共查询到20条相似文献,搜索用时 78 毫秒
1.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
2.
M. V. Korobkov 《Siberian Mathematical Journal》2009,50(5):874-886
We find necessary and sufficient conditions for a curve in ℝ
m×n
to be the gradient range of a C
1-smooth function υ: Ω ⊂ ℝ
n
→ ℝ
m
. We show that this curve has tangents in a weak sense; these tangents are rank 1 matrices and their directions constitute
a function of bounded variation. We prove also that in this case v satisfies an analog of Sard’s theorem, while the level
sets of the gradient mapping ▿υ: Ω → ℝ
m×n
are hyperplanes. 相似文献
3.
Morten Nielsen 《Journal of Geometric Analysis》2012,22(1):12-22
We consider a periodic matrix weight W defined on ℝ
d
and taking values in the N×N positive-definite matrices. For such weights, we prove transference results between multiplier operators on L
p
(ℝ
d
;W) and
Lp(\mathbb Td;W)L_{p}(\mathbb {T}^{d};W), 1<p<∞, respectively. As a specific application, we study transference results for homogeneous multipliers of degree zero. 相似文献
4.
Let k be a positive integer. A Roman k-dominating function on a graph G is a labeling f: V (G) → {0, 1, 2} such that every vertex with label 0 has at least k neighbors with label 2. A set {f
1, f
2, …, f
d
} of distinct Roman k-dominating functions on G with the property that Σ
i=1
d
f
i
(v) ≤ 2 for each v ∈ V (G), is called a Roman k-dominating family (of functions) on G. The maximum number of functions in a Roman k-dominating family on G is the Roman k-domatic number of G, denoted by d
kR
(G). Note that the Roman 1-domatic number d
1R
(G) is the usual Roman domatic number d
R
(G). In this paper we initiate the study of the Roman k-domatic number in graphs and we present sharp bounds for d
kR
(G). In addition, we determine the Roman k-domatic number of some graphs. Some of our results extend those given by Sheikholeslami and Volkmann in 2010 for the Roman
domatic number. 相似文献
5.
Maryam Atapour Seyyed Mahmoud Sheikholeslami Rana Hajypory Lutz Volkmann 《Central European Journal of Mathematics》2010,8(6):1048-1057
Let k ≥ 1 be an integer, and let D = (V; A) be a finite simple digraph, for which d
D
− ≥ k − 1 for all v ɛ V. A function f: V → {−1; 1} is called a signed k-dominating function (SkDF) if f(N
−[v]) ≥ k for each vertex v ɛ V. The weight w(f) of f is defined by $
\sum\nolimits_{v \in V} {f(v)}
$
\sum\nolimits_{v \in V} {f(v)}
. The signed k-domination number for a digraph D is γ
kS
(D) = min {w(f|f) is an SkDF of D. In this paper, we initiate the study of signed k-domination in digraphs. In particular, we present some sharp lower bounds for γ
kS
(D) in terms of the order, the maximum and minimum outdegree and indegree, and the chromatic number. Some of our results are
extensions of well-known lower bounds of the classical signed domination numbers of graphs and digraphs. 相似文献
6.
A. G. Bakan 《Ukrainian Mathematical Journal》2009,61(3):347-360
We prove that the theorem on the incompleteness of polynomials in the space C
0
w
established by de Branges in 1959 is not true for the space L
p
(ℝ, dμ) if the support of the measure μ is sufficiently dense. 相似文献
7.
Abstract
Thom–Pontrjagin constructions are used to give a
computable necessary and sufficient condition for a homomorphism ϕ
: H
n
(L;Z) → H
n
(M;Z) to be realized by a map
f : M → L of degree k for closed (n − 1)-connected 2n-manifolds M and L,
n > 1. A corollary is that
each (n − 1)-connected
2n-manifold admits selfmaps
of degree larger than 1, n
> 1.
In the most interesting case of dimension 4, with the
additional surgery arguments we give a necessary and sufficient
condition for the existence of a degree k map from a closed orientable
4-manifold M to a closed
simply connected 4-manifold L
in terms of their intersection forms; in particular, there is a
map f :
M → L of degree 1 if and only if the
intersection form of L is
isomorphic to a direct summand of that of
M.
Both authors are supported by MSTC, NSFC. The
comments of F. Ding, J. Z. Pan, Y. Su and the referee enhance
the quality of the paper 相似文献
8.
Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L
2 normalized family of functions such that P(h)u(h) is O(h) in L
2(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L
p
norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch
−δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator. 相似文献
9.
