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1.
An equivelar polyhedral 2-manifold in the class ?p,q is one embedded inE 3 in which every face is a convexp-gon and every vertex isq-valent. In this paper, examples are constructed, to show that each of the classes ?3,q (q≧7), ?4,q (q≧5) and ?p,4 (p≧5) contains infinitely many distinct combinatorial types. As particular examples, there are polyhedral 2-manifolds with 576 vertices and genus 577, and with 4096 faces and genus 4097. A modification of one construction shows that there is a constantk, such that for eachg≧2, there exists a closed polyhedral 2-manifold inE 3 of genusg with at mostkg/logg vertices. 相似文献
2.
We give a classification of all equivelar polyhedral maps on the torus. In particular, we classify all triangulations and quadrangulations of the torus admitting a vertex transitive automorphism group. These are precisely the ones which are quotients of the regular tessellations {3,6}, {6,3} or {4,4} by a pure translation group. An explicit formula for the number of combinatorial types of equivelar maps (polyhedral and non-polyhedral) with n vertices is obtained in terms of arithmetic functions in elementary number theory, such as the number of integer divisors of n. The asymptotic behaviour for n→∞ is also discussed, and an example is given for n such that the number of distinct equivelar triangulations of the torus with n vertices is larger than n itself. The numbers of regular and chiral maps are determined separately, as well as the ones for all other kinds of symmetry. Furthermore, arithmetic properties of the integers of type p2+pq+q2 (or p2+q2, resp.) can be interpreted and visualized by the hierarchy of covering maps between regular and chiral equivelar maps or type {3,6} (or {4,4}, resp.). 相似文献
3.
Jan Peleska 《Aequationes Mathematicae》1984,27(1):20-31
Generalizing theorems of Myers-Steenrod and of Hawking, we obtain characterizations for isometries and conformal mappings of pseudo-Riemannian spaces (M, g): Define a local distance function on convex normal neighbourhoods by (p, q) =g(exp
p
–1
q, exp
p
–1
q). Then every homeomorphismf locally preserving these functions is an isometry. If (M, g) has indefinite signature andf locally preserves distance zero, it is a conformal diffeomorphism. 相似文献
4.
In the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation ?Δu + g(x, u) = 0 in a smooth domain Ω ? ?N, for a general class of positive nonlinearities. This class includes every space independent, monotone increasing g which satisfies the Keller‐Osserman condition as well as degenerate nonlinearities gα,q of the form gα,q (x, u) = d(x, ?Ω)α |u|q?1 u, with α > ?2 and q > 1. The boundary trace is given by a positive regular Borel measure which may blow up on compact sets. In the second part we concentrate on the family of nonlinearities {gα,q}, determine the critical value of the exponent q (for fixed α > ?2) and discuss (a) positive solutions with an isolated singularity, for subcritical nonlinearities and (b) the boundary value problem for ?Δu + gα,q (x, u) = 0 with boundary data given by a positive regular Borel measure (possibly unbounded). We show that, in the subcritical case, the problem possesses a unique solution for every such measure. © 2003 Wiley Periodicals, Inc. 相似文献
5.
The genus g of an q-maximal curve satisfies g=g
1≔q(q−1)/2 or . Previously, q-maximal curves with g=g
1 or g=g
2, q odd, have been characterized up to q-isomorphism. Here it is shown that an q-maximal curve with genus g
2, q even, is q-isomorphic to the non-singular model of the plane curve ∑
i
=1}
t
y
q
/2
i
=x
q
+1, q=2
t
, provided that q/2 is a Weierstrass non-gap at some point of the curve.
Received: 3 December 1998 相似文献
6.
In this paper, we establish some sharp Sobolev trace inequalities on n-dimensional, compact Riemannian manifolds with smooth boundaries. More specifically, let q = 2(n - 1)/(n - 2), 1/S = inf {∫ |∇u|2 : ∇u ∈ L2(R+n), ∫ |u|q = 1}. We establish for any Riemannian manifold with a smooth boundary, denoted as (M, g), that there exists some constant A = A(M, g) > 0, (∫dM|u|q dsg)2/q < or = to S ∫M |∇gu|2 dvg + A ∫dMu2 dsg, for all u ∈ H1 (M). The inequality is sharp in the sense that the inequality is false when S is replaced by any smaller number. © 1997 John Wiley & Sons, Inc. 相似文献
7.
Let (Mr)r∈?0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr ≥ 1 for every r ∈ ? and defines a non quasi - analytic class. Let moreover F be a closed proper subset of ?n. Then for every function f on ?n belonging to the non quasi - analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on ?,n F and such that Dαf(x) = Dαg(x) for every α ∈ ?n0 and x ∈ F. 相似文献
8.
We construct irreducible pseudo-Riemannian manifolds (M, g) of arbitrary signature (p, q) with the same curvature tensor as a pseudo-Riemannian symmetric space which is a direct product of a two-dimensional Riemannian
space form M
2(c) and a pseudo-Euclidean space with the signature (p, q − 2), or (p − 2, q), respectively. 相似文献
9.
