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
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 lattic...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.展开更多
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 co...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.展开更多
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...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.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^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 ...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.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
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...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.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
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...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）.展开更多
The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role i...The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role in determining the output performance of the scroll expander.In this study,in order to investigate the output characteristics of a variable cross-section scroll expander,numerical simulation and experimental studies were con-ducted by using Computational Fluid Dynamics(CFD)methods and dynamic mesh techniques.The impact of critical parameters on the output performance of the scroll expander was analyzed through the utilization of the control variable method.It is found that increasing the inlet pressure and temperature within a certain range can improve the output power of the scroll expander.However,the increase in temperature and meshing clearance leads to a decline in the overall output performance of the scroll expander,leading to a decrease in volumetric efficiency by 8.43%and 12.79%,respectively.The experiments demonstrate that under equal inlet pressure conditions,increasing the inlet temperature elevates both the rotational speed and torque output of the scroll expander.Specifically,compared to operating at normal temperatures,the output torque increases by 21.8%under high-temperature conditions.However,the rate of speed and torque variation decreases as a consequence of enlarged meshing clearance,resulting in increased internal leakage and reduction in isentropic efficiency.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.
文摘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.
基金Supported by the National Natural Science Foundation of China（10771023）
文摘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.
文摘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.
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^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.
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.
基金Project supported by the Key Project of the Ministry of Education of China (No. 03060).
文摘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.
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.
基金Foundation item： the National Natural Science Foundation of China （No. 10371029） the Natural Science Foundation of Hebei Province （No. 103144）.
文摘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）.
基金funded by the National Key Research and Development Program of China(No.2024YFE0208100).
文摘The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role in determining the output performance of the scroll expander.In this study,in order to investigate the output characteristics of a variable cross-section scroll expander,numerical simulation and experimental studies were con-ducted by using Computational Fluid Dynamics(CFD)methods and dynamic mesh techniques.The impact of critical parameters on the output performance of the scroll expander was analyzed through the utilization of the control variable method.It is found that increasing the inlet pressure and temperature within a certain range can improve the output power of the scroll expander.However,the increase in temperature and meshing clearance leads to a decline in the overall output performance of the scroll expander,leading to a decrease in volumetric efficiency by 8.43%and 12.79%,respectively.The experiments demonstrate that under equal inlet pressure conditions,increasing the inlet temperature elevates both the rotational speed and torque output of the scroll expander.Specifically,compared to operating at normal temperatures,the output torque increases by 21.8%under high-temperature conditions.However,the rate of speed and torque variation decreases as a consequence of enlarged meshing clearance,resulting in increased internal leakage and reduction in isentropic efficiency.
