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1.
S. A. Amitsur 《Israel Journal of Mathematics》1974,17(3):241-247
LetA=k (X
1, X2..., Xm) be the division ring generated by genericn×n matrices over a fieldk; thenA is not a crossed product in the following cases: (i) there exists a primeq such thatq
3ℛn;(ii)[k:Q]=m, whereQ is the field of rationals, then if eitherq
3ℛn for someq for whichq-1ℛm, orq
2/nn for some other prime; (iii)k=Z
p
r a finite field ofp
r elements and eitherq
3ℛn for sameqℛp
r-1 orq
2ℛn for some other primes. Other cases are also considered. 相似文献
2.
A polynomial Q = Q(X
1, …, X
n
) of degree m in independent identically distributed random variables with distribution function F is an unbiased estimator of a functional q(α
1(F), …, α
m
(F)), where q(u
1, …, u
m
) is a polynomial in u
1, …, u
m
and α
j
(F) is the jth moment of F (assuming the necessary moment of F exists). It is shown that the relation E(Q | X
1 + … + X
n) = 0 holds if and only if q(α
1(θ), …, α
m
(θ)) ≡ 0, where α
j
(θ) is the jth moment of the natural exponential family generated by F. This result, based on the fact that X
1 + … + X
n is a complete sufficient statistic for a parameter θ in a sample from a natural exponential family of distributions F
θ(x) = ∫−∞
x
e
θu−k(θ)
dF(u), explains why the distributions appearing as solutions of regression problems are the same as solutions of problems for
natural exponential families though, at the first glance, the latter seem unrelated to the former. 相似文献
3.
Oleg Pushin 《K-Theory》2004,31(4):307-321
In this short paper we investigate the relation between higher Chern classes and reduced power operations in motivic cohomology.
More precisely, we translate the well-known arguments [5] into the context of motivic cohomology and define higher Chern classes
cp,q : K p(X) → H2q-p (X,Z(q)) → H2q-p(X, Z/l(q)), where X is a smooth scheme over the base field k, l is a prime number and char(k) ≠ l. The same approach produces the classes for K-theory with coefficients as well. Let further Pi : Hm(X, Z/l(n)) → Hm+2i(l-1) (X, Z/l(n + i(l - 1))) denote the ith reduced power operation in motivic cohomology, constructed in [2]. The main result of the paper looks as follows. 相似文献
4.
Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = X n h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q 1 ⊕ Q 2 ⊕ Q 3 such that Q 1 is a ring satisfying S 2n?2, the standard identity of degree 2n ? 2, Q 2 ? M n (E) for some commutative regular self-injective ring E such that, for some fixed q > 1, x q = x for all x ∈ E, and Q 3 is a both faithful S 2n?2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring. 相似文献
5.
Pierre Angl��s 《Advances in Applied Clifford Algebras》2011,21(2):233-246
This self-contained short note deals with the study of the properties of some real projective compact quadrics associated
with a a standard pseudo-hermitian space H
p,q
, namely [(Q(p, q))\tilde], [(Q2p+1,1)\tilde], [(Q1,2q+1)\tilde], [(Hp,q)\tilde]. [(Q(p, q))\tilde]{\widetilde{Q(p, q)}, \widetilde{Q_{2p+1,1}}, \widetilde{Q_{1,2q+1}}, \widetilde{H_{p,q}}. \, \widetilde{Q(p, q)}} is the (2n – 2) real projective quadric diffeomorphic to (S
2p–1 × S
2q–1)/Z
2. inside the real projective space P(E
1), where E
1 is the real 2n-dimensional space subordinate to H
p,q
. The properties of [(Q(p, q))\tilde]{\widetilde{Q(p, q)}} are investigated. [(Hp,q)\tilde]{\widetilde{H_p,q}} is the real (2n – 3)-dimensional compact manifold-(projective quadric)- associated with H
p,q
, inside the complex projective space P(H
p,q
), diffeomorphic to (S
2p–1 × S
2q–1)/S
1. The properties of [(Hp,q)\tilde]{\widetilde{H_{p,q}}} are studied. [(Q2p+1,1)\tilde]{\widetilde{Q_{2p+1,1}}} is a 2p-dimensional standard real projective quadric, and [(Q1,2q+1)\tilde]{\widetilde{Q_{1,2q+1}}} is another standard 2q-dimensional projective quadric. [(Q2p+1,1)\tilde] è[(Q1,2q+1)\tilde]{\widetilde{Q_{2p+1,1}} \cup \widetilde{Q_{1,2q+1}}}, union of two compact quadrics plays a part in the understanding of the "special pseudo-unitary conformal compactification"
of H
p,q
. It is shown how a distribution y → D
y
, where y ? H\{0},H{y \in H\backslash\{0\},H} being the isotropic cone of H
p,q
allows to [(Hp+1,q+1)\tilde]{\widetilde{H_{p+1,q+1}}} to be considered as a "special pseudo-unitary conformal compactified" of H
p,q
× R. The following results precise the presentation given in [1,c]. 相似文献
6.
