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1.
Let Q denote the field of rational numbers. Let K be a cyclic quartic extension of Q. It is known that there are unique integers A, B, C, D such that
where A is squarefree and odd, D=B
2+C
2 is squarefree, B
$$
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0 , C
$$
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0, GCD(A,D)=1. The conductor f(K) of K is f(K) = 2
l
|A|D, where
A simple proof of this formula for f(K) is given, which uses the basic properties of quartic Gauss sums. 相似文献
2.
Dražen Adamović 《Algebras and Representation Theory》2004,7(4):457-469
Let
be the affine Lie algebra associated to the simple finite-dimensional Lie algebra
. We consider the tensor product of the loop
-module
associated to the irreducible finite-dimensional
-module V() and the irreducible highest weight
-module L
k,. Then L
k, can be viewed as an irreducible module for the vertex operator algebra M
k,0. Let A(L
k,) be the corresponding
-bimodule. We prove that if the
-module
is zero, then the
-module
is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras. 相似文献
3.
K. R. Goodearl 《K-Theory》1996,10(5):419-489
For a large class of -unital C
*-algebras A with real rank zero and stable rank one, the structure of the Grothendieck group k
0 of the multiplier algebra
(A) is investigated. The ordered group K
0(
(A)) is shown to be an unperforated Riesz group, and its additive structure is completely determined, as is — in important cases — its order structure. These structures, and the attendant consequences for the ideal structure of
(A), are richer than previously anticipated. In particular, it is shown that the corona algebra
(A)/A can have very large stably finite quotient algebras. For example, there exist simple, separable, approximately finite-dimensional C
*-algebras A such that the maximal stably finite quotient algebra of
(A)/A has uncountably many maximal ideals modulo which a W
*-factor of Type II1 results. The analysis of the additive structure of K
0(
(A)) yields as a byproduct that if A is a -unital approximately finite-dimensional C
*-algebra without nonzero unital quotient algebras, then all quasitraces on
(A) are traces.This research was partially supported by a grant from the National Science Foundation. 相似文献
4.
A. A. Tuganbaev 《Mathematical Notes》2000,68(5-6):627-639
Let A be a bounded hereditary Noetherian prime ring. For an A-module M A , we prove that M is a finitely generated projective ${A \mathord{\left/ {\vphantom {A {r\left( M \right)}}} \right. \kern-0em} {r\left( M \right)}}$ -module if and only if M is a ${\pi }$ -projective finite-dimensional module, and either M is a reduced module or A is a simple Artinian ring. The structure of torsion or mixed ${\pi }$ -projective A-modules is completely described. 相似文献
5.
Certain
-modules related to the kernels ofincidence maps between types in the poset defined by the natural productorder on the set of n-tuples with entries from {1,
,m} are studied as linear codes (whencoefficients are extended to an arbitrary field K). Theirdimensions and minimal weights are computed. The Specht modules areextremal among these submodules. The minimum weight codewords of theSpecht module are shown to be scalar multiples of polytabloids. Ageneralization of t-design arising from the natural permutationS
n-modules labelled by partitions with mparts is introduced. A connection with Reed-Muller codes is noted and acharacteristic free formulation is presented. 相似文献
6.
Masanobu Taniguchi Madan L. Puri 《Annals of the Institute of Statistical Mathematics》1995,47(3):581-600
Suppose thatX
n
=(X
1,...X
n) is a collection ofm-dimensional random vectorsX
i forming a stochastic process with a parameter . Let
be the MLE of . We assume that a transformationA(
) of
has thek-thorder Edgeworth expansion (k=2,3). IfA extinguishes the terms in the Edgeworth expansion up tok-th-order (k2), then we say thatA is thek-th-order normalizing transformation. In this paper, we elucidate thek-th-order asymptotics of the normalizing transformations. Some conditions forA to be thek-th-order normalizing transformation will be given. Our results are very general, and can be applied to the i.i.d. case, multivariate analysis and time series analysis. Finally, we also study thek-th-order asymptotics of a modified signed log likelihood ratio in terms of the Edgeworth approximation.Research supported by the Office of Naval Research Contract N00014-91-J-1020. 相似文献
7.
Let
be the prime factorization of a positive integer k and let b
k
(n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let S
k
(N; M) be the number of positive integers N for which b
k(n
) 0(mod
M). If
we prove that, for every positive integer j
In other words for every positive integer j,
b
k(n) is a multiple of
for almost every non-negative integer n. In the special case when k=p is prime, then in representation-theoretic terms this means that the number ofp -modular irreducible representations of almost every symmetric groupS
n is a multiple of p
j. We also examine the behavior of b
k(n) (mod
) where the non-negative integers n belong to an arithmetic progression. Although almost every non-negative integer n (mod t) satisfies b
k(n) 0 (mod
), we show that there are infinitely many non-negative integers n r (mod t) for which b
k(n) 0 (mod
) provided that there is at least one such n. Moreover the smallest such n (if there are any) is less than 2
. 相似文献
8.
Let k[t] be the polynomial ring over a finite field k. The group SL
2(k[t]) is often referred to as the analogue, in characteristic p, of the classical modular group SL
2(
), where
is the ring of rational integers. It is well-known that the smallest index of a non-congruence subgroup of SL
2(
) is 7. Here we compute this index for SL
2(k[t]). (In all but 6 cases it turns out to be 1 + q, where q is the order of k.) 相似文献
9.
Kh. D. Ikramov 《Journal of Mathematical Sciences》2004,121(4):2458-2464
A matrix
is said to be accretive-dissipative if, in its Hermitian decomposition
, both matrices B and C are positive definite. Further, if B= I
n, then A is called a Buckley matrix. The following extension of the classical Fischer inequality for Hermitian positive-definite matrices is proved. Let
be an accretive-dissipative matrix, k and l be the orders of A
11 and A
22, respectively, and let m = min{k,l}. Then
For Buckley matrices, the stronger bound
is obtained. Bibliography: 5 titles. 相似文献
10.
