THE VECTOR FIELDS ADMITTING ONE-PARAMETER SPATIAL SYMMETRY GROUP AND THEIR REDUCTION

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

A Group Oriented Cryptosystem for the Vector Space Access Structure

A group oriented cryptosystem for the vector space access structure was proposed. This cryptosystem adopts self-certified public keys. It allows the participants of an authorized subset to cooperatively access an encrypted message. All data delivered in the cryptosystem are public. Therefore it does not need a partial decrypting results combiner and any secure communication channel. The security of the group oriented cryptosystem is based on the intractability of the discrete log problem and difficulty of factoring large integers. The suspected attacks can not break it.

Uniquely Decomposable Constellation Group-Based Sparse Vector Coding for Short Packet Communications

Sparse vector coding(SVC)is emerging as a potential technology for short packet communications.To further improve the block error rate(BLER)performance,a uniquely decomposable constellation group-based SVC(UDCG-SVC)is proposed in this article.Additionally,in order to achieve an optimal BLER performance of UDCG-SVC,a problem to optimize the coding gain of UDCG-based superimposed constellation is formulated.Given the energy of rotation constellations in UDCG,this problem is solved by converting it into finding the maximized minimum Euclidean distance of the superimposed constellation.Simulation results demonstrate the validness of our derivation.We also find that the proposed UDCGSVC has better BLER performance compared to other SVC schemes,especially under the high order modulation scenarios.

Some Group Runs Based Multivariate Control Charts for Monitoring the Process Mean Vector

In this article, we propose two control charts namely, the “Multivariate Group Runs’ (MV-GR-M)” and the “Multivariate Modified Group Runs’ (MV-MGR-M)” control charts, based on the multivariate normal processes, for monitoring the process mean vector. Methods to obtain the design parameters and operations of these control charts are discussed. Performances of the proposed charts are compared with some existing control charts. It is verified that, the proposed charts give a significant reduction in the out-of-control “Average Time to Signal” (ATS) in the zero state, as well in the steady state compared to the Hotelling’s T2 and the synthetic T2 control charts.

SOLVABILITY OF THE FOURTH ORDER NONLINEAR SUBELLIPTIC EQUATIONS ON THE HEISENBERG GROUP

In this paper,some existence results for the fourth order nonlinear subelliptic equations on the Heisenberg group are given by means of variational methods.

LAGRANGIAN VECTOR FIELD ON KOHLER MANIFOLD

In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.

An Introduction to Lie Groups

This paper is made out of necessity as a doctoral student taking the exam from Lie groups. Using the literature suggested to me by the professor, I felt the need to, in addition to that literature, and since there was more superficial in that book with some remarks about the examples given in relation to the left group. I decided to try a little harder and collect as much literature as possible, both for the needs of me and the others who will take after me. Searching for literature in my mother tongue I could not find anything, in English as someone who comes from a small country like Montenegro, all I could find was through the internet. I decided to gather what I could find from the literature in my own way and to my observation and make this kind of work. The main content of this paper is to present the Lie group in the simplest way. Before and before I started writing or collecting about Lie groups, it was necessary to say something about groups and subgroups that are taught in basic studies in algebra. In them I cited several deficits and an example. The following content of the paper is related to Lie groups primarily concerning the definition of examples such as The General Linear Group GL(n, R), The Complex General Linear Group GL(n, C), The Special Linear Group SL(n, R)=SL(V), The Complex Special Linear Group SL(n, C), Unitary and Orthogonal Groups, Symplectic Group, The groups R*, C*, S1 and Rn and others. In addition, invariant vector fields and the exponential map and the lie algebra of a lie group. For me, this work has the significance of being useful to all who need it.

Near-Vector Spaces Constructed over Zp, for p a Prime

The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

一类转置与自身的列向量组等价的特殊矩阵

先给出方阵的列向量组和行向量组的转置等价的充分必要条件.再对一类由初等矩阵诱导的列向量组和行向量组的转置等价的矩阵进行了研究,指出这一类特殊矩阵具有对称性和非平凡情况下的退化性.

