Continuum mechanics for isotropic finite thermoelastic deformations have been reviewed. Thermal effects on mechanical responses of rubbers have been captured by the isomorphism continuum stored energy (CSE) functional...Continuum mechanics for isotropic finite thermoelastic deformations have been reviewed. Thermal effects on mechanical responses of rubbers have been captured by the isomorphism continuum stored energy (CSE) functional with the multiplicative decomposition of deformation gradient while preserving the structure of symmetry for finite structural deformation. The CSE finite thermoelastic model fits and predicts experimental data of SR and NR-C60 rubbers at different external temperatures. For internal temperature effects of both NR and NR-SIC rubbers, the CSE finite thermoelastic model of stored energy and entropy, along with the newly developed CTE and CI models, fits both nominal stress-stretch and temperature change-stretch experimental data in uniaxial extension tests.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖ ≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖ ≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation 2f (x + y/2 + z + w) = f(x) + f(y) + 2f(z) + 2f(w).展开更多
Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem (GIP) is a nondeterministic polynomial problem. A simulated annea...Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem (GIP) is a nondeterministic polynomial problem. A simulated annealing (SA) algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.展开更多
If T is an isomorphism of (c0) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||·||T^-1|| ≤ 1 +ε ...If T is an isomorphism of (c0) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||·||T^-1|| ≤ 1 +ε for some ε ∈ (0,1/5), then T/||T|| is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator.展开更多
The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compa...The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn't higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.展开更多
Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorp...Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorphism detection based on the properties of similar vertices.In this paper,an ameliorated multi-order adjacent vertex assignment sequence(AMAVS)method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs.First,the specific definition of AMAVS is described.Through the calculation of the AMAVS,the adjacent vertex value sequence reflecting the uniqueness of the topology features is established.Based on the value sequence,all possible similar vertices,corresponding relations,and isomorphism discrimination can be realized.By checking the topological graph of KCs with a different number of links,the effectiveness and efficiency of the proposed method are verified.Finally,the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-D0F(degree of freedom)planar KCs.展开更多
Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positiv...Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).展开更多
In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particul...In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.展开更多
There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM spac...There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E', d(r), r is an element of (0, 1)). This paper establishes the connection between the two kinds of isometric isomorphism.展开更多
On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌...On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1) G is a finite Abelian group. 2) The order of G is p^3. 3 ) The order of G is p^n+1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4) G is a nilpotent group and if p^││G│, then for any P ∈ Sylp (G), P has a cyclic maximal subgroup, where p is a prime; 5) G is a maximal class group of order p4(p〉3).展开更多
In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach ...In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.展开更多
Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the ov...Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the overhead of a function call and is inlined in the code where it is called. When analyzing the decompiled code with lots of inlined intrinsic functions, reverse engineers may be confused by these detailed and repeated operations and lose the goal. In this paper, we propose a method based graph isomorphism to detect intrinsic function on the CFG (Control Flow Graph) of the target function first. Then we identify the boundary of the intrinsic function, determine the parameter and return value and reduce the intrinsic function to a single function call in the disassembled program. Experimental results show that our method is more efficient at reducing intrinsic functions than the state-of-art decompilers such as Hex-Rays, REC and RD (Retargetable Decompiler).展开更多
Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Bana...Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.展开更多
The isomorphism of planar kinematic chains is studied. The original methods for de- tecting isomorphism is discussed. A new matrix, the link -link path matrix, is presented to show the structures of planar kinematic c...The isomorphism of planar kinematic chains is studied. The original methods for de- tecting isomorphism is discussed. A new matrix, the link -link path matrix, is presented to show the structures of planar kinematic chains. It is simple and reliable to detect isomorphism of planar kinematic chains by using the link-link path matrix.展开更多
The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the pro...The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.展开更多
We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cu...We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs(Discrete Math.,256,301-334(2002)).As an application,a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups,which generalises the earlier formula of Huang et al.dealing with the particular case when n is a prime(Acta Math.Sin.,Engl.Ser.,33,996-1011(2017)).As another application,a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve(arXiv preprint,(2007)).展开更多
