INVOLUTIONS WITH FIXED POINT SET RP(2m)∪P(2m, 2n + 1)

Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.

INVOLUTIONS FIXING ∪（from i=1 to m） CP_i(1) × HP_i(n)

Let （M, T） be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F = ^mUi=1 CPi（1）×HPi（n） are determined, where CP（1） and HP（n） denote the 1-dimensional i=1 complex projective space and n-dimensional quaternionic projective space respectively, and n=2^p-2or n=2^p-1（p〉 1）.

SOME PROPERTIES OF COMMUTING AND ANTI-COMMUTING m-INVOLUTIONS

We define an m-involution to be a matrix K ∈ Cn×n for which Km -= I. In this article, we investigate the class Sm （A） of m-involutions that commute with a diagonalizable matrix A E Cn×n. A number of basic properties of Sm （A） and its related subclass Sm （A, X） are given, where X is an eigenvector matrix of A. Among them, Sm （A） is shown to have a torsion group structure under matrix multiplication if A has distinct eigenvalues and has non-denumerable cardinality otherwise. The constructive definition of Sm （A, X） allows one to generate all m-involutions commuting with a matrix with distinct eigenvalues. Some related results are also given for the class S,, （A） of m-involutions that anti-commute with a matrix A ∈ Cnn×n.

A No—Go Theorem for Compatibility Between Involutions of First Order Differentials on a Lattice and Continuum Limit

We prove that the following three properties cannot match each other on a lattice, that differentials of coordinate functions are algebraically dependent on their involutive conjugates, that the involution on a lattice is an antihomomorphism, and that differential calculus has a natural continuum limit.

基于Involution算子和协调反向注意力的息肉图像分割

结肠影像中的息肉存在形态多变、边缘粘膜模糊的特点。针对现有的结肠息肉分割网络因卷积算子的固有限制而导致的特征提取不充分,以及因区域和边界关系刻画不全导致的分割不完整的问题,提出一种基于Involution算子和协调反向注意力的网络模型IN-CRNet。在编码器部分,设计基于Involution算子的感受野模块InRFB,自适应地捕获不同尺度的上下文语义信息,增强模型对形态复杂的结肠息肉的识别能力;在解码器部分,设计协调反向注意力模块CRA,同时关注区域和边界的重要程度,并构建两者的关系,自底向上地逐渐完善边缘轮廓的分割细节。在5个结肠息肉数据集上的验证实验表明,IN-CRNet具有良好的分割精度和泛化能力。

The Construction of Symplectic Involutions Over Finite Field with CharF=2 and Its Applications

In the present paper, we compute the number of the symplectic involaLions over the finite field F with chafF = 2, and also one Cartesian authentication code is obtained.Furthermore, its size parameters are computed completely. If assume that the coding rules are chosen according to a uniform probability, PI and Ps denote the largest probabilities of a successful impersonation attack and a successful substitution attack respectively, then PI and Ps are also computed.

Bordism Classes of Involutions on RP(2n)、CP(2n) and HP(2n)

In this paper we discuss all possible bordism classes of involutions on RP(2n),CP(2n) and HP(2n).

一种基于Involution卷积的三维人体重建方法

针对从视频中恢复三维人体模型运动序列时,由于图像特征提取能力有限而导致三维人体模型运动序列重建效果不佳的问题,提出了一种基于Involution卷积的三维人体重建方法。首先为了引入自注意力机制,在ResNet50网络结构中加入Involution算子,获取视频图像帧的特征向量,然后使用姿态估计网络和形状估计网络获取人体姿势以及形状参数,最后使用蒙皮多人线性模型(skinned multi-person linear model, SMPL)生成三维人体模型的运动序列。在三维姿态户外数据集(3D pose in the wild, 3DPW)上与视频人体姿态形状估计推理(video inference for body pose and shape estimation, VIBE)方法以及时间一致性网格恢复(temporally consistent mesh recovery, TCMR)方法进行对比实验,平均精度相比于VIBE、TCMR分别提升了3.1%、0.7%,能够为运动捕捉、三维人体动画制作等工作提供更为准确的三维人体模型。

基于Involution Prediction Head的小目标检测算法

针对通用目标检测算法在检测小目标时存在错检和漏检等问题,提出了一种小目标检测算法IPH(Involution Prediction Head),将其运用在YOLOv4和YOLOv5的检测头部分,在VOC2007数据集上的实验结果表明,运用IPH后的YOLOv4小目标检测精度APs(AP for small objects)相比原始算法提升了1.1%,在YOLOv5上的APs更是提升了5.9%。经智能交通检测数据集进一步检验,IPH算法和去下采样能有效提升小目标检测精度,减少错检和漏检的情况。

Renovation and Involution — Paradox of Chinese Literature in Modernity

With a special matter, Chinese literature has differences with traditional theories from western countries in essence, so that Chinese literature demonstrates its renovation and involution. The main reason is its trends of modernity. The transformation from oversea exchange is very important. This paper mainly explains the specific content of paradox of Chinese literature in mo dernity, and explores the reasons for differences between China and western countries.

