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1.
In this paper we solve two open problems posed by Santaló: to obtain complete systems of inequalities for some triples of
measures of a planar convex set.
Received February 17, 1999, and in revised form July 15, 1999. 相似文献
2.
WU WenMing School of Mathematical Computer Science Chongqing Normal University Chongqing China 《中国科学A辑(英文版)》2008,(11)
Given the hyperbolic measure dxdy/y2 on the upper half plane H, the rational actions of PSL2(R) on H induces a continuous unitary representation α of this group on the Hilbert space L2(H, dxdy/y2). Supposing that A = {Mf : f ∈ L∞(H, dxdy/y2)}, we show that the crossed product R(A,α) is of type I. In fact, the crossed product R(A,α) is *-isomorphic to the von Neumann algebra B(L2(P,ν))■LK, where LK is the abelian group von Neumann algebra generated by the left regular representation of K. 相似文献
3.
Let R be a commutative ring with nonzero identity and Z(R) its set of zero-divisors. The zero-divisor graph of R is Γ(R), with vertices Z(R)?{0} and distinct vertices x and y are adjacent if and only if xy = 0. For a proper ideal I of R, the ideal-based zero-divisor graph of R is Γ I (R), with vertices {x ∈ R?I | xy ∈ I for some y ∈ R?I} and distinct vertices x and y are adjacent if and only if xy ∈ I. In this article, we study the relationship between the two graphs Γ(R) and Γ I (R). We also determine when Γ I (R) is either a complete graph or a complete bipartite graph and investigate when Γ I (R) ? Γ(S) for some commutative ring S. 相似文献
4.
Warren WM. McGovern 《代数通讯》2013,41(4):1636-1646
The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. A commutative ring R is said to be Gaussian if c(fg) = c(f)c(g) for every polynomials f and g in R[X]. A number of authors have formulated necessary and sufficient conditions for R(X) (respectively, R?X?) to be semihereditary, have weak global dimension at most one, be arithmetical, or be Prüfer. An open question raised by Glaz is to formulate necessary and sufficient conditions that R(X) (respectively, R?X?) have the Gaussian property. We give a necessary and sufficient condition for the rings R(X) and R?X? in terms of the ring R in case the square of the nilradical of R is zero. 相似文献
5.
6.
We study a Dirichlet problem for the heat equation in C
1-domain D X (0, T) with boundary data in h
c
1
,a subspace of L
1.We derive our results using, in the representation of the solution, the kernel function associated to the caloric measure d 相似文献
7.
Fang Ainong 《数学学报(英文版)》1993,9(2):119-128
Suppose that $$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$ is a Clifford matrix of dimensionn, g(x)=(ax+b)(cx+d) ?1. We study the invariant balls and the more careful classifications of the loxodromic and parabolic elements inM(R n ), prove that the loxodromic elements inM(R 2k+1 ) certainly have an invariant ball, expound the geometric meaning of Ahlfors' hyperbolic elements, and introduce the uniformly hyperbolic and parabolic elements and give their identifications. We prove that $$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$ These results are fundamental in the higher dimensional Möbius groups, especially in Fuchs groups. 相似文献
8.
An L(d1,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0, 1,..., k} for some positive integer k such that {f(x) - f(y)| ≥ di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,... ,dt)labeling with max{f(x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2,1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2,1,..., 1) 相似文献
9.
Jinyong Wu 《代数通讯》2013,41(11):4844-4850
In this note, the coradical filtration of the new class of Hopf algebras D(m, d, ξ) is determined. As consequences, the authors show that 1) D(m, d, ξ) is not pointed; 2) D(m, d, ξ) is a co-Frobenius Hopf algebra; 3) the coradical of D(m, d, ξ) is not a Hopf subalgebra. 相似文献
10.
