共查询到20条相似文献,搜索用时 31 毫秒
1.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
2.
A bijective mapping
defined on a finite group G is complete if the mapping defined by
,
, is bijective. In 1955 M. Hall and L. J. Paige conjectured that a finite group G has a complete mapping if and only if a Sylow 2-subgroup of G is non-cyclic or trivial. This conjecture is still open. In this paper we construct a complete mapping for the projective groups PSL
and PGL(2,q),q odd. As a consequence, we prove that in odd characteristic the projective groups PGL(n,q GL
, admit a complete mapping. 相似文献
3.
The 3-local geometry
of the sporadic simple group Co1 has been known to have a cover
with a flag-transitive automorphism group which is a nonsplit extension of an elementary Abelian 2-group of rank 24 (the Leech lattice modulo 2) by Co1. It was conjectured that
was simply connected. We disprove this conjecture by constructing a double cover
of
. The automorphism group of
is of the shape
. However, it is not isomorphic to the involution centralizer of the Monster sporadic simple group. 相似文献
4.
M. B. Zvyagina 《Journal of Mathematical Sciences》2004,120(4):1591-1602
Let
be an associative ring with identity, and let
be the category of left unitary
-modules. A complete characterization of continuous additive co- and contravariant functors
is given. Such functors are either representable, or equivalent to a tensor product, or trivial ones. The class of categories that are dual to
and, therefore, are equivalent to the category of compact right
-modules is constructed by purely algebraic means. A canonical category is singled out in this class. A purely algebraic structure that is equivalent to the topology-algebraic structure of compact right
-modules is constructed. Algebraic analogs of connection and complete disconnection are given. Bibliography: 6 titles. 相似文献
5.
ALAIN HÉNAUT 《Geometriae Dedicata》1997,65(1):89-101
A d-web in (
,0) is given by d complex analytic foliations of codimension one in (
,0) which are in general position. A d-web
in (
,0) is linear if all the leaves are (pieces of) hyperplanes in
and
is algebraic if it is associated, by duality, to a nondegenerate algebraic curve in
of degree d. We characterize linear webs in (
,0). We give explicit conditions under which a linear d-web in (
,0) is algebraic and we obtain equations for
in this case. Some related problems are discussed and some questions are posed. 相似文献
6.
For a given homogeneous elliptic partial differential operator
with constant complex coefficients, two Banach spaces
and
of distributions in
, and compact sets
and
in
, we study joint approximations in the norms of the spaces
and
(the spaces of Whitney jet-distributions) by the solutions of the equation
in neighborhoods of the set
. We obtain a localization theorem, which, under certain conditions, allows one to reduce the above-cited approximation problem to the corresponding separate problems in each of the spaces. 相似文献
7.
The generating line of the first single shift plane (cf. [11, p. 435]) is a 2-surface of
4 which we call the the affine part
of Knarr's surface. We compute all affinities leaving
invariant. After embedding
4 into PG(4,
) we calculate the uniquely determined projective closure
Kn
of
. Using a suitable projection we transform questions on Knarr's surface to questions on Cayley's surface in PG(3,
). In this way we determine all planes carrying 1-dimensional algebraic varieties of
Kn
. We exhibit all automorphic collineations of
Kn
. 相似文献
8.
Yoshiaki Fukuma 《Geometriae Dedicata》1997,64(2):229-251
Let (X,L) be a quasi-polarized variety, i.e. X is a smooth projective variety over the complex numbers
and L is a nef and big divisor on X. Then we conjecture that g(L) = q(X), whereg(L) is the sectional genus of L and
. In this paper, we treat the case
. First we prove that this conjecture is true for
, and we classify (X,L) withg(L)=q(X), where
is the Kodaira dimension of X. Next we study some special cases of
. 相似文献
9.
Hiroshi Suzuki 《Journal of Algebraic Combinatorics》1998,7(2):165-180
It is well known that imprimitive P-polynomial association schemes
with
are either bipartite or antipodal, i.e., intersection numbers satisfy either
for all
for all
. In this paper, we show that imprimitive
-polynomial association schemes
with
are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either
. 相似文献
10.