一种改进的群组机器人网络路由算法

针对群组机器人系统在应急场景下移动频繁、能量有限的特点,提出了一种基于能量与速度的分簇自组织按需距离矢量协议(Clustered Ad hoc On-Demand Distance Vector Protocol Based on Energy and Speed,ESC-AODV),以延长群组机器人网络运行时间,提高通信可靠性。用路由性能代替跳数作为路由判据,目的节点在重复接收到路由请求(Route Request,RREQ)数据包时,若路由性能更小,则回复路由应答(Routing Reply,RREP)数据包,以此选择更好的路由,引入分簇结构,通过簇头和网关组成的骨干网络减少广播洪泛次数。实验结果证明,节点数量多时,改进的ESC-AODV协议在延长网络生存时间的同时,平均端到端时延、数据包投递率、吞吐量和路由开销均优于AODV以及基于能量、负载和速度的AODV路由协议(AODV Routing Protocol Based on Energy,Load and Speed,ELS-AODV)。ESC-AODV协议能够节约网络能量,提高可靠性,获得更优的网络性能。

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

This paper is devoted to the investigation of the Landau–Ginzburg–Higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron waves.The LGHe finds applications in various scientific fields,including fluid dynamics,plasma physics,biological systems,and electricity-electronics.The study adopts Lie symmetry analysis as the primary framework for exploration.This analysis involves the identification of Lie point symmetries that are admitted by the differential equation.By leveraging these Lie point symmetries,symmetry reductions are performed,leading to the discovery of group invariant solutions.To obtain explicit solutions,several mathematical methods are applied,including Kudryashov's method,the extended Jacobi elliptic function expansion method,the power series method,and the simplest equation method.These methods yield solutions characterized by exponential,hyperbolic,and elliptic functions.The obtained solutions are visually represented through 3D,2D,and density plots,which effectively illustrate the nature of the solutions.These plots depict various patterns,such as kink-shaped,singular kink-shaped,bell-shaped,and periodic solutions.Finally,the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved vectors.These conserved vectors play a crucial role in the study of physical quantities,such as the conservation of energy and momentum,and contribute to the understanding of the underlying physics of the system.

Left Invariant Harmonic Vector Fields on Solvable Lie Groups

It's shown that on an n-dimensional LCS Lie group,there exist harmonic sections and left invariant vector fields defining harmonic maps only when it is endowed with a flat left invariant pseudo-Riemannian metric.Moreover,we determine all the vector fields which are critical points of the energy functional restricted to vector fields of the same length on the n-dimensional pseudo-Riemannian LCS Lie group.

基于混合采样和SE_ResNet_SVM的不平衡多分类研究

针对结构化多分类算法中不平衡数据集类别分布不均导致分类难度增加的问题,本文提出了一种基于混合采样、压缩与激励(squeeze and excitation, SE)模块、改进深度残差网络和支持向量机(support vector machines, SVM)的网络模型SNSMRS (SMOTEENNmixed residual networks-SVM network)。首先,通过合成少数过采样和编辑最近邻技术来改善数据分布;然后,构建融合SE模块与通过融合批次归一化和群组归一化的深度残差网络来提取特征;最后,通过SVM进行输出网络模型。其中,SE模块增强了模型对特征的区分能力,提升了模型的鲁棒性;基于融合归一化的残差网络受批次大小的影响较小,并且避免了传统神经网络梯度消失和精度退化等问题,增强了网络的稳定性与准确度;SVM可以根据特征向量在空间上的分布进行全部特征的分割,特征利用率高,提高了模型的分类精度。在7个不同规模和领域的非平衡公开数据集上进行了对比和消融实验,结果表明,本文所提的网络模型SNSMRS不仅优于其他深度学习模型,而且相对于未改良的ResNet,Macro-F1和G-mean值分别提升了约3%和4%,同时在4个数据集上的Macro-F1和G-mean值均超过了95%。