Let r ∈ N, α, t ∈ R, x ∈ R 2, f: R 2 → C, and denote $ \Delta _{t,\alpha }^r (f,x) = \sum\limits_{k = 0}^r {( - 1)^{r - k} c_r^k f(x_1 + kt\cos \alpha ,x_2 + kt\sin \alpha ).} $ In this paper, we investigate the relation between the behavior of the quantity $ \left\| {\int\limits_E {\Delta _{t,\alpha }^r (f, \cdot )\Psi _n (t)dt} } \right\|_{p,G} , $ as n → ∞ (here, E ? R, G ∈ {R 2, R + 2 }, and ψ n ∈ L 1(E) is a positive kernel) and structural properties of function f. These structural properties are characterized by its “directional” moduli of continuity: $ \omega _{r,\alpha } (f,h)_{p,G} = \mathop {\sup }\limits_{0 \leqslant t \leqslant h} \left\| {\Delta _{t,\alpha }^r (f)} \right\|_{p,G} . $ Here is one of the results obtained. Theorem 1. Let E and A be intervals in R + such that A ? E, f ∈ L p (G), α ∈ [0, 2π] when G =R 2 and α ∈ [0, π/2] when G = R + 2 Denote Δ n, k = ∫ A t k ψ n (t)dt. If there exists an r ∈ N such that, for any m ∈ N, we have Δ m, r > 0, Δ m, r + 1 < ∞, and $ \mathop {\lim }\limits_{n \to \infty } \frac{{\Delta _{n,r + 1} }} {{\Delta _{n,r} }} = 0,\mathop {\lim }\limits_{n \to \infty } \Delta _{n,r}^{ - 1} \int\limits_{E\backslash A} {\Psi _n = 0} , $ then the relations $ \mathop {\lim }\limits_{n \to \infty } \Delta _{n,r}^{ - 1} \left\| {\int\limits_E {\Delta _{t,\alpha }^r (f, \cdot )\Psi _n dt} } \right\|_{p,G} \leqslant K, \mathop {\sup }\limits_{t \in (0,\infty )} t^r \omega _{r,\alpha } (f,t)_{p,G} \leqslant K $ are equivalent. Particular methods of approximation are considered. We establish Corollary 1. Let p, G, α, and f be the same as in Theorem 1, and $ \sigma _{n,\alpha } (f,x) = \frac{2} {{\pi n}}\int\limits_{R_ + } {\Delta _{t,\alpha }^1 (f,x)} \left( {\frac{{\sin \frac{{nt}} {2}}} {t}} \right)^2 dt. $ Then the relations $ \mathop {\underline {\lim } }\limits_{n \to \infty } \frac{{\pi n}} {{\ln n}}\left\| {\sigma _{n,\alpha } (f)} \right\|_{p,G} \leqslant K Let r ∈ N, α, t ∈ R, x ∈ R
2, f: R
2 → C, and denote
In this paper, we investigate the relation between the behavior of the quantity
as n → ∞ (here, E ⊂ R, G ∈ {R
2, R
+2}, and ψ
n
∈ L
1(E) is a positive kernel) and structural properties of function f. These structural properties are characterized by its “directional” moduli of continuity:
Here is one of the results obtained.
Theorem 1. Let E and A be intervals in
R
+
such that A ⊂ E, f ∈ L
p
(G), α ∈ [0, 2π] when G =R
2
and α ∈ [0, π/2] when G = R
+2
Denote Δ
n, k
= ∫
A
t
k
ψ
n
(t)dt. If there exists an r ∈ N
such that, for any m ∈ N, we have Δ
m, r
> 0, Δ
m, r + 1 < ∞, and
then the relations
are equivalent. Particular methods of approximation are considered. We establish
Corollary 1. Let p, G, α, and f be the same as in Theorem 1, and
Then the relations and are equivalent.
Original Russian Text ? N.Yu. Dodonov, V.V. Zhuk, 2008, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1.
Matematika, Mekhanika, Astronomiya, 2008, No. 2, pp. 23–33. 相似文献
11.
12.
《分析论及其应用》1994,(1)
In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), forwhich the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q
相似文献
13.
It is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from thed-dimensional Hardy spaceH p (R×···×R) toL p (R d ) (1/2<p<∞) and is of weak type (H 1 ?i ,L 1) (i=1,…,d), where the Hardy spaceH 1 ?i is defined by a hybrid maximal function. As a consequence, we obtain that the Fejér means of a functionf ∈H 1 ?i ?L(logL) d?1 converge a.e. to the function in question. Moreover, we prove that the Fejér means are uniformly bounded onH p (R×···×R) whenever 1/2<p<∞. Thus, in casef ∈H p (R×···×R) the Fejér means converge tof inH p (R×···×R) norm. The same results are proved for the conjugate Fejér means, too. 相似文献
14.
15.
16.
研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果. 相似文献
17.
Joe Gildea 《代数通讯》2013,41(9):3311-3317
The Structure of the Unit Group of the Group Algebra of the group C 3 × D 6 over a finite field of characteristic 3 is established in terms of split extensions of cyclic groups. 相似文献
18.
《代数通讯》2013,41(5):2043-2052
Abstract Let 𝔤 be a complex semisimple Lie algebra. Let K be an algebraic group acting on the flag variety of 𝔤 with finitely many orbits. We give a geometric interpretation of the coherent continuation on the category of finitely generated (𝔤, K )-modules in terms of the intertwining functors on the category of K-equivariant 𝒟-modules. 相似文献
19.
20.
本文研究了n参数d随机游动(记为RW~d_n)的各种多参数Markov性、单 点转移函数和宽过去转移函数,得到了基本型R叫(B~1(p,q))的一个弱大数定律. 相似文献