超声特征和几何圆度鉴别诊断最大径<2 cm三阴性乳腺癌和纤维腺瘤的价值

目的分析最大径<2 cm三阴性乳腺癌(TNBC)与乳腺纤维腺瘤(FA)的超声图像特征和几何圆度,提高临床鉴别诊断TNBC的准确性。方法回顾性分析我院经手术病理证实的74例最大径<2 cm的TNBC(TNBC组)和125例FA(FA组)患者的超声图像,比较两组年龄、病灶大小、形态、方位、边缘、回声模式、后方回声特征、钙化等特征,以及病灶几何圆度的差异。应用Logistic回归分析最大径<2 cm TNBC的独立影响因素,绘制受试者工作特征(ROC)曲线分析几何圆度对其的诊断效能。结果TNBC组平均年龄(47.3±10.7)岁,FA组(35.5±9.0)岁,差异有统计学意义(P<0.05)。与FA组比较,TNBC组病灶出现不规则形(49/74)、方位不平行(30/74)、边缘不光整(65/74)、后方回声增强(48/74)者更多,差异均有统计学意义(均P<0.05)。TNBC组BI-RADS 4类和5类病灶较FA组更多,差异均有统计学意义(均P<0.05)。TNBC组平均几何圆度81%±9%,大于FA组(66%±11%),差异有统计学意义(P<0.05)。Logistic回归分析显示,患者年龄>45岁(OR=7.81)、病灶形态不规则(OR=4.29)、方位不平行(OR=8.32)、后方回声增强(OR=7.54)、BI-RADS分类为4类(4A类:OR=1.06,4B类:OR=13.54,4C类:OR=31.92)和5类(OR=40.07),以及病灶几何圆度>80%(OR=71.62)是最大径<2 cm TNBC的独立影响因素。ROC曲线分析显示,诊断最大径<2 cm TNBC的几何圆度截断值为80%,曲线下面积为0.816,敏感性、特异性分别为77.2%、74.6%。结论与FA比较,最大径<2 cm的TNBC患者年纪多偏大,表现出更多可疑的超声特征和更大的几何圆度,有助于临床对二者进行鉴别诊断。

巧用几何圆中弦的特征解决磁偏转问题

磁偏转问题难度较大，对学生的空间想像力和几何知识运用能力要求高，学生很难在短时间内正确解决．本文作者在教学实践中，运用知识的有效迁移，从3个方面总结出巧用几何圆中弦的数学特征，快捷、准确地解决这类问题．

超声观察病灶几何圆度及形态特征对乳腺微小病灶良恶性鉴别诊断的效能分析

目的:分析彩超观察病灶几何圆度及形态特征对乳腺微小病灶的鉴别诊断效能。方法:回顾性分析厦门市湖里区禾山街道社区卫生服务中心2020年1月~2022年12月诊治的82例乳腺微小病灶患者临床资料,患者均接受彩超检查,并以术后的病理结果为金标准进行分组,分析彩超观察病灶几何圆度及形态特征对乳腺微小病灶的鉴别诊断效果。结果:两组患者几何圆度、病灶方位、边缘、钙化情况存在差异(P<0.05)。几何圆度对乳腺微小病灶良恶性诊断的AUC为0.883(0.806~0.937),敏感度88.89%,特异度81.01%。彩超采用几何圆度及形态特征鉴别乳腺微小病灶良恶性的敏感度、特异度、准确率、阳性预测值、阴性预测值分别为77.78%、96.20%、91.51%、87.50%、92.68%。结论:彩超可有效鉴别乳腺微小病灶良恶性,在良恶性不同的病灶组织中,超声特征存在明显差异,具有良好的诊断效能。

基于圆的几何性质的无人机纯方位无源定位研究

本文在仅根据无人机发射的方向信息的情况下,研究无人机纯方位无源定位问题.基于圆的几何性质建立定位模型,确定定位模型中所需发射信号无人机的最小数量,并通过迭代法构建调整模型,得到无人机群位置的调整方案.最后对调整模型的精确度进行评估.

几何圆在高中物理中的应用

圆是数学平面几何中一个极其重要的图形,它在解决物理问题中也有其独特的价值.本文结合实例具体阐释"等时圆"、"动态圆"、"磁场圆"等几何圆在解决物理问题中的巧妙应用.

几何圆约束解决的系列问题举隅

圆是最简单的曲线,它有丰富的几何性质,注意圆的几何性质在物理解题中的应用,可减少计算量,进而优化解题,提高解题的效率。

圆素几何和射影配极

总可以在∧ｎＲ２ｎ上定义两个对称的双线性型（Ωαβ）和（Ｊαβ），它们分别由Ｒ２ｎ的体积元和Ｒ２ｎ上的辛形式确定．特别，当ｎ＝２时，视（Ωαβ）和（Ｊαβ）为Ｐ５中的两个配极，我们证明了：存在这两个配极的绝对形的交集和Ｌｉｅ’ｓ圆的集合之间的一一对应，并且，两个Ｌｉｅ′ｓ圆同向相切当且仅当它们在Ｐ５中的像点关于（Ｊαβ）彼此共轭，此外，Ｐ５中的射影变换Ｇ保持（Ωαβ）不变当且仅当Ｇ＝∧，∈ＰＧＬ（４，Ｒ），又如果Ｇ还保持（Ｊαβ）不变，则必∈ＰＧｓｐ（４）．于是，我们得到圆素几何的射影模式，这个几何空间的运动群是ＰＧｓｐ（４）．