基于小波变换和Involution卷积神经网络的滚动轴承故障诊断方法

传统卷积神经网络在滚动轴承故障诊断中存在梯度扩散、参数爆炸和训练时间长等缺点,为此提出一种基于Involution卷积神经网络的滚动轴承故障诊断方法。首先,通过小波变换将原始数据转换为时频图,经过数据预处理后送入基于Involution的神经网络模型;然后,经过不同Convolution卷积核对原始图像的局部区域特征进行不同方式的提取,扩展输入图像通道数;最后,通过Involution对特征图的每个像素点进行进一步特征提取,经过softmax层输出分类结果。CWRU轴承数据集和试验轴承数据集的分析结果表明,基于Involution卷积的神经网络模型所包含的参数较少,训练时间短,故障分类准确率可达99.75%,优于传统的CNN,DBN,自编码器等模型。

Metal Flowing of Involute Spline Cold Roll-beating Forming

The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold roll-beating,etc.However,the research on law of metal flow in the forming process of involute spline cold roll-beating is rare.According to the principle of involute spline cold roll-beating,the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established,and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded.A finite element model of the spline cold roll-beating process is established,the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied,and the node flow tracks of the deformation area are analyzed.The experimental research on the metal flow of cold roll-beating spline is conducted,and the metallographic structure variation,grain characteristics and metal flow line of the different tooth profile area are analyzed.The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance.There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming.The characteristics of involute spline cold roll-beating forming are given,and the forming mechanism of involute spline cold roll-beating is revealed.This paper researches the law of metal flow in the forming process of involute spline cold roll-beating,which provides theoretical supports for solving the tooth profile forming quality problem.

EFFECT OF INVOLUTE CONTACT RATIO ON THE DYNAMIC PERFORMANCE OF SPUR GEAR WITH NOTOOTH PROFILE MODIFICATION

The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.

The Involutive Solutions of the Representation Equation Associated with the Bargmann System

In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.

Numerical simulation of involutes spline shaft in cold rolling forming

Design of forming dies and whole process of simulation of cold rolling involutes spline can be realized by using of CAD software of PRO-E and CAE software of DEFORM-3D. Software DEFORM-3D provides an automatic and optimized remeshing function, especially for the large deformation. In order to use this function sufficiently, simulation of cold rolling involutes spline can be implemented indirectly. The relationship between die and workpiece, forming force and characteristic of deformation in the forming process of cold rolling involutes spline are analyzed and researched. Meanwhile, reliable proofs for the design of dies and deforming equipment are provided.

基于Conv-Involution的红外视频小样本人体行为识别方法

红外视频存在颜色信息缺失较为严重、识别区域易与背景混淆等现象,使得现有小样本特征提取网络常常关注无效信息,导致识别精度较低。针对此问题,本文提出一种基于内卷积(Conv-Involution)算子的红外视频小样本人体行为识别方法。首先,通过InstColorization方法恢复红外视频中的颜色信息;其次,基于空间和通道特异性设计Conv-Involution算子,并利用该算子和改进注意力机制设计特征提取网络,分离背景,更有效地关注行为发生区域;最后,结合小样本学习方法ANIL进行人体行为分类。对比实验结果表明,本文所提方法不但识别精度最高,而且具有出色的稳定性。

Effects of Comprehensive Eccentricity of Involute Cam on Gear Profile Deviations

The manufacturing accuracy of ultra-precision master gears signifies the technological capability of the ultra-precision gear.Currently,there is little report about the manufacturing technologies of ultra-precision master gears at home and aboard.In order to meet the requirement of grinding ultra precision master gear,the gear grinder with flat-faced wheel Y7125 is chosen as the object machine tool and the geometric model of its precision generating part,the involute cam,is established.According to the structure of the involute cam,the effective working section and its adjustable range of the cam are determined,and the mathematical expressions of the effects of comprehensive eccentricity of the involute cam on gear profile deviations are derived.According to the primary harmonic trends of the deviation curve,it is shown that gear profile form and slope deviations in different work generating sections of the involute cam are different which the latter changes with the cam eccentricity obviously.Then,the issues of extreme values and methods of error compensation are studied and the conclusion that large adjustable range is benefit to search the optimal involute-cam section which is responding to the minimum gear profile deviations is obtained.A group of examples are calculated by choosing master gears with d=120 mm and m=2-6 mm and an involute cam with base diameter djcam =117 mm.And it is found that the maximum gear profile deviation counts for no more than 5% of the cam eccentricity after error compensation.A gear-grinding experiment on the master gear with m=2 mm is conducted by choosing different sections of the involute cam and the differences of gear profile deviations then the existence of the cam eccentricity are verified.The research discloses the rule of gear profile deviations caused by the comprehensive eccentricity of the involute cam and provides the theoretical guidance and the processing methods for grinding profile of the ultra precision master gear.

Characteristic of involute slope modification of asymmetric spur gear

The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained.Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters.The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore,the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.

STUDY ON THE LUBRICATION FACTOR OF INVOLUTE SPUR GEARS

Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short) is investigated. The results suggest that gearlubrication effects bear close relations to a dimensionless parameter D which is syntheticallydetermined by gearing rotational speed, load, material, dimension and lubricant viscosity. When D<=8, the gear fatigue life increases as the lubricant viscosity is increased; When D>8, however, thelife decreases with the viscosity addition, which is in marked contrast to the lubrication factorZ_L recommended by the International Standard for Computing Cylindrical Gear Strength. At the end, aset of formulae for calculating gear lubrication factors suitable for different working conditionsare advanced.

GRU和Involution改进的深度伪造视频检测方法

近年来深度伪造视频在网络上广泛传播,造成了负面影响。针对现有检测模型准确率低和信息提取不够充分和全面的问题,提出了一种GRU(gated recurrent unit)和Involution改进的深度伪造视频检测方法。首先使用VGG19作为主干网络提取空间特征,并将Involution算子嵌入主干网络,从空间和通道信息两方面加强了人脸图像的空间建模能力。然后通过主胶囊层关注特征的位置信息和使用GRU提取帧间的时序特征。最后在训练模型阶段使用focalloss作为损失函数来平衡样本。在Deepfakes、FaceSwap和Celeb-DF数据集中进行测试,实验结果表明该方法优于主流检测方法,改进对比实验进一步证明了检测方法的有效性。