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1.
Let G be a finite group. The spectrum of G is the set ω(G) of orders of all its elements. The subset of prime elements of ω(G) is called the prime spectrum and is denoted by π(G). A group G is called spectrum critical (prime spectrum critical) if, for any subgroups K and L of G such that K is a normal subgroup of L, the equality ω(L/K) = ω(G) (π(L/K) = π(G), respectively) implies that L = G and K = 1. In the present paper, we describe all finite simple groups that are not spectrum critical. In addition, we show that a prime spectrum minimal group G is prime spectrum critical if and only if its Fitting subgroup F(G) is a Hall subgroup of G.  相似文献   

2.
3.
Till now, we know Tauberian constants for the ‘Kreisverfahren’ with the conditions lim sup |n 1/2 a n|<∞ and lim sup |n 1 a n|<∞. Now, we obtain constants for the more general condition lim sup |n pan|<∞ with anyp(=∞<p<+∞). These constants are not always 0 or ∞, even if 1/2<p<1; therefore the Tauberian condition lim sup |n pan|<∞ is ‘appropriate’ for 1/2≦p≦1.  相似文献   

4.
Content analysis was performed on the data envelopment analysis (DEA) literature appearing in refereed journals. The extant DEA literature, reported in Gattoufi et al was subdivided into two ways. The first considers all articles appearing during the life cycle of 22 selected major DEA publishing journals. The second considers all post-1995 DEA articles. Content was judged on the basis of a two-point scale representing advancements in theory; a five-point scale indicating contributions to practice; and on seven distinguishable strategies applied by the authors in pursuing their research. Lastly, DEA was compared with similarly obtained results describing the life cycle literatures of flow shop scheduling and of cell manufacturing. This analysis has proven the vitality, robustness, and real-world grounding of DEA on its own and vis-à-vis other OR/MS sub-disciplines. Moreover, the breadth of its diffusion into other disciplines and professions has been shown to be extraordinary.  相似文献   

5.
Let G be a finite group, and let N(G) be the set of conjugacy class sizes of G. By Thompson’s conjecture, if L is a finite non-abelian simple group, G is a finite group with a trivial center, and N(G) = N(L), then L and G are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In this article, we investigate validity of Thompson’s conjecture under a weak condition for the alternating groups of degrees p+1 and p+2, where p is a prime number. This work implies that Thompson’s conjecture holds for the alternating groups of degree p + 1 and p + 2.  相似文献   

6.
This paper reports the results of an online survey conducted with practitioner members of the UK Operational Research (OR) Society. The purpose of the survey was to explore the current practice of supporting the strategy process in terms of activities supported and tools used. The results of the survey are compared to those of previous surveys to explore developments in, inter alia, the use of management/strategy tools and ‘soft’ Operational Research/Management Science (OR/MS) tools. The survey results demonstrate that OR practitioners actively support the strategy process within their organisations. While a wide variety of tools, drawn from the OR/MS and management/strategy fields, are used to support the strategy process within organisations, the findings suggest that soft OR/MS tools are not regularly used. The findings also demonstrate that tools are combined to support the strategy process from both within and across the OR/MS and management/strategy fields. The paper ends by identifying a number of areas for further research.  相似文献   

7.
We show that atoms of the n-generated free left-handed skew Boolean intersection algebra are in a bijective correspondence with pointed partitions of non-empty subsets of \(\{1,2,\dots , n\}\). Furthermore, under the canonical inclusion into the k-generated free algebra, where kn, an atom of the n-generated free algebra decomposes into an orthogonal join of atoms of the k-generated free algebra in an agreement with the containment order on the respective partitions. As a consequence of these results, we describe the structure of finite free left-handed skew Boolean intersection algebras and express several their combinatorial characteristics in terms of Bell numbers and Stirling numbers of the second kind. We also look at the infinite case. For countably many generators, our constructions lead to the ‘partition analogue’ of the Cantor tree whose boundary is the ‘partition variant’ of the Cantor set.  相似文献   

8.
The circular packing problem (CPP) consists of packing n circles C i of known radii r i , iN={1,?…,?n}, into the smallest containing circle ?. The objective is to determine the coordinates (x i ,?y i ) of the centre of C i , iN, as well as the radius r and centre (x,?y) of ?. CPP, which is a variant of the two-dimensional open-dimension problem, is NP hard. This paper presents an adaptive algorithm that incorporates nested partitioning within a tabu search and applies some diversification strategies to obtain a (near) global optimum. The tabu search is to identify the n circles’ ordering, whereas the nested partitioning is to determine the n circles’ positions that yield the smallest r. The computational results show the efficiency of the proposed algorithm.  相似文献   