N. Andruskiewitsch F. Fantino M. Graña L. Vendramin 《Annali di Matematica Pura ed Applicata》2011,190(2):225-245
It is shown that Nichols algebras over alternating groups
\mathbb Am{\mathbb A_m} (m ≥ 5) are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes
isomorphic to
\mathbb Am{\mathbb A_m} is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebras over the symmetric groups
\mathbb Sm{\mathbb S_m} are all infinite-dimensional, except maybe those related to the transpositions considered in Fomin and Kirillov (Progr Math
172:146–182, 1999), and the class of type (2, 3) in
\mathbb S5{\mathbb S_5}. We also show that any simple rack X arising from a symmetric group, with the exception of a small list, collapse, in the sense that the Nichols algebra
\mathfrak B(X, q){\mathfrak B(X, \bf q)} is infinite dimensional, q an arbitrary cocycle. 相似文献
7.
We show the existence of a sequence (λ
n
) of scalars withλ
n
=o(n) such that, for any symmetric compact convex bodyB ⊂R
n
, there is an affine transformationT satisfyingQ ⊂T(B) ⊂λ
n
Q, whereQ is then-dimensional cube. This complements results of the second-named author regarding the lower bound on suchλ
n
. We also show that ifX is ann-dimensional Banach space andm=[n/2], then there are operatorsα:l
2
m
→X andβ:X→l
∞
m
with ‖α‖·‖β‖≦C, whereC is a universal constant; this may be called “the proportional Dvoretzky-Rogers factorization”. These facts and their corollaries
reveal new features of the structure of the Banach-Mazur compactum.
Research performed while this author was visiting IHES. Supported in part by the NSF Grant DMS-8702058 and the Sloan Research
Fellowship. 相似文献
8.
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
9.
A sequence (z
0,z
1,z
2,, ...,z
n, z
n+1) of points fromp=z
0 toq=z
n+1 in a metric spaceX is said to besequentially equidistant ifd(z
i−1,z
i)=d(z
i,z
i+1) for 1≦i≦n. If there is path inX fromp toq (or if a certain weaker condition holds), then such a sequence exists, with all points distinct, for every choice ofn, while ifX is compact and connected, then such a sequence exists at least forn=2. An example is given of a dense connected subspaceS ofR
m
,m≧2, and an uncountable dense subsetE disjoint fromS for which there is no sequentially equidistant sequence of distinct points (n ≧ 2) inS ∪E between any two points ofE. Techniques of dimension theory are utilized in the construction of these examples, as well as in the proofs of some of the
positive results.
Supported in part by NSF Grant DMS-8701666. 相似文献
10.
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
11.
Guglielmo Lunardon 《Geometriae Dedicata》1986,20(2):121-131
Summary In this paper, for q even, we construct an ovoid O
3 and a spread S of the finite classical polar space Q+(7, q) determinated by a hyperbolic quadric Q+ of PG(7, q) such that there is a subgroup of PGO
+
8
(q) isomorphic to PGL2(q
3), which maps O
3 in itself and S in S and is 3-transitive on O
3 and on S; for q>2, S is not a Desarguesian spread of Q+(7, q) and O
3 is a Desarguesian ovoid.
Al Prof. Adriano Barlotti in occasione del suo 60o compleanno 相似文献
Varietà di Segre e ovoidi dello spazio polare Q+(7, q)
Al Prof. Adriano Barlotti in occasione del suo 60o compleanno 相似文献
12.
George Stacey Staples 《Journal of Theoretical Probability》2007,20(2):257-274
Given a fixed probability space (Ω,ℱ,ℙ) and m≥1, let X(t) be an L2(Ω) process satisfying necessary regularity conditions for existence of the mth iterated stochastic integral. For real-valued processes, these existence conditions are known from the work of D. Engel.