肺恶性肿瘤内科诊断组DRG分组方案研究

目的:分析肺恶性肿瘤内科诊断组住院费用的影响因素,设计DRG分组方案,为研究对象分组方案优化提供案例分析和参考。方法:收集洛阳市某三甲医院2019—2022年肺恶性肿瘤内科诊断组的患者住院信息,采用K-means聚类和支持向量机分析住院费用的影响因素,通过CHAID算法构建DRG分组方案。结果:治疗方式、住院天数被纳入分组模型,最终生成6个DRG组,各DRG组的组内一致性好,组间差异性显著,分组效果好。结论:对于肺恶性肿瘤内科诊断组,住院天数分组效果好,但不适合作为分组节点;治疗方式有助于完善研究对象的DRG分组,但其划分方案有待进一步研究。

西湖凹陷N构造花港组厚层砂泥岩地层测井岩性识别方法

西湖凹陷位于东海,钻井取心比较困难,取心资料比较少,岩屑录井资料比较粗略,为了得到比较精细的地层岩性,在无监督机器学习的基础上,采用有监督机器学习的方法进行岩性识别。结果表明:该方法对研究区地层的岩性识别率可达95%以上,能够快速准确地对目的层的岩性进行识别。

基于模糊一致性调整算法的推荐系统评估研究

考虑到一致性调整和排序权重向量确定方法是犹豫模糊语言群决策中的2个重要课题,构造基于一致性调整算法的犹豫模糊语言群决策模型。具体来说,该模型首先运用对数最小二乘法计算犹豫模糊语言偏好关系(hesitant fuzzy linguistic preference relation,HFLPR)的排序权重向量;其次,将一致性指数最小的语言偏好关系对应的排序权重向量作为HFLPR的序权重向量;随后,基于一致性调整算法建立了一种收敛的犹豫模糊语言群决策模型。该模型既没有改变原始犹豫模糊语言术语集,又可以尽可能地避免信息的损失;最后,将建立的模型应用于推荐系统的优选过程。实验表明,构建的群决策算法更合理有效。

Differential-operator representations of Weyl group and singular vectors in Verma modules

Given a suitable ordering of the positive root system associated with a semisimple Lie algebra,there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module can be interpreted as a differential operator action on polynomials, and thus on the corresponding truncated formal power series. We prove that the space of truncated formal power series gives a differential-operator representation of the Weyl group W. We also introduce a system of partial differential equations to investigate singular vectors in the Verma module. It is shown that the solution space of the system in the space of truncated formal power series is the span of {w(1) | w ∈ W }. Those w(1) that are polynomials correspond to singular vectors in the Verma module. This elementary approach by partial differential equations also gives a new proof of the well-known BGG-Verma theorem.

基于时序向量相似性的空间目标群匹配技术研究

分析了空间低轨目标群的运行特点,提出了基于时序向量相似性的空间目标群匹配算法,提高了对低轨巨型星座的识别管理能力。首先,介绍了时序向量的降维方法,将目标群高维观测时序向量简化为空间构型序列;而后,提出了基于动态时间规整(Dynamic Time Warping,DTW)的目标群空间构型序列相似性判别算法;最后,利用星链卫星目标群仿真和实测数据对算法的匹配能力进行验证。结果表明该算法可实现空间目标群监测数据快速匹配,仿真数据匹配过程中,在群内目标缺失30%的条件下匹配成功率可达100%,在低缺失条件下(缺失率5%以内)群内目标识别成功率平均超过75%;实测数据匹配成功率可达100%。

直流法测量极性组别原理及与向量图的关系探究

介绍了单相、三相变压器直流法测试绕组极性两种组别试验方法,以YN,y12和YN,d11两种接线组别为例对直流法测量变压器的原理进行分析,通过向量分解法探究极性组合与向量图的对应关系,找出直流法与向量分解法之间的联系和规律,确保了变压器组别判定的正确性。