AN ALGORITHM FOR DETERMINING CONCAVE VERTEX OF OBJECT BASED ON VECTOR PRODUCT

Concave vertex of an object is an important parameter for analyzing an object’s shape. A new algorithm for searching concave vertex is proposed in this paper. The new algorithm requires tracking the border firstly,and then uses sampling border to obtain coordinates sequence of discrete boundary points. Each sampling point of the discrete border is determined to be either concave or convex according to the value of vector product. Two inflexions can be searched by the change of concavo-convex trend. The region between two inflexions is defined as concave area. The values of distance are calculated between all boundary points on the concave area and a straight line connected by two inflexions. The boundary point corresponding to the greatest distances is max concave vertex,or the object’s concave vertex. Experimental results have proved that the new algorithm can extract the max concave vertexes of an object accurately and reliably.

Vector Product and an Integrable Dynamical System

We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Solution for slab forging with bulge between two parallel platens by strain rate vector inner-product integration and series expansion

A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second, a summation process of term by term integrated results and a formula of the bulging were introduced, and an analytical solution of stress effective factor was obtained. It is proved that the expression of power by the above linear integration is the same as that of traditional immediate integration. Also, the solution was simplified by series expansion and compared by slab forging test with the others. It turns out that the calculated result of total forging pressure is basically in agreement with measured value in the actual press test.

Vector Meson Electro-production in Pomeron Exchange Model

Based on Pomeron exchange model, elastic production of vector meson in electro-proton interaction is investigated with both linear and non-linear Pomeron trajectory. A numerical calculation for J/ψ production is performed. The effect of the energy scale so and photon virtuality Q2 on differential cross section are also predicted. Agood agreement with experimental data is obtained. Our conclusions are that the Pomeron exchange model is a successful description of J/ψ electro-production, the dependence of the differential cross sections on Q2 is negligible, the linear trajectory is a good approximation to non-linearity of the Pomeron trajectory, and the value of the energy scale parameter so is dependent on the momentum transfer, namely its effect is moderate at low momentum transfer but it causes no difference at high momentum transfer | t |≥ 1.25 GeV2.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Inner-product of strain rate vector through direction cosine in coordinates for disk forging

A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined by the ratio of coordinate increments.Furthermore,inner-product of the vector for plastic power was term integrated by term and summed.Thereafter,through a formula for determination of bulge an analytical solution of stress effective factor was obtained.Finally,through compression tests,the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine.It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%.However,when the reduction gets up to 25.34% and 33.12%,the corresponding errors between the calculated and measured results also get up to 6% and 13.5%,respectively.

The Approach to the Covariance of the Outer Producter of Two Independent Random Vector in Inter Productor Space

The purpose of this article is to present by using vector space methods,a formula as how to calculate the covariance of the outer product of two independent random vecters in inter product space and to makes a discussion on the covariance of the orthogonally invariant random vector and that of the weakly spherically distributed outer produt.

Reliability-based multidisciplinary design optimization using incremental shifting vector strategy and its application in electronic product design

Use of multidisciplinary analysis in reliabilitybased design optimization(RBDO) results in the emergence of the important method of reliability-based multidisciplinary design optimization(RBMDO). To enhance the efficiency and convergence of the overall solution process,a decoupling algorithm for RBMDO is proposed herein.Firstly, to decouple the multidisciplinary analysis using the individual disciplinary feasible(IDF) approach, the RBMDO is converted into a conventional form of RBDO. Secondly,the incremental shifting vector(ISV) strategy is adopted to decouple the nested optimization of RBDO into a sequential iteration process composed of design optimization and reliability analysis, thereby improving the efficiency significantly. Finally, the proposed RBMDO method is applied to the design of two actual electronic products: an aerial camera and a car pad. For these two applications, two RBMDO models are created, each containing several finite element models(FEMs) and relatively strong coupling between the involved disciplines. The computational results demonstrate the effectiveness of the proposed method.

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。

THE COMPREHENSION,SOME PROBLEMS AND SUGGES-TIONS TO SYMBOLIC VECTOR METHOD AND SOME DEFENSES FOR GIBBS'SYMBOL

The comprehension of Prof. Tai's symbolic vector method in vector analysis presented, some problems are found and some suggestions are provided to solve them. Some defenses for Gibbs' symbol have been made as well. Key words: symbolic vector(? ?; operator; vector product model

向量混合积的应用探讨

向量的数量积、向量积和混合积是高等数学中向量代数与空间解析几何的重要内容。通过计算四面体体积、平面方程、直线方程和判断两直线异面四个方面探讨向量混合积的应用,为一题多解拓宽解题思路,优化解题方法,有利于提高学生学习兴趣,提升高等数学教学效果和教学质量。