Engel’s work is extended here to L2(Ω) processes defined on Clifford algebras of arbitrary signature (p,q), which reduce to the real case when p=q=0. These include as special cases processes on the complex numbers, quaternion algebra, finite fermion algebras, fermion
Fock spaces, space-time algebra, the algebra of physical space, and the hypercube. Next, a graph-theoretic approach to stochastic
integrals is developed in which the mth iterated stochastic integral corresponds to the limit in mean of a collection of weighted closed m-step walks on a growing sequence of graphs. Combinatorial properties of the Clifford geometric product are then used to create
adjacency matrices for these graphs in which the appropriate weighted walks are recovered naturally from traces of matrix
powers. Given real-valued L2(Ω) processes, Hermite and Poisson-Charlier polynomials are recovered in this manner. 相似文献
13.
K. Halupczok 《Acta Mathematica Hungarica》2008,120(4):315-349
We show that for every fixed A > 0 and θ > 0 there is a ϑ = ϑ(A, θ) > 0 with the following property. Let n be odd and sufficiently large, and let Q
1 = Q
2:= n
1/2(log n)−ϑ
and Q
3:= (log n)
θ
. Then for all q
3 ≦ Q
3, all reduced residues a
3 mod q
3, almost all q
2 ≦ Q
2, all admissible residues a
2 mod q
2, almost all q
1 ≦ Q
1 and all admissible residues a
1 mod q
1, there exists a representation n = p
1 + p
2 + p
3 with primes p
i
≡ a
i
(q
i
), i = 1, 2, 3.
相似文献
14.
Miran Černe 《Arkiv f?r Matematik》2002,40(1):27-45
LetX(-ϱB
m
×C
n
be a compact set over the unit sphere ϱB
m
such that for eachz∈ϱB
m
the fiberX
z
={ω∈C
n
;(z, ω)∈X} is the closure of a completely circled pseudoconvex domain inC
n
. The polynomial hull
ofX is described in terms of the Perron-Bremermann function for the homogeneous defining function ofX. Moreover, for each point (z
0,w
0)∈Int
there exists a smooth up to the boundary analytic discF:Δ→B
m
×C
n
with the boundary inX such thatF(0)=(z
0,w
0).
This work was supported in part by a grant from the Ministry of Science of the Republic of Slovenia. 相似文献
15.
For each natural number n, poset T, and |T|–tuple of scalars Q, we introduce the ramified partition algebra P
n
(T)
(Q), which is a physically motivated and natural generalization of the partition algebra [24, 25] (the partition algebra coincides with case |T|=1). For fixed n and T these algebras, like the partition algebra, have a basis independent of Q. We investigate their representation theory in case ${{T=\underline{{2}}:=({1,2},\leq)}}$. We show that ${{P_n^{(\underline{{2}})$ (Q) is quasi–hereditary over field k when Q
1
Q
2
is invertible in k and k is such that certain finite group algebras over k are semisimple (e.g. when k is algebraically closed, characteristic zero). Under these conditions we determine an index set for simple modules of ${{P_n^{(\underline{{2}})$ (Q), and construct standard modules with this index set. We show that there are unboundedly many choices of Q such that ${{P_n^{(\underline{{2}})$ (Q) is not semisimple for sufficiently large n, but that it is generically semisimple for all n. We construct tensor space representations of certain non–semisimple specializations of ${{P_n^{(\underline{{2}})$ (Q), and show how to use these to build clock model transfer matrices [24] in arbitrary physical dimensions.
Sadly Ahmed died before this work was completed. His memory lives on. 相似文献
16.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
17.
A. D. Kolesnik 《Ukrainian Mathematical Journal》2008,60(12):1915-1926
A symmetric random evolution X(t) = (X
1 (t), …, X
m
(t)) controlled by a homogeneous Poisson process with parameter λ > 0 is considered in the Euclidean space ℝ
m
, m ≥ 2. We obtain an asymptotic relation for the transition density p(x, t), t > 0, of the process X(t) as λ → 0 and describe the behavior of p(x, t) near the boundary of the diffusion domain in spaces of different dimensions.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1631 – 1641, December, 2008. 相似文献
18.
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
19.
《代数通讯》2013,41(11):4387-4413
Abstract In the paper, the deriviation algebras of the associative algebras of the one-variable (resp. multivariable) q-differential operators and of their corresponding Lie algebras are determined. The completeness of the derivation algebras of the algebras of q-differential operators is also discussed. Finally, we calculate H 2(𝒟 q (n)?, C) for n ≥ 1, as well as H 2(g l n (𝒟 q ), C) under the assumption that q is transcendental over the rational numbers field Q. 相似文献
20.
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