Let p be a prime and F_p be a finite field of p elements.Let F_(pG)denote the group algebra of the finite p-group G over the field F_(p)and V(F_(pG))denote the group of normalized units in F_(pG).Suppose that G and H ...Let p be a prime and F_p be a finite field of p elements.Let F_(pG)denote the group algebra of the finite p-group G over the field F_(p)and V(F_(pG))denote the group of normalized units in F_(pG).Suppose that G and H are finite p-groups given by a central extension of the form 1→Z_(p)^(m)→G→Z_(p)×···×Z_(p)→1 and G'≌Z_(p),m≥1.Then V(F_(p)G)≌V(F_(p)H)if and only if G≌H.Balogh and Bovdi only solved the isomorphism problem when p is odd.In this paper,the case p=2 is determined.展开更多
A normal Hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur- Zassenhaus theorem states that every normal Hall subgroup has a complement subgroup, that is a set of coset repr...A normal Hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur- Zassenhaus theorem states that every normal Hall subgroup has a complement subgroup, that is a set of coset representatives H which also forms a subgroup of G. In this paper, we present a framework to test isomorphism of groups with at least one normal Hall subgroup, when groups are given as multiplication tables. To establish the framework, we first observe that a proof of Schur-Zassenhaus theorem is constructive, and formulate a necessary and sufficient condition for testing isomorphism in terms of the associated actions of the semidirect products, and isomorphisms of the normal parts and complement parts. We then focus on the case when the normal subgroup is abelian. Utilizing basic facts of representation theory of finite groups and a technique by Le Gall (STACS 2009), we first get an efficient isomorphism testing algorithm when the complement has bounded number of generators. For the case when the complement subgroup is elementary abelian, which does not necessarily have bounded number of generators, we obtain a polynomial time isomorphism testing algorithm by reducing to generalized code isomorphism problem, which asks whether two linear subspaces are the same up to permutation of coordinates. A solution to the latter can be obtained by a mild extension of the singly exponential (in the number of coordinates) time algorithm for code isomorphism problem developed recently by Babai et al. (SODA 2011). Enroute to obtaining the above reduction, we study the following computational problem in representation theory of finite groups: given two representations ρandτ- of a group H over Zp^d, a prime, determine if there exists an automorphism : ФH→ H, such that the induced representation p Ф= ρ o Ф and τ are equivalent, in time poly(|H|, p^d).展开更多
In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any charac...In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.展开更多
文摘Continuum mechanics for isotropic finite thermoelastic deformations have been reviewed. Thermal effects on mechanical responses of rubbers have been captured by the isomorphism continuum stored energy (CSE) functional with the multiplicative decomposition of deformation gradient while preserving the structure of symmetry for finite structural deformation. The CSE finite thermoelastic model fits and predicts experimental data of SR and NR-C60 rubbers at different external temperatures. For internal temperature effects of both NR and NR-SIC rubbers, the CSE finite thermoelastic model of stored energy and entropy, along with the newly developed CTE and CI models, fits both nominal stress-stretch and temperature change-stretch experimental data in uniaxial extension tests.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖ ≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation 2f (x + y/2 + z + w) = f(x) + f(y) + 2f(z) + 2f(w).
基金the National Natural Science Foundation of China (60373089, 60674106, and 60533010)the National High Technology Research and Development "863" Program (2006AA01Z104)
文摘Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem (GIP) is a nondeterministic polynomial problem. A simulated annealing (SA) algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.
基金National Natural Science Foundation of China(10571090)the Research Fund for the Doctoral Program of Higher Education(20060055010)
文摘If T is an isomorphism of (c0) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||·||T^-1|| ≤ 1 +ε for some ε ∈ (0,1/5), then T/||T|| is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator.
文摘The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn't higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.
基金Supported by National Natural Science Foundation of China(Grant Nos.51675488,51975534)Zhejiang Provincial Natural Science Foundation of China(Grant No.LY19E050021)。
文摘Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorphism detection based on the properties of similar vertices.In this paper,an ameliorated multi-order adjacent vertex assignment sequence(AMAVS)method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs.First,the specific definition of AMAVS is described.Through the calculation of the AMAVS,the adjacent vertex value sequence reflecting the uniqueness of the topology features is established.Based on the value sequence,all possible similar vertices,corresponding relations,and isomorphism discrimination can be realized.By checking the topological graph of KCs with a different number of links,the effectiveness and efficiency of the proposed method are verified.Finally,the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-D0F(degree of freedom)planar KCs.
基金supported by the National Natural Science Foundation of China(11801555 and 11971058)the Fundamental Research Funds for the Central Universities(2020YQLX02)supported by the National Natural Science Foundation of China(11971058,11761131002 and 11671185)。
文摘Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).
基金Supported by the National Natural Science Foundation of China.
