域填充颜色选取方法。结果该方法简化了复杂的等值连通区域搜索算法,等值图的颜色变化趋势能保持一致,数据测试对比证明了所提算法的正确性。结论该算法通过一系列等值线能一次性得到组成封闭区域边界的点集合,因此,可以实现等值线和等值区域边界的完全吻合,当某些等值线发生变化时,只需更新相关的等值区域即可,提高了等值图件的编辑效率。

药物临床研究阶段申办者和生产场地变更研究六:临床研究阶段申办者和生产场地跨境变更的风险分析

目的:通过对临床研究阶段申办者、生产场地发生跨境变更时的风险变化进行分析,为申办者和生产场地的跨境变更管理提供参考。方法:基于申办者和生产场地不同组合情形的初始风险评价结果和采取风险管控措施后的风险再评价结果,比较分析不同组合情形之间发生变更时变更前后的“风险指数水平”变化。结果与结论:基于初始风险评价结果,有两种变更情形的风险指数水平在变更后较变更前降低;基于风险再评价结果,有四种变更情形的风险指数水平在变更后较变更前降低。

跨模态生成技术下面向文化产品的概念设计方法研究

文化产品是传承传统文化的重要方式,但目前市场同质化严重,设计研究效率低,人力成本高。跨模态生成技术可实现文化产品数字原型快速生成迭代,是数字化创新的有效途径。文章提出了一种将跨模态生成技术与当前文化产品概念设计过程相结合的方法。根据文化产品特点和跨模态生成技术特点,结合文化意象层次知识,将设计过程中需要人为处理的大量跨模态设计任务,通过跨模态技术处理传递设计信息,快速生成创新概念方案,并对此设计方法流程进行研究。以“基于海晏河清文化的加湿器”为例,进行有效设计实践,获得相关文化产品初步概念设计方案。利用该概念设计方法可以促进文化产品概念设计阶段快速迭代,为文化产品的创新和发展提供有力支持。

面向新质生产力的交叉学科人才培养逻辑重构

加快发展新质生产力重要论断的提出,为我国人才培养模式变革带来了新的要求,尤其呼唤交叉学科人才培养的逻辑重构。在价值层面,应以实现人的全面发展为价值基础、以价值理性与工具理性相统一为价值取向、以落实立德树人根本任务为价值目标。在认识层面,须凸显由确定性思维到关系性思维的新思维、由聚焦知识学习到问题解决导向的新方式、由单一学科规制到交叉学科文化营造的新视角。在实践层面,须加强导向鲜明、特色突出的顶层设计,开发新质赋能、开放创新的培养模式,搭建多元主体、机制互通的合作平台。