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1.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
2.
A (k,n)-arc in PG(2,q) is usually defined to be a set
of k points in the plane such that some line meets
in n points but such that no line meets
in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow
to be a multiset, that is, permit
to contain multiple points. The case k=q
2+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q
2+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q
2+q+2 and minimum distance q
2. Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q
2+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem. 相似文献
3.
The automorphism group of the Barnes-Wall lattice L
m in dimension 2
m
(m ; 3) is a subgroup of index 2 in a certain Clifford group
of structure 2
+
1+2m
. O
+(2m,2). This group and its complex analogue
of structure
.Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge@apos;s 1996 result that the space of invariants for
of degree 2k is spanned by the complete weight enumerators of the codes
, where C ranges over all binary self-dual codes of length 2k; these are a basis if m k - 1. We also give new constructions for L
m and
: let M be the
-lattice with Gram matrix
. Then L
m is the rational part of M
m, and
= Aut(Mm). Also, if C is a binary self-dual code not generated by vectors of weight 2, then
is precisely the automorphism group of the complete weight enumerator of
. There are analogues of all these results for the complex group
, with doubly-even self-dual code instead of self-dual code. 相似文献
4.
Kenzi Akiyama 《Designs, Codes and Cryptography》2001,23(2):213-222
In this paper, we consider Schur rings on a finite group G of ordern(n-1) suchthat G has a partition
with
. Then Gis characterized as follows. (a) G has subgroups E andH of order n andn-1 respectively, and
, or(b)G has subgroupsK andH( K) of order 2(n-1) and n-1 respectively,and
. In addition assume that G has a subsetR of sizen-1 satisfying
in the groupalgebraC[G]. Then G is characterized as a collineation groupof a projective plane of order n such that G has five orbits ofpoints of lengthsn(n-1), n, n-1, 1 and 1. In particular, we characterize projective planesof ordern admitting a quasiregular collineation group of order n(n-1)as the case that E and H are normal subgroups ofG. 相似文献
5.
Zhi-Wei Sun 《Combinatorica》2003,23(4):681-691
For a finite system
of arithmetic sequences
the covering function is w(x)
= |{1 s
k : x as (mod
ns)}|. Using equalities
involving roots of unity we characterize those systems with a
fixed covering function w(x). From the characterization we reveal
some connections between a period n0 of
w(x) and the moduli
n1, .
. . , nk in such a system
A. Here are three central
results: (a) For each r=0,1,
. . .,nk/(n0,nk)–1 there exists a
Jc{1, . . . ,
k–1} such that
. (b) If
n1
···nk–l <nk–l+1 =···=nk (0 <
l <
k), then for any positive
integer r <
nk/nk–l with
r 0 (mod
nk/(n0,nk)), the binomial
coefficient
can be written as the
sum of some (not necessarily distinct) prime divisors of
nk. (c)
max(xw(x)
can be written in the form
where
m1, .
. .,mk are positive
integers.The research is supported by the Teaching and
Research Award Fund for Outstanding Young Teachers in Higher
Education Institutions of MOE, and the National Natural Science
Foundation of P. R. China. 相似文献
6.
Let X,X
n
;n1 be a sequence of real-valued i.i.d. random variables with E(X)=0. Assume B(u) is positive, strictly increasing and regularly-varying at infinity with index 1/2<1. Set b
n
=B(n),n1. If
and
for some [0,), then it is shown that
and
for every real triangular array (a
n,k
;1kn,n1) and every array of bounded real-valued i.i.d. random variables W,W
n,k
;1kn,n1`` independent of {X,X
n
;n1}, where (W)=(E(W–E(W))2)1/2. An analogous law of the iterated logarithm for the unweighted sums
n
k=1
X
k
;n1} is also given, along with some illustrative examples. 相似文献
7.