圆（球）素几何（八）变态辛反演与实辛反演的辛相似分类

本文求出反常第一类非仿射变态辛反演（阵）的标准型，证明它与反常第一类的常态反演以及同类型的仿射辛反演辛相似，验明三者的不变李氏圆集，即双曲型二次李氏圆列与双曲型双李氏圆列以及双曲型线性李氏圆列辛等价，即是说，一切反常第一类辛反演构成一个完整的辛相似类，实辛反演分为五个辛相似类，它们的标准辛阵和不变圆集都已求得，这些问题至此完全解决。

Modeling and Analysis of Vibration Characteristics of Rectangular Plate with Circular Through Hole Under Complex Boundary Conditions

This paper presents a method to study the free vibration of a plate with circular holes.The circular hole is regarded as a virtual small plate in which the mass density and Young's modulus are zero.Therefore,the free vibration problem of the circular hole plate can be transformed into the free vibration problem of the equivalent rectangular plate with non-uniform thickness.The model is derived from the spectral geometry method(SGM),and the displacement of the plate with circular holes is expanded by the modified Fourier series.Virtual springs are added to the boundary of the plate to simulate the boundary conditions of simply supported and fixed supports.The accuracy of this method is verified by comparison with the finite element calculation results.The relationship between modal numerical solutions of plates with circular holes and boundary conditions and geometry of the plate is studied.

以形补型——圆在环境设计中的应用探究

中国是一个尚"圆"的民族,从远古神力说到古代道家,圆代表着万物生成本源的认识。在建筑设计方案和装潢中大量存在圆形造型,圆形用它柔美的外形点缀着环境中的点滴。如可以更加妥善的利用,这将以形补型,让设计更加赋有韵味。通过查阅大量文献资料,梳理了圆、环境设计以及圆在环境设计中的应用相关研究,为本研究的深入探讨起到铺垫作用。接着分析了圆在环境设计中的实例,进一步表明圆的应用非常广泛;最后说明了用圆形来做造型的具体方法,为以后设计师在设计方案时提供思路。

习探究之道 悟研究之妙——利用单位圆的性质研究正弦、余弦函数的性质

文章利用单位圆的几何性质开展正弦、余弦函数性质的探究,以“选题、开题、做题、结题”作为探究的明线,以基于数学实验的“直观感知、提出猜想、论证猜想”作为探究的暗线.从论证已知到探索未知,从初步尝试到多角度探究,创设基于深度学习的探究课堂.

快速准确的虹膜定位算法

针对经典虹膜定位算法速度较慢的问题,提出一种基于圆几何特征的粗定位与精定位结合的快速虹膜定位算法。基于行列扫描的方法找到瞳孔内4条弦,利用弦的中垂线结合瞳孔边界阈值定位四对切点,取切点坐标参数的均值为内边缘粗略定位参数,然后利用微积分方法对内边缘进行精确定位;利用内外边缘圆心非常接近的先验知识,缩小微积分方法定位外边缘的搜索范围,从而显著提高了虹膜定位速度。实验结果表明,该算法显著提高了虹膜定位速度且具有较高的定位精度。

PCB基准点的探针式鲁棒定位方法

为了提高印刷电路板(PCB)基准点的定位鲁棒性与定位精度,减少因基准点损坏而定位不准或者不能定位现象,提出了探针式基准点定位方法。该方法分粗定位与精定位两步,粗定位阶段首先采用区域增长法进行图像分割,通过圆度阈值筛选出圆形区域,运用所提出的探针定位方法建立探针法数学模型,实现基准点的粗定位。基于粗定位所得基准点区域图像,提取其图像亚像素边缘,提出基于稳健估计算法的几何距离法圆拟合方法,实现基准点的精定位。实验结果表明:在复杂背景下该探针式定位法的基准点识别结果的正确率达100%,可有效降低基准点误定率;定位方法对基准点污损不敏感,在基准点损坏50%的情况下定位精度还能达到0.021个像素。

Further Improvement of Klamkin Inequality

In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.

数学与信息学的古典标记——来自易经的太极符号

本文描述怎样在数学教育中开发太极符号的几何性质,用以强化对圆的研究,在新视角下审视某些基本概念,诸如圆的直径、圆面的剖分和圆弧的矫直等.同时,在太极符号的哲学背景下,我们可以把不同学科之间及不同文化之间的问题整合到数学教育中去。

Cylindrical KP-Burgers Equation for Two-Temperature Ions in Dusty Plasma with Dissipative Effects and Transverse Perturbations

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unrsagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coeiffcient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effecta of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.

CIRCLE DETECTION USING FAST FINDING AND FITTING (FFF) ALGORITHM

This paper describes a Fast Finding and Fitting (FFF)Algorithm based on the geometric symmetry of the circle. A comparison with other circle detection approaches, in par- ticular the Hough Transform and its extensions is presented. A method to determine a rele- vant estimation of accuracy is also given. Experiments show that FFF possesses advantages in memory usage, high speed, reliability and accuracy are also presented.

Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

A Remark on Concircularly Flat Totally Real Minimal Submanifolds in CP^n

Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.

The Pulsed Plasma-Liquid Systems at Cylindrical Geometry with Possibility of Convergent Acoustic Waves Efficient Generation

This research investigates the possibility of convergent acoustic waves generation in the liquid by means of the sotmd waves reflection from the solid cylindrical surface, emerged in the pulsed electric discharge. The spectra of pulse discharge plasma emission in the water and in the air-water mixture were obtained. The temperature of cuprum and oxygen atoms electronic excitation levels and the temperature tendencies during the discharge current existence were calculated.