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1.
Alp Bassa 《Journal of Number Theory》2011,131(3):561-577
In this article we study Drinfeld modular curves X0(pn) associated to congruence subgroups Γ0(pn) of GL(2,Fq[T]) where p is a prime of Fq[T]. For n>r>0 we compute the extension degrees and investigate the structure of the Galois closures of the covers X0(pn)→X0(pr) and some of their variations. The results have some immediate implications for the Galois closures of two well-known optimal wild towers of function fields over finite fields introduced by Garcia and Stichtenoth, for which the modular interpretation was given by Elkies. 相似文献
2.
Consider the diagonal action ofSL
n
(K) on the affine spaceX = V⊕m ⊕ (V*)⊕q whereV = K
n
,K an algebraically closed field of arbitrary characteristic andm,q >
n. We construct a ‘standard monomial’’ basis for the ring of invariantsK[X]
SL
n
(K). As a consequence, we deduce thatK[X]
SL
n
(K) is Cohen-Macaulay. We also present the first and second fundamental theorems forSL
n
(K)- actions. 相似文献
3.
M. Ahsanullah 《Annals of the Institute of Statistical Mathematics》1978,30(1):163-166
Summary LetX be a non-negative random variable with probability distribution functionF. SupposeX
i,n (i=1,…,n) is theith smallest order statistics in a random sample of sizen fromF. A necessary and sufficient condition forF to be exponential is given which involves the identical distribution of the random variables (n−i)(X
i+1,n−Xi,n) and (n−j)(X
j+1,n−Xj,n) for somei, j andn, (1≦i<j<n).
The work was partly completed when the author was at the Dept. of Statistics, University of Brasilia, Brazil. 相似文献
4.
We derive explicit equations for the maximal function fields F over 𝔽 q 2n given by F = 𝔽 q 2n (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field 𝔽 q 2n , and where A(Y) is q-additive and deg(f) = q n + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over 𝔽 q 2n (i.e., the extension H/F is Galois). 相似文献
5.
Fix an integern≧3. We show that the alternating groupA
n appears as Galois group over any Hilbertian field of characteristic different from 2. In characteristic 2, we prove the same
whenn is odd. We show that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in anS
n-extension (i.e. a Galois extension with the symmetric groupS
n as Galois group). Forn≠6, it will follow thatA
n has the so-called GAR-property over any field of characteristic different from 2. Finally, we show that any polynomialf=X
n+…+a1X+a0 with coefficients in a Hilbertian fieldK whose characteristic doesn’t dividen(n-1) can be changed into anS
n-polynomialf
* (i.e the Galois group off
* overK Gal(f
*, K), isS
n) by a suitable replacement of the last two coefficienta
0 anda
1. These results are all shown using the Newton polygon.
The author acknowledges the financial support provided through the European Community’s Human Potential Programme under contract
HPRN-CT-2000-00114, GTEM. 相似文献
6.
E. E. Goryahko 《Journal of Mathematical Sciences》2010,168(3):379-384
We present a direct proof of the simplicity of the branching of representations of the groups GL(n, q) under the parabolic restrictions. The proof consists of three steps. First, we reduce the problem to the statement that
a certain pair of finite groups is a Gelfand pair. Then, we obtain a criterion for establishing this fact, which generalizes
the classical Gelfand’s criterion. Finally, we check the obtained criterion with the help of some matrix computations. Bibliography:
7 titles. 相似文献
7.
N. V. Maslova 《Algebra and Logic》2011,50(2):133-145
We give a classification of maximal subgroups of odd index in finite groups whose socle is isomorphic to one of the groups
PSL
n
(q), PSU
n
(q), or PSp
n
(q) for n ≥ 13. 相似文献
8.
It is proved that for every 1≦p<∞, 1≦q<∞ and for every sequence {p
n}, 1≦p
n<∞,p
n→p, the spaceX=(Σ⊕l
p
n)
q
(resp.U=(Σ⊕L
p
n(0, 1))
q
) is uniformly homeomorphic toX⊕l
p (resp.U⊕L
p(0, 1)). This extends Ribe’s result from the casep=1 to generalp<∞ and thus provides examples of uniformly convex, uniformly homeomorphic Banach spaces which are not Lipschitz equivalent. 相似文献
9.
