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.

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).

基于改进YOLOv7-tiny的高空作业人员安防装备检测算法

针对现有高空作业人员安防装备检测算法参数量较大且检测目标相对单一,难以适应复杂的高空作业场景等问题,提出一种基于改进YOLOv7-tiny的高空作业人员安防装备检测算法。首先,将主干网络重新设计为更轻量的YOLOv7-FasterNet,并调整空间金字塔池化结构,实现模型参数量的压缩;其次,在ELAN-L模块中扩展梯度传输路径的分支,解决了模型压缩造成的通道信息缺失问题,提升了特征信息的提取能力;最后,将网络中下采样部分替换为Involution模块,降低参数冗余,增强网络对全局的捕获能力。实验结果表明,改进的YOLOv7-tiny算法能够更好地适应复杂高空作业场景,在开源数据集上具备良好的性能。该算法的平均检测精度达到94.7%,较原模型提升1.5%,参数量较原模型下降11.6%,实验结果验证了算法改进措施的有效性。

Application of Isogeometric Analysis Method in Three-Dimensional Gear Contact Analysis

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.

Hyperbolicity of unitary involutions

We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.

Involutions in Weyl group of type F4

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）.

Involutions Fixing the Disjoint Union of Copies of Even Projective Space

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.

基于改进SSD的钢材表面缺陷检测

工业生产过程中,钢材表面缺陷的检测对于钢材的质量控制发挥着十分重要的作用,针对钢材表面缺陷检测中存在的检测精度低、检测速度慢等问题,提出了一种钢材表面缺陷检测的改进SSD算法。在所提算法中,采用Transformer多头注意力机制模块代替原SSD结构中的Conv5_1层,以提高小目标检测的能力;原SSD结构中的Conv7操作替换为Involution算子操作,以减少运算的参数量;对网络结构进行特征融合处理,以更全面地检测特征图中所包含的信息。利用NEU-DET数据集进行实验,实验结果表明改进后的SSD算法是有效的,可以高效检测到钢材表面的小目标缺陷,相比改进前平均检测精度提高了4.5%,检测速度提高了13.6%。

Anti-holomorphic involutions and almost complex structures on four-manifold

Let σ be an anti-holomorphic involution on almost complex manifold X, the existence of almost complex structure on Y=X/σ is discussed.

Decomposition of Steinberg group into involutions

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

Quotient spaces of anti-holomorphic involutions

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.

MANIFOLDS WITH INVOLUTIONS WHOSE FIXED POINT SET HAS CONSTANT CODIMENSION

Let (M^n, T) be a smooth involution T on a closed manifold M^n. The fixed point set of T has a constant codimension k. Let J_n^k be the set of n-dimensional cobordism class in MO_n (unoriented cobordism group), which has such a representative. In this paper, we obtain a necessary and sufficient condition of α∈J_n^(2k), α∈J_n^(2l+1) for 2k≤40, 2t+1≤19.

A new construction for involutions over finite fields

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.

Products of Involutions in Steinberg Group over Skew Fields

Consider the stable Steinberg group St（K） over a skew field K. An element x is called an involution if x^2 = 1. In this paper, an involution is allowed to be the identity. The authors prove that an element A of GLn（K） up to conjugation can be represented as BC, where B is lower triangular and C is simultaneously upper triangular. Furthermore. B and C can be chosen so that the elements in the main diagonal of B are β1,β2,…,βn,and of C are γ1,γ2,…,γncn,where cn∈[K^n,K^n] and ∏j=1^n βjγj=det A,it is Also proved that every element δin St（K） is a product of 10 involutions.

Skew-symmetric Elements in Nonlinear Involutions in Group Rings

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.

Involutions Fixing RP（2^m） U P（2^m, 2n- 1）

Let （M^2m＋4n＋k-2, T） be a smooth closed manifold with a smooth involution T whose fixed point set is RP（2^m） ∪ P（2^m, 2n - 1） （m 〉 3, n 〉 0）. For 2n ≥ 2^m, （M^2m＋4n＋k-2, T） is bordant to （P（2^m, RP（2n））, To）.