Behrooz Mirzaii 《Mathematische Annalen》2008,340(1):159-184
The homology of GL
n
(R) and SL
n
(R) is studied, where R is a commutative ‘ring with many units’. Our main theorem states that the natural map H
4(GL3(R), k) → H
4(GL4(R), k) is injective, where k is a field with char(k) ≠ 2, 3. For an algebraically closed field F, we prove a better result, namely, is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the
K-group K
4(R). 相似文献
10.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
11.
V. E. Maiorov 《Ukrainian Mathematical Journal》2010,62(3):452-466
We study the approximation of the classes of functions by the manifold R
n
formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W
r
p
from the set R
n
of ridge functions in the space L
q
(B
d
) satisfies the sharp order n
-r/(d-1). 相似文献
12.
Edgardo Roldán-Pensado 《Discrete and Computational Geometry》2012,47(2):288-300
Let K be a convex body in ℝ
d
. It is known that there is a constant C
0 depending only on d such that the probability that a random copy ρ(K) of K does not intersect ℤ
d
is smaller than
\fracC0|K|\frac{C_{0}}{|K|} and this is best possible. We show that for every k<d there is a constant C such that the probability that ρ(K) contains a subset of dimension k is smaller than
\fracC|K|\frac{C}{|K|}. This is best possible if k=d−1. We conjecture that this is not best possible in the rest of the cases; if d=2 and k=0 then we can obtain better bounds. For d=2, we find the best possible value of C
0 in the limit case when width(K)→0 and |K|→∞. 相似文献
13.
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
14.
A finite group G is called p
i
-central of height k if every element of order p
i
of G is contained in the k
th
-term ζ
k
(G) of the ascending central series of G. If p is odd, such a group has to be p-nilpotent (Thm. A). Finite p-central p-groups of height p − 2 can be seen as the dual analogue of finite potent p-groups, i.e., for such a finite p-group P the group P/Ω1(P) is also p-central of height p − 2 (Thm. B). In such a group P, the index of P
p
is less than or equal to the order of the subgroup Ω1(P) (Thm. C). If the Sylow p-subgroup P of a finite group G is p-central of height p − 1, p odd, and N
G
(P) is p-nilpotent, then G is also p-nilpotent (Thm. D). Moreover, if G is a p-soluble finite group, p odd, and P ∈ Syl
p
(G) is p-central of height p − 2, then N
G
(P) controls p-fusion in G (Thm. E). It is well-known that the last two properties hold for Swan groups (see [11]). 相似文献
15.
We introduce and solve a natural geometrical extremal
problem. For the set E
(n,w) = {x
n
{0,1}
n
:
x
n
has
w ones } of vertices of
weight w in the unit cube of
n
we determine M (n,k,w)
max{|U
k
n
E(n,w)|:U
k
n
is a
k-dimensional subspace of
n
. We also present an extension to multi-sets and explain a
connection to a higher dimensional Erds–Moser type
problem. 相似文献
16.
In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk(Ω,R2) for any k ≥ 1, which attracts any bounded set of Hk(Ω,R2) in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong's conclusion. 相似文献
17.
Let R be a ring, n a fixed nonnegative integer and FP
n
(F
n
) the class of all left (right) R-modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module F) is called n-FI-injective (resp., n-FI-flat) if Ext
1(N,M) = 0 (resp., Tor
1(F,N) = 0) for any N ∈ FP
n
. It is shown that a left R-module M over any ring R is n-FI-injective if and only if M is a kernel of an FP
n
-precover f: A → B with A injective. For a left coherent ring R, it is proven that a finitely presented right R-module M is n-FI-flat if and only if M is a cokernel of an F
n
-preenvelope K → F of a right R-module K with F projective if and only if M ∈⊥
F
n
. These classes of modules are used to construct cotorsion theories and to characterize the global dimension of a ring. 相似文献
18.
19.
Štefan Gyürki 《Mathematica Slovaca》2009,59(2):193-200
Let k be an integer. A 2-edge connected graph G is said to be goal-minimally k-elongated (k-GME) if for every edge uv ∈ E(G) the inequality d
G−uv
(x, y) > k holds if and only if {u, v} = {x, y}. In particular, if the integer k is equal to the diameter of graph G, we get the goal-minimally k-diametric (k-GMD) graphs. In this paper we construct some infinite families of GME graphs and explore k-GME and k-GMD properties of cages.
This research was supported by the Slovak Scientific Grant Agency VEGA No. 1/0406/09. 相似文献