G. V. Kuz'mina 《Journal of Mathematical Sciences》2004,122(6):3654-3666
In the present paper, we solve some problems on the maximum of the weighted sum
(M(Dk,ak) denotes the reduced module of the domain Dk with respect to the point ak Dk in the family of all nonoverlapping simple connected domains Dk, ak Dk, k=1,... ,n, where the points a1,... ,an are free parameters satisfying certain geometric conditions. The proofs involve a version of the method of extremal metric, which reveals a certain symmetry of the extremal system of the points a1,... ,an. The problem on the maximum of the conformal invariant
for all systems of points b1,... ,bs is also considered. In the case where the systems {b1,... ,b5} are symmetric with respect to a certain circle, the problem was solved earlier. A theorem formulated in the author's previous work asserts that the maximum of invariant (*) for all system of points {b1,... ,b5} is attained in a certain well-defined case. In the present work, it is shown that the proof of this theorem contains mistake. A possible proof of the theorem is outlined. Bibliography: 10 titles. 相似文献
8.
Let
= {a
1, a
2,...} be a set of positive integers and let p
(n) and q
(n) denote the number of partitions of n into a's, resp. distinct a's. In an earlier paper the authors studied large values of log(max (2,p
(n)))/log(max(2,q
(n))). In this paper the small values of the same quotient are studied. 相似文献
9.
G. A. Kalyabin 《Functional Analysis and Its Applications》2004,38(3):184-191
We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities
Specifically, we prove that
for all and k{0,...,n-1}. We establish symmetry and regularity properties of the numbers A
n,k
and study their asymptotic behavior as n for the cases k=O(n
2/3) and k/n(0,1).Similar problems were previously studied by Gabushin and Taikov. 相似文献
10.
Massimo Giulietti Fernanda Pambianco Fernando Torres Emanuela Ughi 《Designs, Codes and Cryptography》2002,25(3):237-246
We point out an interplay between
-Frobenius non-classical plane curves and complete
-arcs in
. A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete
-arcs with parameters
and
being a power of the characteristic. In addition, for q a square, new complete
-arcs with either
and
or
and
are constructed by using certain reducible plane curves. 相似文献
11.
Prof.Dr. Wolfgang M. Schmidt 《Monatshefte für Mathematik》1982,93(1):63-74
Hua andChen gave estimates of sums
wheree(z)=e
2iz
and
is a polynomial of the typef(x)/q wheref(x)=a
k
x
k
+...+a
1
x with integer coefficients having gcd (q, a
k
,...,a
1)=1 But no good estimates hold for these sums whenq is small in comparison tok. We therefore consider here a related but different class of polynomials. Special emphasis is given to the cubic case.In subsequent papers of this series we shall deal with cubic exponential sums in many variables and withp-adic and rational zeros of systems of cubic forms.Partially supported by NSF contract NSF-MCS-8015356. 相似文献
12.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
13.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
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are words in
. A braid is called strongly positive if
1$$
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for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献
14.
M. Wiessner 《Periodica Mathematica Hungarica》1993,26(3):205-210
Given
and a sequence of Dirichlet polynomials
estimates for the coefficientsa
n are proved if {n} is uniformly bounded on a region containing a half plane. Thereby a result is obtained which is an analogue of a known result for polynomials, that is for theA-transforms of the geometric sequence; moreover a Jentzsch type theorem for {n(z)} is derived. 相似文献
15.
G. V. Kuz’mina 《Journal of Mathematical Sciences》2005,129(3):3843-3851
Let a1,..., an be a system of distinct points on the z-sphere
, and let
be a system of all non-overlapping simply-connected domains D1,..., Dn on
such that ak ∈ Dk, k = 1,..., n. Let M (Dk, ak) be the reduced module of the domain Dk with respect to the point ak ∈ Dk. In the present paper, we solve some problems concerning the maximum of weighted sums of the reduced modules M (Dk, ak) in certain families of systems of domains {Dk} described above, where the systems of points {ak} satisfy prescribed symmetry conditions. In each case, the proof is based on an explicit construction of an admissible metric of the module problem, which is equivalent to the extremal problem under consideration, from known extremal metrics of simpler module problems. Bibliography: 7 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 302, 2003, pp. 52–67. 相似文献
16.
