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 cl...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.展开更多
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 C...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).展开更多
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...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.展开更多
Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a thre...Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.展开更多
Let W be the Weyl group of type F4. We explicitly describe a finite set of basic braid I*-transformations and show that any two reduced I*-expressions for a given involution in W can be transformed into each other t...Let W be the Weyl group of type F4. We explicitly describe a finite set of basic braid I*-transformations and show that any two reduced I*-expressions for a given involution in W can be transformed into each other through a series of basic braid/,-transformations. Our main result extends the earlier work on the Weyl groups of classical types (i.e., An, Bn, and Dn).展开更多
We show that for any differentiable involution on an r-dimensional manifold(M,T) whose fixed point set F is a disjoint union of real projective spaces of constant dimension 2n,we have:if r=4n then(M,T)is bordant to(F&...We show that for any differentiable involution on an r-dimensional manifold(M,T) whose fixed point set F is a disjoint union of real projective spaces of constant dimension 2n,we have:if r=4n then(M,T)is bordant to(F×F,twist),if 2n【r≠4n then(M,T)bounds.展开更多
1 PreliminaryIT is a classical problem in the research of classical groups to represent an element of a matrixgroup as a product of matrices of a special nature (such as involution and commutator) and todetermine the ...1 PreliminaryIT is a classical problem in the research of classical groups to represent an element of a matrixgroup as a product of matrices of a special nature (such as involution and commutator) and todetermine the smallest number of the factors in the representation. We have known that everyelernent of SL_nF(= E_nF), the special linear group over a field, can be written as a product展开更多
Let σ be an anti-holomorphic involution on an almost complex four manifold X,a necessary and sufficient condition is given to determine weather X/σ admits an almost complex structure.
Let (M<sup>n</sup>, T) be a smooth involution T on a closed manifold M<sup>n</sup>. The fixed point set of T has a constant codimension k. Let J<sub>n</sub><sup>k</sup>...Let (M<sup>n</sup>, T) be a smooth involution T on a closed manifold M<sup>n</sup>. The fixed point set of T has a constant codimension k. Let J<sub>n</sub><sup>k</sup> be the set of n-dimensional cobordism class in MO<sub>n</sub> (unoriented cobordism group), which has such a representative. In this paper, we obtain a necessary and sufficient condition of α∈J<sub>n</sub><sup>2k</sup>, α∈J<sub>n</sub><sup>2l+1</sup> for 2k≤40, 2t+1≤19.展开更多
In 2020,Niu et al.[Cryptogr.Commun.,2020,12(2):165–185]studied the fixed points of involutions over the finite field with q-elements.This paper further discusses the relationship between the fixed points set and the ...In 2020,Niu et al.[Cryptogr.Commun.,2020,12(2):165–185]studied the fixed points of involutions over the finite field with q-elements.This paper further discusses the relationship between the fixed points set and the non-fixed points set of two involutions f_(1)(x)and f_(2)(x)over the finite field F_(q),and then obtains a necessary and sufficient condition for that the composite function f_(1)■f_(2)(x)is also an involution over F_(q).In particular,a special class of involutions over some finite fields is determined completely.展开更多
Given an involution in a group G, it can be extended in various ways to an involution in the group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear extensions are considered and necessa...Given an involution in a group G, it can be extended in various ways to an involution in the group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear extensions are considered and necessary and sufficient conditions are given on the group G, its involution, the ring R and the extension for the set of skew-symmetric elements to be commutative and for it to be anticommutative.展开更多
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...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。展开更多
针对一般手势识别算法的参数量、计算量和精度难以平衡的问题,提出一种轻量化篮球裁判手势识别算法。该算法在YOLOV5s(You Only Look Once Version 5s)算法的基础上进行重构:首先,用Involution算子替代CSP1_1的卷积算子,以扩大上下文信...针对一般手势识别算法的参数量、计算量和精度难以平衡的问题,提出一种轻量化篮球裁判手势识别算法。该算法在YOLOV5s(You Only Look Once Version 5s)算法的基础上进行重构:首先,用Involution算子替代CSP1_1的卷积算子,以扩大上下文信息捕获范围并减少核冗余;其次,在C3模块后加入协同注意力(CA)机制,以得到更强的手势特征提取能力;然后,用轻量化内容感知上采样算子改进原始上采样模块,并将采样点集中在目标区域而忽略背景部分;最后,利用以SiLU作为激活函数的Ghost-Net进行轻量化剪枝。在自制的篮球裁判手势数据集上的实验结果表明,该轻量化篮球裁判手势识别算法的计算量、参数量和模型大小分别为3.3 GFLOPs、4.0×10^(6)和8.5 MB,与YOLOV5s算法相比,分别减少了79%、44%和40%,mAP@0.5为91.7%,在分辨率为1920×1280的比赛视频上的检测帧率达到89.3 frame/s,证明该算法能满足低误差、高帧率和轻量化的要求。展开更多
基金Supported by NSFC(11371118)SRFDP(20121303110004)+1 种基金HNSF(A2011205075)HNUHH(20110403)
文摘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.