We determine the maximum number of colors in a coloring of the edges of Km,n such that every cycle of length 2k contains at least two edges of the same color. One of our main tools is a result on generalized path covers in balanced bipartite graphs. For positive integers q≤ a, let g(a,q) be the maximum number of edges in a spanning subgraph G of Ka,a such that the minimum number of vertex‐disjoint even paths and pairs of vertices from distinct partite sets needed to cover V(G) is q. We prove that g(a,q) = a2 ? aq + max {a, 2q ? 2}. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 9–28, 2004 相似文献
10.
Some infinite family is constructed of orientable three-dimensional closed manifoldsM
n
(p, q), where n ≥ 2, p ≥ 3, 0 < q < p, and (p, q) = 1, such that M
n
(p, q) is an n-fold cyclic covering of the lens space L(p, q) branched over a two-component link. 相似文献
11.
A Riemann surface M is said to be K-quasiconformally homogeneous if, for every two points p, q ∈ M, there exists a K-quasiconformal homeomorphism f: M→M such that f(p) = q. In this paper, we show there exists a universal constant K > 1 such that if M is a K-quasiconformally homogeneous hyperbolic genus zero surface other than ⅅ2, then K ≥ K. This answers a question by Gehring and Palka [10]. Further, we show that a non-maximal hyperbolic surface of genus g ≥ 1 is not K-quasiconformally homogeneous for any finite K ≥ 1. 相似文献
12.
It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold (M
n
, g) blow-up at a point p ? M{p \in M} , then all derivatives of the Weyl tensor W
g
of g, of order less than or equal to
[\fracn-62]{[\frac{n-6}{2}]} , vanish at p ? M{p \in M} . In this paper, we will construct smooth counterexamples to the Weyl Vanishing Conjecture for any n ≥ 25. 相似文献
13.
14.
Some geometry of Hermitian matrices of order three over GF(q2) is studied. The variety coming from rank 2 matrices is a cubic hypersurface M73of PG(8,q ) whose singular points form a variety H corresponding to all rank 1 Hermitian matrices. BesideM73 turns out to be the secant variety of H. We also define the Hermitian embedding of the point-set of PG(2, q2) whose image is exactly the variety H. It is a cap and it is proved that PGL(3, q2) is a subgroup of all linear automorphisms of H. Further, the Hermitian lifting of a collineation of PG(2, q2) is defined. By looking at the point orbits of such lifting of a Singer cycle of PG(2, q2) new mixed partitions of PG(8,q ) into caps and linear subspaces are given. 相似文献
15.
John Rizkallah 《代数通讯》2017,45(4):1785-1792
16.
S. P. Voitenko 《Ukrainian Mathematical Journal》2009,61(9):1404-1416
We obtain exact order estimates for the best M -term trigonometric approximations of the classes Bp,qW B_{p,\theta }^\Omega of periodic functions of many variables in the space L
q
. 相似文献
17.
We prove that there does not exist a [q4+q3−q2−3q−1, 5, q4−2q2−2q+1]q code over the finite field
for q≥ 5. Using this, we prove that there does not exist a [gq(5, d), 5, d]q code with q4 −2q2 −2q +1 ≤ d ≤ q4 −2q2 −q for q≥ 5, where gq(k,d) denotes the Griesmer bound.MSC 2000: 94B65, 94B05, 51E20, 05B25 相似文献
18.
Let K be a (algebraically closed ) field. A morphism A ⟼ g
−1
Ag, where A ∈ M(n) and g ∈ GL(n), defines an action of a general linear group GL(n) on an n × n-matrix space M(n), referred to as an adjoint action. In correspondence with the adjoint action is the coaction α: K[M(n)] → K[M(n)] ⊗ K[GL(n)] of a Hopf algebra K[GL(n)] on a coordinate algebra K[M(n)] of an n × n-matrix space, dual to the conjugation morphism. Such is called an adjoint coaction. We give coinvariants of an adjoint coaction
for the case where K is a field of arbitrary characteristic and one of the following conditions is satisfied: (1) q is not a root of unity; (2) char K = 0 and q = ±1; (3) q is a primitive root of unity of odd degree. Also it is shown that under the conditions specified, the category of rational
GL
q
× GL
q
-modules is a highest weight category. 相似文献
19.
In this paper, we shall prove that the minimum length nq(5,d) is equal to gq(5,d) +1 for q4−2q2−2q+1≤ d≤ q4 − 2q2 − q and 2q4 − 2q3 − q2 − 2q+1 ≤ d ≤ 2q4−2q3−q2−q, where gq(5,d) means the Griesmer bound
.
Communicated by: J.D. Key 相似文献
20.
We know that the polyhedra corresponding to the Platonic solids are equivelar. In this article we have classified completely
all the simplicial equivelar polyhedra on ≤ 11 vertices. There are exactly 27 such polyhedra. For each n\geq -4 , we have classified all the (p,q) such that there exists an equivelar polyhedron of type {p,q} and of Euler characteristic n . We have also constructed five types of equivelar polyhedra of Euler characteristic -2m , for each m\geq 2 .
Received February 14, 2000, and in revised form August 15, 2000. Online publication March 26, 2001. 相似文献