共查询到20条相似文献,搜索用时 31 毫秒
1.
For an additive subgroup G of a field F of characteristic zero, a Lie algebra B(G) of Block type is defined with basis {Lα,i| α∈G, i∈Z+} and relations [Lα,i, Lβ,j] = (β-α)Lα+β,i+j+(αj-βi)Lα+β,Lα+β,i+j-1.It is proved that an irreducible highest weight B(Z)-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B(G)0^*(the dual space of B(G)0 = span{L0,i|i∈Z+}), a Verma B(G)-module M(∧,λ) is defined, and the irreducibility of M(A,λ) is completely determined. 相似文献
2.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
3.
Erika Hausenblas 《Probability Theory and Related Fields》2007,137(1-2):161-200
The article deals with SPDEs driven by Poisson random measure with non Lipschitz coefficients. Let A:E→E be a generator of an analytic semigroup on E, E being a certain Banach space. Let be a stochastic basis carrying an E-valued Poisson random measure η with characteristic measure ν and compensator γ. Let 1≤p≤2. Our point of interest is the existence of solutions to SPDE's of e.g.the following type
where g:E→L(E,E
0) is some mapping satisfying ∫
E
|g(x,z)−g(y,z)|
p
ν(dz)≤C|x−y|
rp
, x,y ∈ E, where 0<r<1 satisfy certain condition specified later and is again a certain Banach space.
This work was supported by the Austrian Academy of Science, APART 700 and FWF-Project P17273-N12 相似文献
4.
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valuated functions defined on V(G) such that g(x) ≤f(x) for all x∈V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤d
H
(x) ≤f(x) for all x∈V(G). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let
= {F
1, F
2, ..., F
m
} be a factorization of G and H be a subgraph of G with mr edges. If F
i
, 1 ≤i≤m, has exactly r edges in common with H, then
is said to be r-orthogonal to H. In this paper it is proved that every (mg + kr, mf−kr)-graph, where m, k and r are positive integers with k < m and g≥r, contains a subgraph R such that R has a (g, f)-factorization which is r-orthogonal to a given subgraph H with kr edges.
This research is supported by the National Natural Science Foundation of China (19831080) and RSDP of China 相似文献
5.
Dong Hyun Cho 《Czechoslovak Mathematical Journal》2009,59(2):431-452
Let C[0, T] denote the space of real-valued continuous functions on the interval [0, T] with an analogue w
ϕ of Wiener measure and for a partition 0 = t
0 < t
1 < ... < t
n
< t
n+1 = T of [0, T], let X
n
: C[0, T] → ℝ
n+1 and X
n+1: C[0, T] → ℝ
n+2 be given by X
n
(x) = (x(t
0), x(t
1), ..., x(t
n
)) and X
n+1(x) = (x(t
0), x(t
1), ..., x(t
n+1)), respectively.
In this paper, using a simple formula for the conditional w
ϕ-integral of functions on C[0, T] with the conditioning function X
n+1, we derive a simple formula for the conditional w
ϕ-integral of the functions with the conditioning function X
n
. As applications of the formula with the function X
n
, we evaluate the conditional w
ϕ-integral of the functions of the form F
m
(x) = ∫0
T
(x(t))
m
for x ∈ C[0, T] and for any positive integer m. Moreover, with the conditioning X
n
, we evaluate the conditional w
ϕ-integral of the functions in a Banach algebra
which is an analogue of the Cameron and Storvick’s Banach algebra
. Finally, we derive the conditional analytic Feynman w
ϕ-integrals of the functions in
.
相似文献
6.
Simple graphs are considered. Let G be a graph andg(x) andf(x) integer-valued functions defined on V(G) withg(x)⩽f(x) for everyxɛV(G). For a subgraphH ofG and a factorizationF=|F
1,F
2,⃛,F
1| ofG, if |E(H)∩E(F
1)|=1,1⩽i⩽j, then we say thatF orthogonal toH. It is proved that for an (mg(x)+k,mf(x) -k)-graphG, there exists a subgraphR ofG such that for any subgraphH ofG with |E(H)|=k,R has a (g,f)-factorization orthogonal toH, where 1⩽k<m andg(x)⩾1 orf(x)⩾5 for everyxɛV(G).
Project supported by the Chitia Postdoctoral Science Foundation and Chuang Xin Foundation of the Chinese Academy of Sciences. 相似文献
7.
Let
be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every maximal subgroup of all Sylow subgroups of H is either c-normal or S-quasinormally embedded in G. (2) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every maximal subgroup of all Sylow subgroups of F*(H), the generalized Fitting subgroup of H, is either c-normal or S-quasinormally embedded in G. (3) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every cyclic subgroup of F*(H) of prime order or order 4 is either c-normal or S-quasinormally embedded in G.
Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi Autonomous Region (No.
0249001).
Corresponding author. Supported in part by the Natural Science Foundation of China (10571181), NSF of Guangdong Province (06023728)
and ARF(GDEI). 相似文献
8.
Let
\mathbbF\mathbb{F} be a field of characteristic 0, and let G be an additive subgroup of
\mathbbF\mathbb{F}. We define a class of infinite-dimensional Lie algebras
\mathbbF\mathbb{F}-basis {L
μ, V
μ, W
μ | μ ∈ G}, which are very closely related to W-algebras. In this paper, the second cohomology group of is determined. 相似文献
9.