Judita Lihová 《Czechoslovak Mathematical Journal》1999,49(1):67-80
Let
be a partially ordered set, Int
the system of all (nonempty) intervals of
partially ordered by the set-theoretical inclusion
. We are interested in partially ordered sets
with Int
isomorphic to Int
. We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If
is a directed partially ordered set, the only
with Int
isomorphic to Int
are
corresponding to direct decompositions
of
(
denotes the dual of
. The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11]. 相似文献
11.
A family
of convex sets is said to be in convex position, if none of its members is contained in the convex hull of the others. It is proved that there is a function N(n) with the following property. If
is a family of at least N(n) plane convex sets with nonempty interiors, such that any two members of
have at most two boundary points in common and any three are in convex position, then
has n members in convex position. This result generalizes a theorem of T. Bisztriczky and G. Fejes Tóth. The statement does not remain true, if two members of
may share four boundary points. This follows from the fact that there exist infinitely many straight-line segments such that any three are in convex position, but no four are. However, there is a function M(n) such that every family of at least M(n) segments, any four of which are in convex position, has n members in convex position. 相似文献
12.
We consider the extremal problem to determine the maximal number
of columns of a 0-1 matrix with
rows and at most
ones in each column such that each
columns are linearly independent modulo
. For fixed integers
and
, we shall prove the probabilistic lower bound
=
; for
a power of
, we prove the upper bound
which matches the lower bound for infinitely many values of
. We give some explicit constructions. 相似文献
13.
Dorothee Schueth 《Geometriae Dedicata》2004,105(1):77-83
A nonflat Einstein solvmanifold (
, g) is said to be of standard type if in the associated metric Lie algebra
, the orthogonal complement
of the derived algebra is Abelian. It is an open question whether the standard condition is automatically satisfied for all
nonflat Einstein solvmanifolds. We derive certain properties of the metric Lie algebra
of a nonflat Einstein solvmanifold (
, g) under the assumption
. In particular, we obtain some new sufficient conditions which imply standard type. 相似文献
14.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
15.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
16.
E. G. Goluzina 《Journal of Mathematical Sciences》2002,110(6):3052-3057
Let
be the class of functions satisfying the following conditions: these functions are regular and typically real in the unit disk, they have the form
, and the equality
holds for some fixed
and
with
. We find the set of values of the first two coefficients for functions from this class. Boundary functions for these sets of values are found. Some previous results of the author are supplemented. Boundary functions for the sets of values for the functionals
and
in the class
are found. Bibliography: 5 titles. 相似文献
17.
Renate Jaritz 《Geometriae Dedicata》1997,64(3):365-372
An ordered plane is an incidence structure (
) with an order function , which satisfies the axioms (G), (V) and (S), but no continuation--axiom is required. Points a, b E are said to be in distinct sides of a line
iff
and in the same side if
, respectively. For any lines
,
and
we prove that if b,c are in the same side of line A and a,c are in the same side of B , then a and b are in distinct sides of C. As conclusions we deduce that is harmonic and that in each complete quadrangle the intersection points of the diagonals are never collinear, which is known as the axiom of Fano. So the Fano-axiom holds in each ordered plane, and also in those with boundary points. 相似文献
18.
We study a version of the Gauss map
for a surface
immersed in
and prove an analog of the Ruh--Vilms theorem which states that this map is harmonic iff
has a constant mean curvature. As a corollary, we conclude that an embedded flat torus
with constant mean curvature is a spherical Delonay surface. 相似文献
19.
Frédéric Paulin 《Geometriae Dedicata》2002,95(1):65-85
The aim of this paper is to give a geometric interpretation of the continued fraction expansion in the field
of formal Laurent series in X
–1 over
, in terms of the action of the modular group
on the Bruhat–Tits tree of
, and to deduce from it some corollaries for the diophantine approximation of formal Laurent series in X
–1 by rational fractions in X. 相似文献
20.
Daniel T. Wise 《Geometriae Dedicata》2002,92(1):59-62
This note describes an example of a compact aspherical 2-complex X with a covering space
, such that
is finitely presented but
has no compact core.I thank John Stallings for being my 'Senior Scientist' in 1996–1997, and for many superimaginative e-mails that led to this relationship. 相似文献