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1.
The group PGL(2,q) has an embedding into PGL(3,q) such that it acts as the group fixing a nonsingular conic in PG(2,q). This action affords a coherent configuration (q) on the set (q) of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions +(q) and (q) of (q) to the set +(q) of secant (hyperbolic) lines and to the set (q) of exterior (elliptic) lines, respectively, are both association schemes; moreover, we show that the elliptic scheme (q) is pseudocyclic.We further show that the coherent configurations (q 2) with q even allow certain fusions. These provide a 4-class fusion of the hyperbolic scheme +(q 2), and 3-class fusions and 2-class fusions (strongly regular graphs) of both schemes +(q 2) and (q 2). The fusion results for the hyperbolic case are known, but our approach here as well as our results in the elliptic case are new.  相似文献   

2.
In this paper, we study the minimality of the map for the weighted energy functional , where is a continuous function. We prove that for any integer and any non-negative, non-decreasing continuous function f, the map minimizes E f,p among the maps in which coincide with on . The case p = 1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst. Poincaré Anal. Non-linéaire 17: 35–46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥  7 for any real with , the map minimizes E f,p among the maps in which coincide with on .   相似文献   

3.
Let be a proper partial geometry pg(s,t,2), and let G be an abelian group of automorphisms of acting regularly on the points of . Then either t≡2±od s+1 or is a pg(5,5,2) isomorphic to the partial geometry of van Lint and Schrijver (Combinatorica 1 (1981), 63–73). This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting characterization of the geometry of van Lint and Schrijver.The author is Postdoctoral Fellow of the Fund for Scientific Research Flanders (FWO-Vlaanderen).  相似文献   

4.
Michael Falk 《Extremes》2006,9(1):63-68
It is known that a bivariate extreme value distribution (EVD) with reverse exponential margins can be represented as , , where is a suitable norm on . We prove in this paper the converse implication, i.e., given an arbitrary norm on , , , defines an EVD with reverse exponential margins, if and only if the norm satisfies for the condition . This result is extended to bivariate EVDs with arbitrary margins as well as to extreme value copulas. By identifying an EVD , , with the unit ball corresponding to the generating norm , we obtain a characterization of the class of EVDs in terms of compact and convex subsets of .  相似文献   

5.
We consider existence and qualitative properties of standing wave solutions $\Psi(x,t) = e^{-iEt/h}u(x)We consider existence and qualitative properties of standing wave solutions to the nonlinear Schr?dinger equation with E being a critical frequency in the sense that inf . We verify that if the zero set of WE has several isolated points x i () near which WE is almost exponentially flat with approximately the same behavior, then for h > 0 small enough, there exists, for any integer k, , a standing wave solution which concentrates simultaneously on , where is any given subset of . This generalizes the result of Byeon and Wang in 3 (Arch Rat Mech Anal 165: 295–316, 2002).Supported by the Alexander von Humboldt foundation and NSFC(No:10571069).  相似文献   

6.
Let and be two monoids (algebras) in a monoidal category . Further let be a distributive law in the sense of [J. Beck, Lect. Notes Math., 80:119–140, 1969]; naturally yields a monoid . Consider a word in the symbols , , and . The first coherence theorem proved in this paper asserts that all morphisms coincide in , provided they arise as composites of morphisms which are -products of ’s ‘canonical’ structure morphisms, and of , , , , , , , and . Assume now that an object is endowed with both an -object structure , and an -object structure . Further assume that these two structures are compatible, in the sense that they naturally yield an -object . Let be a word in , , , and , which contains a single instance of , in the rightmost position. The second coherence theorem states that all morphisms coincide in , provided they arise as composites of morphisms which are -products of ’s ‘canonical’ structure morphisms, and of , , , , , , , , , and .  相似文献   

7.
Let V and V′ be 2n-dimensional vector spaces over fields F and F′. Let also Ω: V× VF and Ω′: V′× V′→ F′ be non-degenerate symplectic forms. Denote by Π and Π′ the associated (2n−1)-dimensional projective spaces. The sets of k-dimensional totally isotropic subspaces of Π and Π′ will be denoted by and ${\mathcal G}'_{k}$, respectively. Apartments of the associated buildings intersect and by so-called base subsets. We show that every mapping of to sending base subsets to base subsets is induced by a symplectic embedding of Π to Π′.  相似文献   

8.
We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups , symmetric groups S n and quantum symmetric groups , by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.  相似文献   

9.
A circular distribution is a Galois equivariant map ψ from the roots of unity μ to an algebraic closure of such that ψ satisfies product conditions, for ϵμ and , and congruence conditions for each prime number l and with (l, s) = 1, modulo primes over l for all , where μ l and μ s denote respectively the sets of lth and sth roots of unity. For such ψ, let be the group generated over by and let be , where U s denotes the global units of . We give formulas for the indices and of and inside the circular numbers P s and units C s of Sinnott over . This work was supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R11-2007-035-01001-0). This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00455).  相似文献   

10.
Let G be a connected graph. For at distance 2, we define , and , if then . G is quasi-claw-free if it satisfies , and G is P 3-dominated() if it satisfies , for every pair (x, y) of vertices at distance 2. Certainly contains as a subclass. In this paper, we prove that the circumference of a 2-connected P 3-dominated graph G on n vertices is at least min or , moreover if then G is hamiltonian or , where is a class of 2-connected nonhamiltonian graphs.  相似文献   