E. Ballico 《Annali dell'Universita di Ferrara》1982,38(1):33-40
Summary Here we prove the following result. Fix integersq, τ,a’, b’, a’
i, 1≤i≤τ,a’, b’, a’
i, 1≤i≤τ; then there is an integerew such that for every integert≥w, for every algebraically closed fieldK for every smooth complete surfaceX with negative Kodaira dimension, irregularityq andK
X
2
=8(1−q)−τ, the following condition holds; ifX→S is a sequence fo τ blowing-downs which gives a relatively minimal model with ruling ρ:S→C, take as basis of the Neron Severi groupNS(X) a smooth rational curve which is the total transform of a fiber ofC, the total transform of a minimal section of ρ and the total transformD
i, 1≤i≤τ, of the exceptional curver; then for everyH andL∈Pic (X) withH ample,H (resp.L) represented by the integersa’, b’, a’
i, (resp.a’, b’, a’
i), 1≤i≤τ, in the chosen basis ofNS(X) the moduli spaceM(ZX, 2,H, L, t) of rank 2H-stable vector bundles onX with determinantL andc
2=t is generically smooth and the number, dimension and ?birational structure? of the irreducible components ofM(X, 2,H, L, t)red do not depend on the choice ofK andX. Furthermore the birational structure of these irreducible components can be loosely described in terms of the birational
structure of the components of suitableM(S, 2,H’, L’, t’)red withS a relatively minimal model ofX.
Sunto SiaX una superficie algebrica liscia completa con dimensione di Kodaira negativa e definita su un campo algebricamente chiusoK; fissiamoH eL∈Pic (X),t∈Z; siaq l’irregolarità diX e τ≔8(1−q)−K X Emphasis>2 ; siaM(X, 2,H, L, t) to schema dei moduli dei fibrati vettorialiH-stabili di rango 2 suX con determinateL ec 2=t. Si dimostra che esiste una costantew che dipende solo daq, da τ e dalla classe numerica diH e diL (ma non da char (K) o dalla classe di isomorphismo diX) tale che per ognit≥w il numero, la dimensione e ?la struttura birazionale? delle componenti irriducibili diM(X, 2,H, L, t)red non dipende dalla scelta di char (K),K eX ma solo daq, τ e dalle classi diH eL inNS(X). Inoltre la ?struttura birazionale? di queste componenti irriducibili può essere grossolanamente descritta in termini delle componenti di opportuni spazi di moduliM(S, 2,H’, L’, t’) (doveS è un modello minimale diX).相似文献
10.
We prove a removal lemma for systems of linear equations over finite fields: let X
1, …, X
m
be subsets of the finite field F
q
and let A be a (k × m) matrix with coefficients in F
q
; if the linear system Ax = b has o(q
m−k
) solutions with x
i
∈ X
i
, then we can eliminate all these solutions by deleting o(q) elements from each X
i
. This extends a result of Green [Geometric and Functional Analysis 15 (2) (2005), 340–376] for a single linear equation in abelian groups to systems of linear equations. In particular, we also
obtain an analogous result for systems of equations over integers, a result conjectured by Green. Our proof uses the colored
version of the hypergraph Removal Lemma. 相似文献
11.
Stanley M. Einstein-Matthews Clement H. Lutterodt 《Israel Journal of Mathematics》1999,109(1):253-271
LetX be a complete intersection algebraic variety of codimensionm>1 in ℂ
m+n
. We define the notion of (p,q)-order and (p,q)-K-type for transcendental entire functionsfεO(ℂ
m+n
) whereK is a non-pluripolar compact subset of ℂ
m+n
. Further, we consider the analogues of (p,q)-order and (p,q)-K-type inO(X). We discuss the series expansions of the functions inO(X) in terms of an orthogonal basis in a Hilbert spaceL
2(X, μ), where μ is a capacitary extremal measure onK.
Author is grateful to the NSA for partial support during the period of this research. 相似文献
12.
In this note we give elementary examples of the naturalness of generalized Clifford algebras appearance, in some particular
quantum mechanical models.
First Weyl’s program [1] for quantum kinematics for the case of simplest Galois fieldsZ
n
is realized in terms of generalized Clifford algebras. Dynamics might then be introduced, following the ideas of Hanney and
Berry [2], as shown in [3].
Second the coherent state picture of the finite dimensional “Z
n
— Quantum Mechanics” is presented.
In the last part the known coherent states ofq-deformed quantum oscillators (q≡ω) are explicitly shown in the generalized Grassman algebras and the generalized Clifford algebras settings.
Presented atThe Polish-Mexican Seminar, Kazimierz Dolny, August 1998 — Poland. 176 相似文献
13.
A Study of the Equivalence of the BLUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models 总被引:6,自引:0,他引:6
Abstract
Consider the partitioned linear regression model
and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2
V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X
1 : X
2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased
estimators of M
2
X
1β1under the model
and its best linear unbiased estimators under the reduced linear models of
are given, where M
2 = I -X
2
X
2
+ . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of
M
2
X
1β1 under the model
and those under its reduced linear models are established. Lastly, we also study the connections between the model
and its linear transformation model.