In this paper we prove that if
is a set of
k positive integers and
{A
1,
..., A
m
} is a family of subsets
of an n-element set
satisfying
, for all 1
i <
j m, then
. The case
k = 1 was proven 50 years ago
by Majumdar. 相似文献
11.
Jun Wang 《Annals of Combinatorics》1998,2(1):85-101
Let
(p) denote the subgroup lattice of the abelianp-group
. It is conjectured that the lattice has the Sperner property. Whenk=1, the conjecture is true since it is isomorphic to the subspace lattice, and Stanley has confirmed it fork=2. In this paper, we prove that the conjecture is generally true. 相似文献
12.
We consider k-th power of upper bound graphs. According
to the characterization of upper bound graphs, we obtain a characterization of
k-th power of upper bound graphs. That is,
for a connected upper bound graph
G, Gk is an upper bound graph if
and only if for any pair of
Ak
-simplicial vertices s1,
s2 such that
, there exists a
Gk
-simplicial vertex s satisfying
the conditions:
and
. Furthermore we also get some properties on squares of upper bound graphs.AMS Subject Classification: 05C62. 相似文献
13.
Gonzalo Perera 《Journal of Theoretical Probability》1997,10(3):581-603
We study the asymptotic distribution of
where A is a subset of
, A
N
= A[–N, N]
d
, v(A) = lim
N
card(A
N) (2N+1)
–d
(0, 1) and X is a stationary weakly dependent random field. We show that the geometry of A has a relevant influence on the problem. More specifically, S
N(A, X) is asymptotically normal for each X that satisfies certain mixting hypotheses if and only if
has a limit F(n; A) as N for each
. We also study the class of sets A that satisfy this condition. 相似文献
14.
Marilyn Breen 《Aequationes Mathematicae》2004,67(3):263-275
Summary.
We establish the following Helly-type result for infinite families
of starshaped sets in
Define the function f on
{1, 2} by
f(1) = 4,
f(2) = 3.
Let
be a fixed positive number, and let
be a uniformly bounded family of compact sets
in the plane. For k = 1, 2, if every
f(k)
(not necessarily distinct) members of
intersect in a starshaped set whose
kernel contains a k-dimensional
neighborhood of radius
, then
is a starshaped set whose kernel is at least
k-dimensional.
The number f(k) is best in each case.
In addition, we present a few results concerning the dimension of
the kernel in an intersection of starshaped sets in
Some of these involve finite families of sets, while others
involve infinite families and make use of the Hausdorff metric. 相似文献
15.
Pavel Valtr 《Discrete and Computational Geometry》1992,7(1):135-152
For a finite setA of points in the plane, letq(A) denote the ratio of the maximum distance of any pair of points ofA to the minimum distance of any pair of points ofA. Fork>0 letc
(k) denote the largest integerc such that any setA ofk points in general position in the plane, satisfying
for fixed
, contains at leastc convex independent points. We determine the exact asymptotic behavior ofc
(k), proving that there are two positive constants=(), such thatk
1/3c
(k)k
1/3. To establish the upper bound ofc
(k) we construct a set, which also solves (affirmatively) the problem of Alonet al. [1] about the existence of a setA ofk points in general position without a 7-hole (i.e., vertices of a convex 7-gon containing no other points fromA), satisfying
. The construction uses Horton sets, which generalize sets without 7-holes constructed by Horton and which have some interesting properties. 相似文献
16.
Johannes Schoißengeier 《manuscripta mathematica》1982,38(2):257-263
In this paper we compute the values of series of the form
if k N is add. This was done by Glaisher [4] if k1 (mod 4), but if k 3 (mod 4) the result seems to be new. 相似文献
17.
Walter Benz 《Journal of Geometry》2004,79(1-2):19-26
Suppose that X is a real inner product
space of (finite or infinite) dimension at least 2. A distance preserving mapping
, where
is a (finite or infinite) subset of a
finite-dimensional subspace of X, can be extended
to an isometry
of X. This holds true for
euclidean as well as for hyperbolic geometry. To both geometries there exist examples
of non-extentable distance preserving
, where S
is not contained in a finite-dimensional subspace of
X. 相似文献
18.
Anastasios D. Simalarides 《Periodica Mathematica Hungarica》2000,40(1):71-75
Let be a primitive character mod k, k > 2. In [1], the following elementary estimate
was given, where
by definition. In the present note we sharpen this estimate by a factor 3/4 in the case of an even primitive character , by improving upon the proof given in [1] in a way which does not alter the elementary character of the method. 相似文献
19.
Sjoerd E. Crans 《K-Theory》2003,28(1):39-105
Let
be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor
, i.e., a functor 2
q
, induce a right q-transfor
, i.e., a functor
More generally, does a functor
induce a functor
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a q-transfor
, for appropriate k-arrows
For k-arrows c and
whose (k – 1)-sources and targets agree, does a q-transfor
induce a (q + k + 1)-transfor
, for appropriate k-arrows
I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation
, where
is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A. 相似文献
20.
N. A. Shirokov 《Journal of Mathematical Sciences》2003,115(2):2287-2295
A function
analytic in the unit disk is called (p, A)-lacunary if the inequalities n
k Ak
p hold for all k 0 with some 1 < p < and A > 0. In this paper, for 1 < p < 2 and A > 0, we construct a (p, A)-lacunary function f
1,p,A
(z) decreasing as x 1 – 0 at a rate close to the optimal rate for (p, A)-lacunary functions. Bibliography: 6 titles. 相似文献