文摘In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.
文摘There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E', d(r), r is an element of (0, 1)). This paper establishes the connection between the two kinds of isometric isomorphism.
文摘On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1) G is a finite Abelian group. 2) The order of G is p^3. 3 ) The order of G is p^n+1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4) G is a nilpotent group and if p^││G│, then for any P ∈ Sylp (G), P has a cyclic maximal subgroup, where p is a prime; 5) G is a maximal class group of order p4(p〉3).
文摘In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.
文摘Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the overhead of a function call and is inlined in the code where it is called. When analyzing the decompiled code with lots of inlined intrinsic functions, reverse engineers may be confused by these detailed and repeated operations and lose the goal. In this paper, we propose a method based graph isomorphism to detect intrinsic function on the CFG (Control Flow Graph) of the target function first. Then we identify the boundary of the intrinsic function, determine the parameter and return value and reduce the intrinsic function to a single function call in the disassembled program. Experimental results show that our method is more efficient at reducing intrinsic functions than the state-of-art decompilers such as Hex-Rays, REC and RD (Retargetable Decompiler).
文摘Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.
文摘The isomorphism of planar kinematic chains is studied. The original methods for de- tecting isomorphism is discussed. A new matrix, the link -link path matrix, is presented to show the structures of planar kinematic chains. It is simple and reliable to detect isomorphism of planar kinematic chains by using the link-link path matrix.
文摘The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.
基金Supported by the Slovenian Research Agency (research program P1-0285 and research projects N1-0062,J1-9108,J1-1695,N1-0140,J1-2451,N1-0208 and J1-3001)。
文摘We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs(Discrete Math.,256,301-334(2002)).As an application,a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups,which generalises the earlier formula of Huang et al.dealing with the particular case when n is a prime(Acta Math.Sin.,Engl.Ser.,33,996-1011(2017)).As another application,a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve(arXiv preprint,(2007)).
基金National Natural Science Foundation of China(Grant No.12171142)。
文摘Let p be a prime and F_p be a finite field of p elements.Let F_(pG)denote the group algebra of the finite p-group G over the field F_(p)and V(F_(pG))denote the group of normalized units in F_(pG).Suppose that G and H are finite p-groups given by a central extension of the form 1→Z_(p)^(m)→G→Z_(p)×···×Z_(p)→1 and G'≌Z_(p),m≥1.Then V(F_(p)G)≌V(F_(p)H)if and only if G≌H.Balogh and Bovdi only solved the isomorphism problem when p is odd.In this paper,the case p=2 is determined.
基金supported in part by the National Natural Science Foundation of China under Grant No. 60553001the National Basic Research 973 Program of China under Grant Nos. 2007CB807900 and 2007CB807901
文摘A normal Hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur- Zassenhaus theorem states that every normal Hall subgroup has a complement subgroup, that is a set of coset representatives H which also forms a subgroup of G. In this paper, we present a framework to test isomorphism of groups with at least one normal Hall subgroup, when groups are given as multiplication tables. To establish the framework, we first observe that a proof of Schur-Zassenhaus theorem is constructive, and formulate a necessary and sufficient condition for testing isomorphism in terms of the associated actions of the semidirect products, and isomorphisms of the normal parts and complement parts. We then focus on the case when the normal subgroup is abelian. Utilizing basic facts of representation theory of finite groups and a technique by Le Gall (STACS 2009), we first get an efficient isomorphism testing algorithm when the complement has bounded number of generators. For the case when the complement subgroup is elementary abelian, which does not necessarily have bounded number of generators, we obtain a polynomial time isomorphism testing algorithm by reducing to generalized code isomorphism problem, which asks whether two linear subspaces are the same up to permutation of coordinates. A solution to the latter can be obtained by a mild extension of the singly exponential (in the number of coordinates) time algorithm for code isomorphism problem developed recently by Babai et al. (SODA 2011). Enroute to obtaining the above reduction, we study the following computational problem in representation theory of finite groups: given two representations ρandτ- of a group H over Zp^d, a prime, determine if there exists an automorphism : ФH→ H, such that the induced representation p Ф= ρ o Ф and τ are equivalent, in time poly(|H|, p^d).
基金This work was supported by the National Natural Science Foundation of China,Hundred Talents Program of Chinese Academy of Sciences and a Fund from National Education Ministry of China. Su Yucai was partially supported by Academy of Mathematics and Syst
文摘In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.