9.
Let Y 0 be a not very well approximable m × n matrix, and let \({\mathcal {M}}\) be a connected analytic submanifold in the space of m × n matrices containing Y 0. Then almost all \({Y \in \mathcal {M}}\) are not very well approximable. This and other similar statements are cast in terms of properties of certain orbits on homogeneous spaces and deduced from quantitative nondivergence estimates for‘quasi-polynomial’ flows on the space of lattices.  相似文献   

10.
A set S of vertices is independent or stable in a graph G, and we write S ∈ Ind (G), if no two vertices from S are adjacent, and α(G) is the cardinality of an independent set of maximum size, while core(G) denotes the intersection of all maximum independent sets. G is called a König–Egerváry graph if its order equals α(G) + μ(G), where μ(G) denotes the size of a maximum matching. The number def (G) = | V(G) | ?2μ(G) is the deficiency of G. The number \({d(G)=\max\{\left\vert S\right\vert -\left\vert N(S)\right\vert :S\in\mathrm{Ind}(G)\}}\) is the critical difference of G. An independent set A is critical if \({\left\vert A\right\vert -\left\vert N(A)\right\vert =d(G)}\) , where N(S) is the neighborhood of S, and α c (G) denotes the maximum size of a critical independent set. Larson (Eur J Comb 32:294–300, 2011) demonstrated that G is a König–Egerváry graph if and only if there exists a maximum independent set that is also critical, i.e., α c (G) = α(G). In this paper we prove that: (i) \({d(G)=\left \vert \mathrm{core}(G) \right \vert -\left \vert N (\mathrm{core}(G))\right\vert =\alpha(G)-\mu(G)=def \left(G\right)}\) holds for every König–Egerváry graph G; (ii) G is König–Egerváry graph if and only if each maximum independent set of G is critical.  相似文献   

11.
We first demonstrate that mixed strategies are relevant in decision analysis for a maximin decision-maker quite apart from any game-theory considerations. This rectifies the apparent misconception that results from MS/OR textbooks which discuss mixed strategies only in the game-theory setting. Next we show an example of an implementable mixed strategy, by which we mean a mixed decision strategy which does not require randomization for its implementation. This application is to portfolio construction.  相似文献   

12.
Using the method of diagram techniques for the spin and Fermi operators in the framework of the SU(2)-invariant spin-fermion model of the electron structure of the CuO2plane of copper oxides, we obtain an exact representation of the Matsubara Green’s function D(k, m ) of the subsystem of localized spins. This representation includes the Larkin mass operator ΣL(k, m ) and the strength and polarization operators P(k, m ) and Π(k, m ). The calculation in the one-loop approximation of the mass and strength operators for the Heisenberg spin system in the quantum spin-liquid state allows writing the Green’s function D(k, m ) explicitly and establishing a relation to the result of Shimahara and Takada. An essential point in the developed approach is taking the spin-polaron nature of the Fermi quasiparticles in the spin-fermion model into account in finding the contribution of oxygen holes to the spin response in terms of the polarization operator Π(k, m ).  相似文献   

13.
We obtain bivariate forms of Gumbel’s, Fréchet’s and Chung’s linear inequalities for P(Su, Tv) in terms of the bivariate binomial moments {S i, j }, 1 ≤ ik,1 ≤ jl of the joint distribution of (S, T). At u = v = 1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k, l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.  相似文献   

14.
Given a tournament T?=?(X, A), we consider two tournament solutions applied to T: Slater’s solution and Copeland’s solution. Slater’s solution consists in determining the linear orders obtained by reversing a minimum number of directed edges of T in order to make T transitive. Copeland’s solution applied to T ranks the vertices of T according to their decreasing out-degrees. The aim of this paper is to compare the results provided by these two methods: to which extent can they lead to different orders? We consider three cases: T is any tournament, T is strongly connected, T has only one Slater order. For each one of these three cases, we specify the maximum of the symmetric difference distance between Slater orders and Copeland orders. More precisely, thanks to a result dealing with arc-disjoint circuits in circular tournaments, we show that this maximum is equal to n(n???1)/2 if T is any tournament on an odd number n of vertices, to (n 2???3n?+?2)/2 if T is any tournament on an even number n of vertices, to n(n???1)/2 if T is strongly connected with an odd number n of vertices, to (n 2???3n???2)/2 if T is strongly connected with an even number n of vertices greater than or equal to 8, to (n 2???5n?+?6)/2 if T has an odd number n of vertices and only one Slater order, to (n 2???5n?+?8)/2 if T has an even number n of vertices and only one Slater order.  相似文献   