一种基于支持向量机回归的制氧系统寿命预估方法

随着我国老龄化程度的加深及后疫情时代大背景下国内医疗系统市场规模的不断扩大,制氧系统行业的发展进入快速扩容阶段。同时,制氧系统突发故障对吸氧人群生命与心理造成不可逆损伤的问题接踵而至。制氧行业迫切需要一种针对制氧系统寿命的预估方法,以解决制氧系统突发故障影响吸氧人群生命与财产安全的问题。该研究提出一种基于支持向量机回归(SVR)的制氧系统寿命预估方法。首先,基于SVR原理建立一种寿命预估模型,通过对某制氧系统3500h的氧浓度监测数据进行SVR训练,得到制氧系统的寿命预估模型。然后,规律选取300组氧浓度数据分别进行训练集预测和预测集预测,结果显示,该预测模型的准确性较高,且模型对预测集样本的预测结果与氧浓度监测的真实值基本保持一致。最后,对该制氧系统的吸附塔进行拆机验证,发现分子筛确有失效现象,经实际测量失效程度为6%,表明该模型可应用于制氧系统的寿命预估,并取得了良好的结果。因此,基于SVR的制氧系统寿命预估方法可以准确、有效地预估制氧系统的使用寿命,避免其突发故障,同时也为后续制氧系统的寿命预估方法提供了思路。

向量混合积与四面体体积公式的联系与应用

在解析几何中求解四面体的体积,传统的方法是选取一个顶点作为原点,并使用从这个顶点出发的三个不共面的向量,通过计算它们的混合积来得到四面体的体积。然而,实际上只需要从四个顶点中选择任意三个不共线的向量,计算它们的混合积即可求解四面体的体积。提出了一种更加通用的方法,利用向量混合积来求解四面体的体积,并且证明了此方法的准确性。最后,通过一个数值算例来说明这种方法的简便性和有效性。

固定资产投资对建筑业劳动生产率的影响——基于房地产和制造业领域投资占比视角

提升劳动生产率是建筑业高质量发展的关键。运用Eviews 10.0建立VAR(向量自回归)模型,利用脉冲响应和方差分解分析,研究房地产开发投资占固定资产投资比例和制造业投资占固定资产投资比例对建筑业劳动生产率的影响。实证结果显示,固定资产投资中的房地产开发投资占比和制造业投资占比均会促进建筑业劳动生产率的提高,但制造业投资占比的影响程度更大。在此基础上对建筑业未来的发展提出建议。

3D矢量空间和最优最劣法在绿色产品设计决策方法中的应用

为了解决目前绿色产品设计方案中产品基础属性考虑欠缺,以及缺乏可视化比较方法的问题,提出一种基于3D矢量空间和最优最劣法(Best worst method,BWM)的绿色产品设计多属性决策方法。通过功能、外观和可持续3个维度为绿色产品设计的基础属性构建3D矢量空间,并对每个维度扩充其包含的下级属性;利用间隔方法优化的BWM获得三个维度及各维度下级属性的权重分配;通过3D矢量空间求得各备选方案的总体评价得分,实现客观科学的绿色产品设计多属性决策。以电动汽车的绿色产品设计方案为例,验证了所提方法的可行性和有效性。

基于句法规则与情感词的隐式特征提取

针对当前句法关系研究存在过多考虑主谓关系、情感词识别能力有限、忽视隐式特征提取等方面的不足,提出一种基于句法规则与情感词的隐式特征提取方法。借助中文情感词典资源,基于外部语料与实验语料训练的词向量分别构建混合情感词典和产品特征词典,通过词典和定义的句法规则提取显式特征及情感词,根据其共现关系提取隐式特征。在相机评论语料集上进行实验并与现有方法进行对比,实验结果表明,该方法能有效提取显式及隐式特征,在获取全面特征信息上具有较好的性能。

基于矩阵半张量积解四元数广义Sylvester矩阵方程组

该文利用矩阵半张量积求解四元数广义Sylvester矩阵方程组.首先将实矩阵半张量积运算推广到四元数矩阵,进而利用四元数矩阵半张量积提出四元数矩阵在向量算子下的一些新结论,利用这些结论将四元数矩阵方程组转化为四元数线性方程组,最后转化为实线性方程组,从而得到四元数广义Sylvester矩阵方程组有解的充要条件及通解表达式,并给出其极小范数解.最后通过数值算例说明该方法的有效性.

基于GWO-SVM算法的油气井产能预测模型研究

油气井产能对于油藏完井方式选择及相关作业起着决定性作用,是油气藏开发的关键指标之一。当前基于机器学习算法的油气井产能预测过程中预测结果受样本数据影响明显。针对支持向量机方法和灰狼算法在处理小数据样本时的特征及优势,将支持向量机与灰狼算法相结合,形成了灰狼算法—支持向量机算法(GWO-SVM算法)。利用某油田数据实际井数据对优化前后的算法及当前常用的机器学习算法进行对比测试,结果表明,优化后的GWO-SVM算法在计算速度和计算精度上表现出了明显优势,能更准确地确定油气井产能。研究结果对油气井产能预测具有一定指导意义。