All elements in the cyclic group are generated by a generator g. The number of generators of of , namely is known to be Euler’s totient function;however, the average prob...All elements in the cyclic group are generated by a generator g. The number of generators of of , namely is known to be Euler’s totient function;however, the average probability of an element being a generator has not been discussed before. Several analytic properties of have been investigated for a long time. However, it seems that some issues still remain unresolved. In this study, we derive the average probability of an element being a generator using previous classical studies.展开更多
Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommut...Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.展开更多
All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting ...All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.展开更多
Let G be the finite cyclic group Z_2 and V be a vector space of dimension 2n with basis x_1,...,x_n,y_1,...,y_n over the field F with characteristic 2.If σ denotes a generator of G,we may assume that σ（x_i）= ayi,...Let G be the finite cyclic group Z_2 and V be a vector space of dimension 2n with basis x_1,...,x_n,y_1,...,y_n over the field F with characteristic 2.If σ denotes a generator of G,we may assume that σ（x_i）= ayi,σ（y_i）= a～-1x_i,where a ∈ F.In this paper,we describe the explicit generator of the ring of modular vector invariants of F[V]～G.We prove that F[V]～G = F[l_i = x_i ＋ ay_i,q_i = x_iy_i,1 ≤ i ≤ n,M_I = X_I ＋ a～-I-Y_I],where I∈An = {1,2,...,n},2 ≤-I-≤ n.展开更多
For a cyclic groupG and an access structureA, the sufficient and necessary condition under whichA isG-ideal homomorphic is given by using the fine-representation of the corresponding matroid over the ring $\mathbb{Z}_...For a cyclic groupG and an access structureA, the sufficient and necessary condition under whichA isG-ideal homomorphic is given by using the fine-representation of the corresponding matroid over the ring $\mathbb{Z}_m $ . Furthermore, the clasification ofG-ideal homomorphic graphic access structures is shown.展开更多
Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The followi...Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.展开更多
Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), ...Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.展开更多
Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper,...Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.展开更多
For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.展开更多
The pile group with elevated cap is widely used as foundation of offshore structures such as turbines, power transmission towers and bridge piers, and understanding its behavior under cyclic lateral loads induced by w...The pile group with elevated cap is widely used as foundation of offshore structures such as turbines, power transmission towers and bridge piers, and understanding its behavior under cyclic lateral loads induced by waves, tide water and winds, is of great importance to designing. A large-scale model test on 3×3 pile group with elevated cap subjected to cyclic lateral loads was performed in saturated silts. The preparation and implementation of the test is presented. Steel pipes with the outer diameter of 114 mm, thickness of 4.5 mm, and length of 6 m were employed as model piles. The pile group was cyclic loaded in a multi-stage sequence with the lateral displacement controlled. In addition, a single pile test was also conducted at the same site for comparison. The displacement of the pile cap, the internal forces of individual piles, and the horizontal stiffness of the pile group are presented and discussed in detail. The results indicate that the lateral cyclic loads have a greater impact on pile group than that on a single pile, and give rise to the significant plastic strain in the soil around piles. The lateral loads carried by each row of piles within the group would be redistributed with loading cycles. The lateral stiffness of the pile group decreases gradually with cycles and broadly presents three different degradation patterns in the test. Significant axial forces were measured out in some piles within the group, owing to the strong restraint provided by the cap, and finally lead to a large settlement of the pile group. These findings can be referred for foundation designing of offshore structures.展开更多
In 1986, G.X. Viennot introduced the theory of heaps of pieces as a visualization of Cartier and Foata’s “partially commutative monoids”. These are essentially labeled posets satisfying a few additional properties,...In 1986, G.X. Viennot introduced the theory of heaps of pieces as a visualization of Cartier and Foata’s “partially commutative monoids”. These are essentially labeled posets satisfying a few additional properties, and one natural setting where they arise is as models of reduced words in Coxeter groups. In this paper, we introduce a cyclic version of a heap, which loosely speaking, can be thought of as taking a heap and wrapping it into a cylinder. We call this object a toric heap, because we formalize it as a labeled toric poset, which is a cyclic version of an ordinary poset. Defining the category of toric heaps leads to the notion of certain morphisms such as toric extensions. We study toric heaps in Coxeter theory, because a cyclic shift of a reduced word is simply a conjugate by an initial or terminal generator. As such, we formalize and study a framework that we call cyclic reducibility in Coxeter theory, which is closely related to conjugacy. We introduce what it means for elements to be torically reduced, which is a stronger condition than simply being cyclically reduced. Along the way, we encounter a new class of elements that we call torically fully commutative (TFC), which are those that have a unique cyclic commutativity class, and comprise a strictly bigger class than the cyclically fully commutative (CFC) elements. We prove several cyclic analogues of results on fully commutative (FC) elements due to Stembridge. We conclude with how this framework fits into recent work in Coxeter groups, and we correct a minor flaw in a few recently published theorems.展开更多
文摘All elements in the cyclic group are generated by a generator g. The number of generators of of , namely is known to be Euler’s totient function;however, the average probability of an element being a generator has not been discussed before. Several analytic properties of have been investigated for a long time. However, it seems that some issues still remain unresolved. In this study, we derive the average probability of an element being a generator using previous classical studies.
