共查询到20条相似文献,搜索用时 254 毫秒
1.
Branko Sarić 《Czechoslovak Mathematical Journal》2010,60(4):1043-1048
Let [a, b] be an interval in ℝ Rand let F be a real valued function defined at the endpoints of [a, b] and with a certain number of discontinuities within [a, b]. Assuming F to be differentiable on a set [a, b] | E to the derivative f, where E is a subset of [a, b] at whose points F can take values ±∞ or not be defined at all, we adopt the convention that F and f are equal to 0 at all points of E and show that KH-vt ∝
a
b
f = F(b) − F(a), where KH-vt denotes the total value of the Kurzweil-Henstock integral. The paper ends with a few examples that illustrate the theory. 相似文献
2.
Leila Goudarzi 《代数通讯》2017,45(9):4093-4098
Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and ML?C and C∕ML contains no non-zero ideal of L∕ML, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra. 相似文献
3.
Let A and B be C*-algebras. A linear map T : A → B is said to be a *-homomorphism at an element z ∈ A if ab* = z in A implies T (ab*) = T (a)T (b)* = T (z), and c*d = z in A gives T (c*d) = T (c)*T (d) = T (z). Assuming that A is unital, we prove that every linear map T : A → B which is a *-homomorphism at the unit of A is a Jordan *-homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *-homomorphism if and only if T is a *-homomorphism at the unit of A. For a general unital C*-algebra A and a linear map T : A → B, we prove that T is a *-homomorphism if, and only if, T is a *-homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a ?-homomorphism at p and at 1 ? p, then we prove that T is a Jordan *-homomorphism. We also study bounded linear maps that are *-homomorphisms at a unitary element in A. 相似文献
4.
Marcin KRZYWKOWSKI 《数学年刊B辑(英文版)》2012,33(1):113-126
A vertex of a graph is said to dominate itself and all of its neighbors.A double dominating set of a graph G is a set D of vertices of G,such that every vertex of G is dominated by at least two vertices of D.The double domination number of a graph G is the minimum cardinality of a double dominating set of G.For a graph G =(V,E),a subset D V(G) is a 2-dominating set if every vertex of V(G) \ D has at least two neighbors in D,while it is a 2-outer-independent dominating set of G if additionally the set V(G)\D is independent.The 2-outer-independent domination number of G is the minimum cardinality of a 2-outer-independent dominating set of G.This paper characterizes all trees with the double domination number equal to the 2-outer-independent domination number plus one. 相似文献
5.
Ki-perfect graphs are a special instance of F - G perfect graphs, where F and G are fixed graphs with F a partial subgraph of G. Given S, a collection of G-subgraphs of graph K, an F - G cover of S is a set of T of F-subgraphs of K such that each subgraph in S contains as a subgraph a member of T. An F - G packing of S is a subcollection S′? S such that no two subgraphs in S′ have an F-subgraph in common. K is F - G perfect if for all such S, the minimum cardinality of an F - G cover of S equals the maximum cardinality of an F - G packing of S. Thus Ki-perfect graphs are precisely Ki-1 - Ki perfect graphs. We develop a hypergraph characterization of F - G perfect graphs that leads to an alternate proof of previous results on Ki-perfect graphs as well as to a characterization of F - G perfect graphs for other instances of F and G. 相似文献
6.
《Quaestiones Mathematicae》2013,36(4):591-603
Abstract Let R be a ring with involution *. We show that if R is a *-prime ring which is not a prime ring, then R is “essentially” a direct product of two prime rings. Moreover, if P is a *-prime *-ideal of R, which is not a prime ideal of R, and X is minimal among prime ideals of R containing P, then P is a prime ideal of X, P = X ∩ X* and either: (1) P is essential in X and X is essential in R; or (2) for any relative complement C of P in X, then C* is a relative complement of X in R. Further characterizations of *-primeness are provided. 相似文献
7.
Huberta Lausch 《Geometriae Dedicata》1995,56(2):121-127
All normal subloops of a loopG form a modular latticeL
n
(G). It is shown that a finite loopG has a complemented normal subloop lattice if and only ifG is a direct product of simple subloops. In particular,L
n
(G) is a Boolean algebra if and only if no two isomorphic factors occurring in a decomposition ofG are abelian groups. The normal subloop lattice of a finite loop is a projective geometry if and only ifG is an elementary abelianp-group for some primep. 相似文献
8.
Let R be a ring with identity and let M be a unital left R-module. A proper submodule L of M is radical if L is an intersection of prime submodules of M. Moreover, a submodule L of M is isolated if, for each proper submodule N of L, there exists a prime submodule K of M such that N ? K but L ? K. It is proved that every proper submodule of M is radical (and hence every submodule of M is isolated) if and only if N ∩ IM = IN for every submodule N of M and every (left primitive) ideal I of R. In case, R/P is an Artinian ring for every left primitive ideal P of R it is proved that a finitely generated submodule N of a nonzero left R-module M is isolated if and only if PN = N ∩ PM for every left primitive ideal P of R. If R is a commutative ring, then a finitely generated submodule N of a projective R-module M is isolated if and only if N is a direct summand of M. 相似文献
9.