Guiying Yan 《Graphs and Combinatorics》1999,15(3):365-371
Let G be a simple graph. Let g(x) and f(x) be integer-valued functions defined on V(G) with g(x)≥2 and f(x)≥5 for all x∈V(G). It is proved that if G is an (mg+m−1, mf−m+1)-graph and H is a subgraph of G with m edges, then there exists a (g,f)-factorization of G orthogonal to H.
Received: January 19, 1996 Revised: November 11, 1996 相似文献
10.
Let (, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on × ⋯ × for the m-linear singular integral operators with nonsmooth kernels which were first introduced by Duong, Grafakos and Yan. 相似文献
11.
HaoZHAO GuiZhenLIU XiaoXiaYAN 《数学学报(英文版)》2005,21(2):413-422
Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integervalued functions defined on V(G) such that 2k - 2 ≤g(x)≤f(x) for all x∈V(G). Let H be a subgraph of G with mk edges. In this paper, it is proved that every (mg m-1,mf-m 1)-graph G has (g, f)-factorizations randomly k-orthogonal to H under some special conditions. 相似文献
12.
Yu Cheng Li 《数学学报(英文版)》2008,24(10):1737-1750
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z^ng(z) (n ≥1), g(z) = b0 + b1z^p1 +b2z^p2 +.. , bk ≠ 0 (k = 0, 1, 2,...), our main result is =A′(Mf) = A′(Mzn)∩A′(Mg) = A′(Mz^s), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. 相似文献
13.
Cheng Jun Hou 《数学学报(英文版)》2008,24(6):983-996
We introduce two notions of the pressure in operator algebras, one is the pressure Pα(π, T) for an automorphism α of a unital exact C^*-algebra A at a self-adjoint element T in A with respect to a faithful unital *-representation π the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T. 相似文献
14.
Ladislav Nebeský 《Czechoslovak Mathematical Journal》2006,56(2):317-338
If G is a connected graph of order n ⩾ 1, then by a hamiltonian coloring of G we mean a mapping c of V (G) into the set of all positive integers such that |c(x) − c(y)| ⩾ n − 1 − D
G
(x, y) (where D
G
(x, y) denotes the length of a longest x − y path in G) for all distinct x, y ∈ V (G). Let G be a connected graph. By the hamiltonian chromatic number of G we mean
, where the minimum is taken over all hamiltonian colorings c of G.
The main result of this paper can be formulated as follows: Let G be a connected graph of order n ⩾ 3. Assume that there exists a subgraph F of G such that F is a hamiltonian-connected graph of order i, where 2 ⩽ i ⩽ 1/2 (n+1). Then hc(G) ⩽ (n−2)2+1−2(i−1)(i−2). 相似文献
15.
Sergiy Maksymenko 《Central European Journal of Mathematics》2009,7(2):272-298
Let F be a C
∞ vector field defined near the origin O ∈ ℝ
n
, F(O) = 0, and (F
t
) be its local flow. Denote by
the set of germs of orbit preserving diffeomorphisms h: ℝ
n
→ ℝ
n
at O, and let
, (r ≥ 0), be the identity component of
with respect to the weak Whitney W
r
topology. Then
contains a subset
consisting of maps of the form F
α(x)(x), where α: ℝ
n
→ ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then
=
.
In this paper we present a class of examples of vector fields with degenerate singularities at O for which
formally coincides with
, i.e. on the level of ∞-jets at O.
We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials
in two variables.
相似文献
16.
Wenguang Zhai 《中国科学A辑(英文版)》1999,42(11):1173-1183
Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x
1
c
1,⋯,c
k
) denote the number of primesp withp⩽x,
, where 1<c
1<⋯<c
k
are fixed constants. It is proved that π(x;c
1,⋯,c
k
) has an asymptotic formula ifc
1
−1
+⋯+c
k
−1
>k−k/(4k
2+2).
Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation
of Shandong Province (Grant No.Q98A02110). 相似文献
17.
Ján Jakubík 《Mathematica Slovaca》2008,58(2):143-154
For an MV-algebra
let J
0(
) be the system of all closed ideals of
; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever
∈ X and
is an MV-algebra with J
0(
) ≅ J
0(
), then
∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that
there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information,
Grant I/2/2005. 相似文献
18.
R. Rimányi V. Schechtman V. Tarasov A. Varchenko 《Functional Analysis and Its Applications》2011,45(4):252-264
We interpret the equivariant cohomology HGLn *H_{GL_n }^* (ℱ
λ
,ℂ) of a partial flag variety ℱ
λ
parametrizing chains of subspaces 0 = F
0 ⊂ F
1 ⊂ … ⊂ F
N
= ℂ
n
, dimF
i
/F
i−1 = λ
i
, as the Bethe algebra of the -weight subspace of a [t]-module . 相似文献
19.
Ming DING 《Frontiers of Mathematics in China》2011,6(2):231-240
We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra (Q) generated by all cluster characters is exactly the quantum cluster algebra (Q). 相似文献
20.
Claude Tardif 《Combinatorica》2005,25(5):625-632
We prove that the identity
holds for all directed graphs G and H. Similar bounds for the usual chromatic number seem to be much harder to obtain: It is still not known whether there exists
a number n such that χ(G×H) ≥ 4 for all directed graphs G, H with χ(G) ≥ χ(H) ≥ n. In fact, we prove that for every integer n ≥ 4, there exist directed graphs Gn, Hn such that χ(Gn) = n, χ(Hn) = 4 and χ(Gn×Hn) = 3. 相似文献