基金国家攀登计划，国家自然科学基金，Doctoral Programme Foundation of Institution of Higher Education of China
文摘Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.
基金The NSF (60776810,10871205) of Chinathe NSF (08JCYBJC13900) of Tianjin
文摘All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.
基金Supported by the National Natural Science Foundation of China (Grant No.10771023)
文摘Let G be the finite cyclic group Z_2 and V be a vector space of dimension 2n with basis x_1,...,x_n,y_1,...,y_n over the field F with characteristic 2.If σ denotes a generator of G,we may assume that σ（x_i）= ayi,σ（y_i）= a～-1x_i,where a ∈ F.In this paper,we describe the explicit generator of the ring of modular vector invariants of F[V]～G.We prove that F[V]～G = F[l_i = x_i ＋ ay_i,q_i = x_iy_i,1 ≤ i ≤ n,M_I = X_I ＋ a～-I-Y_I],where I∈An = {1,2,...,n},2 ≤-I-≤ n.
文摘For a cyclic groupG and an access structureA, the sufficient and necessary condition under whichA isG-ideal homomorphic is given by using the fine-representation of the corresponding matroid over the ring $\mathbb{Z}_m $ . Furthermore, the clasification ofG-ideal homomorphic graphic access structures is shown.
文摘Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.
基金TheNationalNaturalScienceFoundationofChina (No .10 1710 74 )
文摘Let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite, G∈F, f(∞)f(p), f(p)≠ for each p∈π. The following conclutions are obtained: (1) if there exists a maximal submodule B of A such that A/B is F-central in G and B has no nonzero F-central ZG-factors, then A has an F-decomposition; (2) if there exists an irreducible F-central submodule B of A such that all ZG-composition factors of A/B are F-ecentric, then A has an F-decomposition.
文摘Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51225804 and U1234204)the Zhejiang Electric Power Design Institute
文摘The pile group with elevated cap is widely used as foundation of offshore structures such as turbines, power transmission towers and bridge piers, and understanding its behavior under cyclic lateral loads induced by waves, tide water and winds, is of great importance to designing. A large-scale model test on 3×3 pile group with elevated cap subjected to cyclic lateral loads was performed in saturated silts. The preparation and implementation of the test is presented. Steel pipes with the outer diameter of 114 mm, thickness of 4.5 mm, and length of 6 m were employed as model piles. The pile group was cyclic loaded in a multi-stage sequence with the lateral displacement controlled. In addition, a single pile test was also conducted at the same site for comparison. The displacement of the pile cap, the internal forces of individual piles, and the horizontal stiffness of the pile group are presented and discussed in detail. The results indicate that the lateral cyclic loads have a greater impact on pile group than that on a single pile, and give rise to the significant plastic strain in the soil around piles. The lateral loads carried by each row of piles within the group would be redistributed with loading cycles. The lateral stiffness of the pile group decreases gradually with cycles and broadly presents three different degradation patterns in the test. Significant axial forces were measured out in some piles within the group, owing to the strong restraint provided by the cap, and finally lead to a large settlement of the pile group. These findings can be referred for foundation designing of offshore structures.
文摘In 1986, G.X. Viennot introduced the theory of heaps of pieces as a visualization of Cartier and Foata’s “partially commutative monoids”. These are essentially labeled posets satisfying a few additional properties, and one natural setting where they arise is as models of reduced words in Coxeter groups. In this paper, we introduce a cyclic version of a heap, which loosely speaking, can be thought of as taking a heap and wrapping it into a cylinder. We call this object a toric heap, because we formalize it as a labeled toric poset, which is a cyclic version of an ordinary poset. Defining the category of toric heaps leads to the notion of certain morphisms such as toric extensions. We study toric heaps in Coxeter theory, because a cyclic shift of a reduced word is simply a conjugate by an initial or terminal generator. As such, we formalize and study a framework that we call cyclic reducibility in Coxeter theory, which is closely related to conjugacy. We introduce what it means for elements to be torically reduced, which is a stronger condition than simply being cyclically reduced. Along the way, we encounter a new class of elements that we call torically fully commutative (TFC), which are those that have a unique cyclic commutativity class, and comprise a strictly bigger class than the cyclically fully commutative (CFC) elements. We prove several cyclic analogues of results on fully commutative (FC) elements due to Stembridge. We conclude with how this framework fits into recent work in Coxeter groups, and we correct a minor flaw in a few recently published theorems.