11.
We study hypersurfaces in Euclidean space whose position vector x satisfies the condition L k x = Ax + b, where L k is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed , is a constant matrix and is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature and open pieces of round hyperspheres and generalized right spherical cylinders of the form , with . This extends a previous classification for hypersurfaces in satisfying , where is the Laplacian operator of the hypersurface, given independently by Hasanis and Vlachos [J. Austral. Math. Soc. Ser. A 53, 377–384 (1991) and Chen and Petrovic [Bull. Austral. Math. Soc. 44, 117–129 (1991)].   相似文献   

12.
The peak algebra is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks. By exploiting the combinatorics of sparse subsets of [n−1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of . We discuss two peak analogs of the first Eulerian idempotent and construct a basis of semi-idempotent elements for the peak algebra. We use these bases to describe the Jacobson radical of and to characterize the elements of in terms of the canonical action of the symmetric groups on the tensor algebra of a vector space. We define a chain of ideals of , j = 0,..., , such that is the linear span of sums of permutations with a common set of interior peaks and is the peak algebra. We extend the above results to , generalizing results of Schocker (the case j = 0). Aguiar supported in part by NSF grant DMS-0302423 Orellana supported in part by the Wilson Foundation  相似文献   

13.
We consider the following implicit quasi-variational inequality problem: given two topological vector spaces E and F, two nonempty sets X E and C F, two multifunctions Γ : X → 2 X and Ф : X → 2 C , and a single-valued map ψ : , find a pair such that , Ф and for all . We prove an existence theorem in the setting of Banach spaces where no continuity or monotonicity assumption is required on the multifunction Ф. Our result extends to non-compact and infinite-dimensional setting a previous results of the authors (Theorem 3.2 of Cubbiotti and Yao [15] Math. Methods Oper. Res. 46, 213–228 (1997)). It also extends to the above problem a recent existence result established for the explicit case (C = E * and ).  相似文献   

14.
In this paper, we prove that the only compact two-sided hypersurfaces with constant mean curvature H which are weakly stable in and have constant scalar curvature are (i) the twofold covering of a totally geodesic projective space; (ii) the geodesic spheres in ; and (iii) the quotient to of the hypersurface obtained as the product of two spheres of dimensions k and nk, with k = 1,..., n − 1, and radii r and , respectively, with .  相似文献   

15.
Let and denote the complexifications of Heisenberg hypersurfaces in and , respectively. We show that non-degenerate holomorphic Segre mappings from into with possess a partial rigidity property. As an application, we prove that the holomorphic Segre non-transversality for a holomorphic Segre map from into with propagates along Segre varieties. We also give an example showing that this propagation property of holomorphic Segre transversality fails when N > 2n − 2.  相似文献   

16.
We compute the geometric invariants of a product G × H of groups in terms of and . This gives a sufficient condition in terms of and for a normal subgroup of G × H with abelian quotient to be of type F n . We give an example involving the direct product of the Baumslag–Solitar group BS1,2 with itself.   相似文献   

17.
Via an integral transformation, we establish two embedding results between the Emden-Fowler type equation , tt 0 > 0, with solutions x such that as , , and the equation , u > 0, with solutions y such that for given k > 0. The conclusions of our investigation are used to derive conditions for the existence of radial solutions to the elliptic equation , , that blow up as in the two dimensional case.   相似文献   

18.
We consider the following anisotropic Emden–Fowler equation where is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quantity can approach to as . These results show a striking difference with the isotropic case [ Constant].  相似文献   

19.
The hyperoctahedral group H in n dimensions (the Weyl group of Lie type B n ) is the subgroup of the orthogonal group generated by all transpositions of coordinates and reflections with respect to coordinate hyperplanes.With e 1 , ..., e n denoting the standard basis vectors of n and letting x k = e 1 + ··· + e k (k = 1, 2, ..., n), the set
is the vertex set of a generalized regular hyperoctahedron in n . A finite set with a weight function is called a Euclidean t-design, if
holds for every polynomial f of total degree at most t; here R is the set of norms of the points in ,W r is the total weight of all elements of with norm r, S r is the n-dimensional sphere of radius r centered at the origin, and is the average of f over S r . Here we consider Euclidean designs which are supported by orbits of the hyperoctahedral group. Namely, we prove that any Euclidean design on a union of generalized hyperoctahedra has strength (maximum t for which it is a Euclidean design) equal to 3, 5, or 7.We find explicit necessary and sufficient conditions for when this strength is 5 and for when it is 7.In order to establish our classification, we translate the above definition of Euclidean designs to a single equation for t = 5, a set of three equations for t = 7, and a set of seven equations for t = 9. Neumaier and Seidel (1988), as well as Delsarte and Seidel (1989), proved a Fisher-type inequality for the minimum size of a Euclidean t-design in n on p = |R| concentric spheres (assuming that the design is antipodal if t is odd).A Euclidean design with exactly N (n, p, t) points is called tight. We exhibit new examples of antipodal tight Euclidean designs, supported by orbits of the hyperoctahedral group, for N(n, p, t) = (3, 2, 5), (3, 3, 7), and (4, 2, 7).  相似文献   

20.
We show that if the number of directions not determined by a pointset of , of size q2 is at least pe q then every plane intersects in 0 modulo pe+1 points and apply the result to ovoids of the generalised quadrangles and .  相似文献   

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