共查询到20条相似文献，搜索用时 31 毫秒
1.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
2.
LetX be a Banach space and letA be the infinitesimal generator of a differentiable semigroup {T(t) |t ≥ 0}, i.e. aC
0-semigroup such thatt ↦T(t)x is differentiable on (0, ∞) for everyx εX. LetB be a bounded linear operator onX and let {S(t) |t ≥ 0} be the semigroup generated byA +B. Renardy recently gave an example which shows that {S(t) |t ≥ 0} need not be differentiable. In this paper we give a condition on the growth of ‖T′(t)‖ ast ↓ 0 which is sufficient to ensure that {S(t) |t ≥ 0} is differentiable. Moreover, we use Renardy’s example to study the optimality of our growth condition. Our results can
be summarized roughly as follows:
We also show that if lim sup
t→0+t
p ‖T′(t)‖<∞ for a givenp ε [1, ∞), then lim sup
t→0+t
p‖S′(t)‖<∞; it was known previously that if limsup
t→0+t
p‖T′(t)‖<∞, then {S(t) |t ≥ 0} is differentiable and limsup
t→0+t
2p–1‖S′(t)‖<∞. 相似文献
| (i) | If lim sup t→0+t log‖T′(t)‖/log(1/2) = 0 then {S(t) |t ≥ 0} is differentiable. |
| (ii) | If 0<L=lim sup t→0+t log‖T′(t)‖/log(1/2)<∞ thent ↦S(t ) is differentiable on (L, ∞) in the uniform operator topology, but need not be differentiable near zero |
| (iii) | For each function α: (0, 1) → (0, ∞) with α(t)/log(1/t) → ∞ ast ↓ 0, Renardy’s example can be adjusted so that limsup t→0+t log‖T′(t)‖/α(t) = 0 andt →S(t) is nowhere differentiable on (0, ∞). |
3.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
| 1. | It does not self-overlap: it is a simple polygon. |
| 2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
| • | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
| • | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
| • | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
4.
José Rodríguez 《Archiv der Mathematik》2007,88(1):62-70
Let X be a weakly Lindel?f determined Banach space. We prove that the following two statements are equivalent:
Some applications and related examples are given.
Received: 11 January 2006; Revised: 24 May 2006 相似文献
| (i) | Every Radon probability measure on (BX*, w*) has separable support. |
| (ii) | Every countably additive X*-valued measure with σ-finite variation has norm separable range. |
5.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
| (i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
| (ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
| (iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
| (iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
| (v) | We investigate the properties of the operators from X α,p spaces to their predual. |
6.
Belmesnaoui Aqzzouz 《Rendiconti del Circolo Matematico di Palermo》2006,55(2):147-162
We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK
x with the followings properties:
相似文献
| 1 | The categoryK is a full subcategory ofK x. |
| 2 | The free objects ofK are projectives inK x. |
| 3 | A sequence ofK-morphismes isK-exact if, and only if, it isK x-exact. |
| 4 | To each objectU ofK x we can associate a surjections:X→U whereX is an object ofK. |
7.
LetK be a class of spaces which are eigher a pseudo-opens-image of a metric space or ak-space having a compact-countable closedk-network. LetK′ be a class of spaces which are either a Fréchet space with a point-countablek-network or a point-G
δ
k-space having a compact-countablek-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many
spaces in the classK orK′ are ak-space. The main results are that
Project supported by the Mathematical Tianyuan Foundation of China 相似文献
| Theorem A | If X, Y∈K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka's condition. |
| Theorem B | The following are equivalent: |
| (a) | BF(ω 2)is false. |
| (b) | For each X, Y ∈ K′, X x Y is a k-space if and only if (X,Y) has the Tanaka's condition. |
8.
Eric Schmutz 《Central European Journal of Mathematics》2008,6(3):482-487
It is known that the unit sphere, centered at the origin in ℝ
n
, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds
on the complexity of the coordinates: for every point ν on the unit sphere in ℝ
n
, and every ν > 0; there is a point r = (r
1; r
2;…;r
n) such that:
One consequence of this result is a relatively simple and quantitative proof of the fact that the rational orthogonal group
O(n;ℚ) is dense in O(n;ℝ) with the topology induced by Frobenius’ matrix norm. Unitary matrices in U(n;ℂ) can likewise be approximated by matrices in U(n;ℚ(i))
相似文献
| – | ⊎ ‖r-v‖∞ < ε. |
| – | ⊎ r is also a point on the unit sphere; Σ r i 2 = 1. |
| – | ⊎ r has rational coordinates; for some integers a i , b i . |
| – | ⊎ for all . |
9.