*This work is supported by the National Natural Science Foundation of China, Tian Yuan Special Foundation (No. 10226024),
Postdoctoral Foundation of China and Lab. of Math. for Nonlinear Sciences at Fudan University.
This research is supported in part by The International Organizing Committee and The Local Organizing Committee at the University
of Tampere for this Workshop
**The work is supported in part by an NSF grant of China.
Results in this paper were presented by the first author at The Eighth International Workshop on Matrices and Statistics:
Tampere, Finland, August 1999 相似文献
14.
In this paper,the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions.It is shown that if the two-component nonlinear vector differential operator F=(F 1,F 2) with orders {k 1,k 2 } (k 1 ≥ k 2) preserves the invariant subspace W 1 n 1 × W 2 n 2 (n 1 ≥ n 2),then n 1 n 2 ≤ k 2,n 1 ≤ 2(k 1 + k 2) + 1,where W q n q is the space generated by solutions of a linear ordinary differential equation of order n q (q=1,2).Several examples including the (1+1)-dimensional diffusion system and Ito 's type,Drinfel'd-Sokolov-Wilson's type and Whitham-Broer-Kaup's type equations are presented to illustrate the result.Furthermore,the estimate of dimension for m-component nonlinear systems is also given. 相似文献
15.
E. Ballico 《Finite Fields and Their Applications》2002,8(4):554
Let YPn be a cubic hypersurface defined over GF(q). Here, we study the Finite Field Nullstellensatz of order [q/3] for the set Y(q) of its GF(q)-points, the existence of linear subspaces of PG(n,q) contained in Y(q) and the possibility to join any two points of Y(q) by the union of two lines of PG(n,q) entirely contained in Y(q). We also study the existence of linear subspaces defined over GF(q) for the intersection of Y with s quadrics and for quartic hypersurfaces. 相似文献
16.
Frank Jonas 《manuscripta mathematica》1990,67(1):35-39
Zusammenfassung LetD:G→GL(n,C) be an irreducible linear representation of a finite groupG with the characterX. IfD is realizible in Q(ξ
m
) and Q(ξ
m′
) we give a condition for then realizability ofD in Q(ξ(m′)). If the degreen is a prime ≠ 2, we show thatD realizible in Q(ξ
f
), wheref is the conductor of the abelian extensionQ(X)/Q. 相似文献
17.
Very little is known aboutH
*(Ωn
X) whenn is larger than the connectivity ofX. In this paper we calculate this whenX=Ω∞
S
∞ andn=1 or 2, and whenX=JU(q) or JSO(3) andn is arbitrary. Some information is also given whenX is a sphere.
The authors were partially supported by the NSF. 相似文献
18.
Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X
0(6). We obtain a new asymptotic formula for p(n) with an effective error term which is
O(n-(\frac12+d)){O(n^{-(\frac{1}{2}+\delta)})} for some δ > 0. We then use this asymptotic formula to sharpen the classical bounds of Hardy and Ramanujan, Rademacher, and Lehmer on
the error term in Rademacher’s exact formula for p(n). 相似文献
19.
Let S be the multiplicative semigroup of q×q matrices with positive entries such that every row and every column contains a strictly positive element. Denote by (X
n
)
n≥1 a sequence of independent identically distributed random variables in S and by X
(n)=X
n
⋅⋅⋅
X
1, n≥1, the associated left random walk on S. We assume that (X
n
)
n≥1 satisfies the contraction property
where S° is the subset of all matrices which have strictly positive entries. We state conditions on the distribution of the random
matrix X
1 which ensure that the logarithms of the entries, of the norm, and of the spectral radius of the products X
(n), n≥1, are in the domain of attraction of a stable law.
相似文献
20.
Elin Götmark 《Arkiv f?r Matematik》2008,46(1):43-68
We present a method of finding weighted Koppelman formulas for (p,q)-forms on n-dimensional complex manifolds X which admit a vector bundle of rank n over X×X, such that the diagonal of X×X has a defining section. We apply the method to ℙ
n
and find weighted Koppelman formulas for (p,q)-forms with values in a line bundle over ℙ
n
. As an application, we look at the cohomology groups of (p,q)-forms over ℙ
n
with values in various line bundles, and find explicit solutions to the -equation in some of the trivial groups. We also look at cohomology groups of (0,q)-forms over ℙ
n
×ℙ
m
with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds. 相似文献