Roy F. Le Henderson 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1965,16(6):788-803
Zusammenfassung Durch das Theorem der arithmetischen und geometrischen Mitte kann man den maximalen Wert des Produktes von Variablen, die einer linearen Beschränkung unterworfen sind, feststellen. Die vorliegende Arbeit untersucht einige einfache Versionen des Theorems. Die allgemeinste Version ergibt den maximalen Wert des Produktes vonn Variablen, wenn jede Variable zu einer höheren Potenz erhoben wird und die Variablen einer Gruppe vonr linearen Beschränkungen unterworfen sind (r<n). Das Theorem wird dann auf das Problem des maximalen totalen Druckwiedergewinns über einem Stosswellensystem angewandt und schliesslich wird daraus ein ziemlich allgemeines Theorem über das adiabatische Fliessen eines Gases hergeleitet.
List of Symbols a ij given positive constants - b , - f i , - g i , - h , - k , - m the arithmetic mean ofn variables, see Equation (2) - M the Mach number - n the number of variables - P T the total pressure - q the geometric mean ofn variables, see Equation (1) - r the number of constraining conditions on the function to be maximised - R the gas constant - S the entropy - x i for the Oswatitsch analysis, otherwisex i represents any variable - y i - ratio of specific heats - j Lagrange multiplier - i given positive constant - W i shock wave angle of (i–1)th shock 相似文献
List of Symbols a ij given positive constants - b , - f i , - g i , - h , - k , - m the arithmetic mean ofn variables, see Equation (2) - M the Mach number - n the number of variables - P T the total pressure - q the geometric mean ofn variables, see Equation (1) - r the number of constraining conditions on the function to be maximised - R the gas constant - S the entropy - x i for the Oswatitsch analysis, otherwisex i represents any variable - y i - ratio of specific heats - j Lagrange multiplier - i given positive constant - W i shock wave angle of (i–1)th shock 相似文献
17.
TATSUYA MARUTA 《Geometriae Dedicata》1997,65(3):299-304
Let
be the smallest integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). In this paper we determine
for
for all q, using a geometric method. 相似文献
18.
Noboru Hamada 《Designs, Codes and Cryptography》1997,10(1):41-56
Let k and d be any integers such that k 4 and
. Then there exist two integers and in {0,1,2} such that
. The purpose of this paper is to prove that (1) in the case k 5 and (,) = (0,1), there exists a ternary
code meeting the Griesmer bound if and only if
and (2) in the case k 4 and (,) = (0,2) or (1,1), there is no ternary
code meeting the Griesmer bound for any integers k and d and (3) in the case k 5 and
, there is no projective ternary
code for any integers k and such that 1k-3, where
and
for any integer i 0. In the special case k=6, it follows from (1) that there is no ternary linear code with parameters [233,6,154] , [234,6,155] or [237,6,157] which are new results. 相似文献
19.
A submanifold M
n
r
of Minkowski space
is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of
to the tangent space of M
n
r
at every point of M
n
r
. In this paper we completely classify hypersurfaces of restricted type in
. More precisely, we prove that a hypersurface of
is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S
k
×
, S
k
1
×
, H
k
×
, S
n
1
, H
n
, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium. 相似文献
20.
John B. Polhill 《Designs, Codes and Cryptography》2002,25(3):299-309
There have been several recent constructions of partial difference sets (PDSs) using the Galois rings
for p a prime and t any positive integer. This paper presents constructions of partial difference sets in
where p is any prime, and r and t are any positive integers. For the case where
2$$
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many of the partial difference sets are constructed in groups with parameters distinct from other known constructions, and the PDSs are nested. Another construction of Paley partial difference sets is given for the case when p is odd. The constructions make use of character theory and of the structure of the Galois ring
, and in particular, the ring
×
. The paper concludes with some open related problems. 相似文献