基金supported by NSFC (1097105011001073+3 种基金10901045)HNSFC(A2010000828)FHUST (XL201043QD201021)
文摘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).
文摘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.
基金support provided by the National Nature Science Foundation of China (Grant Nos.52075340,51875360)Project of Science and Technology Commission of Shanghai Municipality (No.19060502300).
文摘Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.
文摘Let W be the Weyl group of type F4. We explicitly describe a finite set of basic braid I*-transformations and show that any two reduced I*-expressions for a given involution in W can be transformed into each other through a series of basic braid/,-transformations. Our main result extends the earlier work on the Weyl groups of classical types (i.e., An, Bn, and Dn).
文摘We show that for any differentiable involution on an r-dimensional manifold(M,T) whose fixed point set F is a disjoint union of real projective spaces of constant dimension 2n,we have:if r=4n then(M,T)is bordant to(F×F,twist),if 2n【r≠4n then(M,T)bounds.
文摘1 PreliminaryIT is a classical problem in the research of classical groups to represent an element of a matrixgroup as a product of matrices of a special nature (such as involution and commutator) and todetermine the smallest number of the factors in the representation. We have known that everyelernent of SL_nF(= E_nF), the special linear group over a field, can be written as a product
基金supported by the National Natural Science Foundation of China(Grant No.10371008).
文摘Let σ be an anti-holomorphic involution on an almost complex four manifold X,a necessary and sufficient condition is given to determine weather X/σ admits an almost complex structure.
文摘Let (M<sup>n</sup>, T) be a smooth involution T on a closed manifold M<sup>n</sup>. The fixed point set of T has a constant codimension k. Let J<sub>n</sub><sup>k</sup> be the set of n-dimensional cobordism class in MO<sub>n</sub> (unoriented cobordism group), which has such a representative. In this paper, we obtain a necessary and sufficient condition of α∈J<sub>n</sub><sup>2k</sup>, α∈J<sub>n</sub><sup>2l+1</sup> for 2k≤40, 2t+1≤19.
基金supported by the Notional Natural Science Foundation of China(Grant No.12071321).
文摘In 2020,Niu et al.[Cryptogr.Commun.,2020,12(2):165–185]studied the fixed points of involutions over the finite field with q-elements.This paper further discusses the relationship between the fixed points set and the non-fixed points set of two involutions f_(1)(x)and f_(2)(x)over the finite field F_(q),and then obtains a necessary and sufficient condition for that the composite function f_(1)■f_(2)(x)is also an involution over F_(q).In particular,a special class of involutions over some finite fields is determined completely.
文摘Given an involution in a group G, it can be extended in various ways to an involution in the group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear extensions are considered and necessary and sufficient conditions are given on the group G, its involution, the ring R and the extension for the set of skew-symmetric elements to be commutative and for it to be anticommutative.
文摘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。
文摘针对一般手势识别算法的参数量、计算量和精度难以平衡的问题,提出一种轻量化篮球裁判手势识别算法。该算法在YOLOV5s(You Only Look Once Version 5s)算法的基础上进行重构:首先,用Involution算子替代CSP1_1的卷积算子,以扩大上下文信息捕获范围并减少核冗余;其次,在C3模块后加入协同注意力(CA)机制,以得到更强的手势特征提取能力;然后,用轻量化内容感知上采样算子改进原始上采样模块,并将采样点集中在目标区域而忽略背景部分;最后,利用以SiLU作为激活函数的Ghost-Net进行轻量化剪枝。在自制的篮球裁判手势数据集上的实验结果表明,该轻量化篮球裁判手势识别算法的计算量、参数量和模型大小分别为3.3 GFLOPs、4.0×10^(6)和8.5 MB,与YOLOV5s算法相比,分别减少了79%、44%和40%,mAP@0.5为91.7%,在分辨率为1920×1280的比赛视频上的检测帧率达到89.3 frame/s,证明该算法能满足低误差、高帧率和轻量化的要求。