Let Rbe a prime algebra over a field .F, d a nonzero derivation of Rand ρ a nonzero right ideal of R. Suppose that for every x∈ ρ,d(x) is algebraic over Fof bounded degree. Then Ris a primitive ring with a minimal right ideal eR, where e=e2 ∈Rand eReis a finite-dimensional central division algebra, except when dis an inner derivation induced by an element a in the two-sided Martindale quotient ring of Rsuch that aρp = 0. An analogous result is also proved for the Lie ideal case. 相似文献
10.
Tung-Yang Ho Ting-Yi Sung Lih-Hsing Hsu Chang-Hsiung Tsai Jeng-Yan Hwang 《Journal of Algorithms in Cognition, Informatics and Logic》1998,28(2):216-257
Given a series-parallel network (network, for short)N, its dual networkN′ is given by interchanging the series connection and the parallel connection of networkN. We usually use a series-parallel graph to represent a network. LetG[N] andG[N′] be graph representations ofNandN′, respectively. A sequence of edgese1, e2,…,ekis said to form a common trail on (G[N], G[N′]) if it is a trail on bothG[N] andG[N′]. If a common trail covers all of the edges inG[N] andG[N′], it is called adouble Euler trail.However, there are many different graph representations for a network. We say that a networkNhas a double Euler trail (DET) if there is a common Euler trail for someG[N] and someG[N′]. Finding a DET in a network is essential for optimizing the layout area of a complementary CMOS functional cell. Maziasz and Hayes (IEEE Trans. Computer-Aided Design9(1990), 708–719) gave a linear time algorithm for solving the layout problem in fixedG[N] andG[N′] and an exponential algorithm for finding the optimal cover in a network without fixing graph representations. In this paper, we study properties of subnetworks of a DET network. According to these properties, we propose an algorithm that automatically generates the rules for composition of trail cover classes. On the basis of these rules, a linear time algorithm for recognizing DET networks is presented. Furthermore, we also give a necessary and sufficient condition for the existence of a double Euler circuit in a network. 相似文献
11.
Elias Dahlhaus Jens Gustedt Ross M. McConnell 《Journal of Algorithms in Cognition, Informatics and Logic》2001,41(2):360
A module of an undirected graph G = (V, E) is a set X of vertices that have the same set of neighbors in V\X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O(n + mα(m, n)) time bound and a variant with a linear time bound. 相似文献
12.
We call a subgroup A of a finite group G a solitary subgroup of G if G does not contain another isomorphic copy of A. We call a normal subgroup A of a finite group G a normal solitary subgroup of G if G does not contain another normal isomorphic copy of A. The property of being (normal) solitary can be viewed as a strengthening of the requirement that A is normal in G. We derive various results on the existence of (normal) solitary subgroups. 相似文献
13.
J. W. Wamsley 《Israel Journal of Mathematics》1972,11(3):297-298
LetG be a finitep-group,d(G)=dimH
1 (G, Z
p) andr(G)=dimH
2(G, Zp). Thend(G) is the minimal number of generators ofG, and we say thatG is a member of a classG
p
of finitep-groups ifG has a presentation withd(G) generators andr(G) relations. We show that ifG is any finitep-group, thenG is the direct factor of a member ofG
p
by a member ofG
p
. 相似文献
14.
15.
If a domain R, with quotient field K, has a finite saturated chain of overrings from R to K, then the integral closure of R is a Prüfer domain. An integrally closed domain R with quotient field K has a finite saturated chain of overrings from R to K with length m ≥ 1 iff R is a Prüfer domain and |Spec(R)| =m + 1. In particular, we prove that a domain R has a finite saturated chain of overrings from R to K with length dim(R) iff R is a valuation domain and that an integrally closed domain R has a finite saturated chain of overrings from R to K with length dim (R) +1 iff R is a Prüfer domain with exactly two maximal ideals such that at most one of them fails to contain every non-maximal prime. The relationship with maximal non-valuation subrings is also established. 相似文献
16.
A multisecret threshold scheme is a system which protects a number of secret keys among a group of n participants. There is a secret sK associated with every subset K of k participants such that any t participants in K can reconstruct the secret sK, but a subset of w participants cannot get any information about a secret they are not associated with. This paper gives a construction for
the parameters t = 2, k = 3 and for any n and w that is optimal in the sense that participants hold the minimal amount of information.
Communicated by: P. Wild 相似文献
17.
Muhammet Tamer Koşan 《Proceedings Mathematical Sciences》2009,119(4):453-458
Let R be a commutative Noetherian ring with non-zero identity and a be a maximal ideal of R. An R-module M is called minimax if there is a finitely generated submodule N of M such that M/N is Artinian. Over a Gorenstein local ring R of finite Krull dimension, we proved that the Socle of H
a
n
(R) is a minimax R-module for each n ≥ 0. 相似文献
18.
19.
Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V(G) (the ground set) the image of V(H) under the isomorphism. We consider connectivity and minimum degree or degree sum conditions sufficient to imply there is
a spanning subgraph of G isomorphic to a subdivision of H on the same ground set S. These results generalize a number of theorems in the literature. 相似文献
20.
Huanyin Chen 《数学年刊B辑(英文版)》2007,28(6):617-628
A ring R is a QB-ring provided that aR + bR = R with a, b ∈ R implies that there exists a y ∈ R such that
It is said that a ring R is a JB-ring provided that R/J(R) is a QB-ring, where J(R) is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J(R)2. 相似文献