15.
We consider a formally integrable, strictly pseudoconvex CR manifold M of hypersurface type, of dimension 2n?1≥7. Local CR, i.e., holomorphic, embeddings of M are known to exist from the works of Kuranishi and Akahori. We address the problem of regularity of the embedding in standard Hölder spaces C a (M), aR. If the structure of M is of class C m , mZ, 4≤m≤∞, we construct a local CR embedding near each point of M. This embedding is of class C a , for every a, 0≤a<m+(1/2). Our method is based on Henkin’s local homotopy formula for the embedded case, some very precise estimates for the solution operators in it, and a substantial modification of a previous Nash–Moser argument due to the second author.  相似文献   

16.
An asymptotic formula is obtained for the sum of terms σ it (n-it (N - n) (t is real) over 0 < n < N with a remainder estimated by O ε((1+|t|)1+ε N 3/4+ε) for any ε > 0. As a consequence, Porter’s result on a power scale for the average number of steps in the Euclidean algorithm is improved.  相似文献   

17.
Consumers' expressed Intentions-to-buy different brands are frequently measured in marketing research. Study of several hundred surveys shows that a relationship between the percentage I of consumers expressing such an Intention-to-buy and the percentage U claiming current Usage of the brand can be represented by a single one-parameter relationship I = KU ± 3. This holds for different brands (large and small) in over 20 product-fields, for different demographic subgroups, for certain different definitions of the Intentions and Usage variables, for some American as well as British data, and even for trends over time.Both the nature of this relationship between I and U and the paradoxical finding that relatively few people express an Intention-to-buy a new brand which is sub-sequently successful and that relatively many people do so for a brand which is slowly dying are explained by the effect of past Usage. Methodological conclusions of the findings are indicated.  相似文献   

18.
We study the Nikol’skii inequality for algebraic polynomials on the interval [?1, 1] between the uniform norm and the norm of the space L q (α,β) , 1 ≤ q < ∞, with the Jacobi weight ?(α,β)(x) = (1 ? x) α (1 + x) β , αβ > ?1. We prove that, in the case α > β ≥ ?1/2, the polynomial with unit leading coefficient that deviates least from zero in the space L q (α+1,,β) with the Jacobi weight ? (α+1,β)(x) = (1?x) α+1(1+x) β is the unique extremal polynomial in the Nikol’skii inequality. To prove this result, we use the generalized translation operator associated with the Jacobi weight. We describe the set of all functions at which the norm of this operator in the space L q (α,β) for 1 ≤ q < ∞ and α > β ≥ ?1/2 is attained.  相似文献   

19.
Let g(t) be a solution of Bernhard List’s flow on a closed manifold. We obtain a pointwise control on the volume of g(t). Then under an essential assumption, we achieve a formula for the evolution of the Yamabe constant Y(g(t)) when g(t) is evolving by Bernhard List’s flow.  相似文献   

20.
Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, let F, G and H be three generalized derivations of R, I an ideal of R and f(x1,..., x n ) a multilinear polynomial over C which is not central valued on R. If
$$F(f(r))G(f(r)) = H(f(r)^2 )$$
for all r = (r1,..., r n ) ∈ I n , then one of the following conditions holds:
  1. (1)
    there exist aC and bU such that F(x) = ax, G(x) = xb and H(x) = xab for all xR
     
  2. (2)
    there exist a, bU such that F(x) = xa, G(x) = bx and H(x) = abx for all xR, with abC
     
  3. (3)
    there exist bC and aU such that F(x) = ax, G(x) = bx and H(x) = abx for all xR
     
  4. (4)
    f(x1,..., x n )2 is central valued on R and one of the following conditions holds
    1. (a)
      there exist a, b, p, p’ ∈ U such that F(x) = ax, G(x) = xb and H(x) = px + xp’ for all xR, with ab = p + p
       
    2. (b)
      there exist a, b, p, p’ ∈ U such that F(x) = xa, G(x) = bx and H(x) = px + xp’ for all xR, with p + p’ = ab ∈ C.
       
     
  相似文献   

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