We introduce a notion which is intermediate between that of taking thew*-closed convex hull of a set and taking the norm closed convex hull of this set. This notion helps to streamline the proof
(given in [FLP]) of the famous result of James in the separable case. More importantly, it leads to stronger results in the
same direction. For example:
相似文献
| 1. | AssumeX is separable and non-reflexive and its unit sphere is covered by a sequence of balls of radiusa<1. Then for every sequence of positive numbers tending to 0 there is anf εX*, such that ‖f‖ = 1 andf (x)≤1 −ε i , wheneverx εC i ,i=1,2,… |
| 2. | AssumeX is separable and non-reflexive and letT:Y →X* be a bounded linear non-surjective operator. Then there is anf εX* which does not attain its norm onB X such thatf ∉T(Y). |
10.
Abstract This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF
(the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here is a language with a distinguished linear order <, and REF
consists of formulas of the form
where φ is an -formula, φ
<x
is the -formula obtained by restricting all the quantifiers of φ to the initial segment determined by x, and x is a variable that does not appear in φ. Our results include:
Theorem
The following five conditions are equivalent for a complete first order theory T in a countable language
with a distinguished linear order:
Moreover, if κ is a regular cardinal satisfying κ = κ
<κ
, then each of the above conditions is equivalent to:
相似文献
| (1) | Some model of T has an elementary end extension with a first new element. |
| (2) | T ⊢ REF . |
| (3) | T has an ω 1-like model that continuously embeds ω 1. |
| (4) | For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ. |
| (5) | For some regular uncountable cardinal κ, T has a κ-like model that has an elementary extension in which the supremum of M exists. |
| (6) | T has a κ + -like model that continuously embeds a stationary subset of κ. |
11.
Amir Mafi 《Czechoslovak Mathematical Journal》2009,59(4):1095-1102
Let (R,m) be a complete local ring, a an ideal of R and N and L two Matlis reflexive R-modules with Supp(L) ⊆ V(a). We prove that if M is a finitely generated R-module, then Exti
R
i
(L, H
a
j
(M,N)) is Matlis reflexive for all i and j in the following cases:
In these cases we also prove that the Bass numbers of H
a
j
(M, N) are finite. 相似文献
| (a) | dim R/a = 1 |
| (b) | cd(a) = 1; where cd is the cohomological dimension of a in R |
| (c) | dim R ⩽ 2. |
12.
LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:
相似文献
| (1) | Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|. |
| (2) | |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group. |
| (3) | |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group. |
13.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2).
The online version of the original article can be found at . 相似文献
| (1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
| (2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
14.
In this paper, we show the equivalence of somequasi-random properties for sparse graphs, that is, graphsG with edge densityp=|E(G)|/(
2
n
)=o(1), whereo(1)→0 asn=|V(G)|→∞. Our main result (Theorem 16) is the following embedding result. For a graphJ, writeN
J(x) for the neighborhood of the vertexx inJ, and letδ(J) andΔ(J) be the minimum and the maximum degree inJ. LetH be atriangle-free graph and setd
H=max{δ(J):J⊆H}. Moreover, putD
H=min{2d
H,Δ(H)}. LetC>1 be a fixed constant and supposep=p(n)≫n
−1
D
H. We show that ifG is such that
Moreover, we discuss a setting under which an arbitrary graphH (not necessarily triangle-free) can be embedded inG. We also present an embedding result for directed graphs.
Research supported by a CNPq/NSF cooperative grant.
Partially supported by MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997-4) and by CNPq (Proc. 300334/93-1 and 468516/2000-0).
Partially supported by NSF Grant 0071261.
Supported by NSF grant CCR-9820931. 相似文献
| (i) | deg G (x)≤C pn for allx∈V(G), | ||
| (ii) |
for all 2≤r≤D
H and for all distinct verticesx
1, ...,x
r ∈V(G), |
||
| (iii) |
for all but at mosto(n
2) pairs {x
1,x
2} ⊆V(G), |
15.
M. K. Sen 《Semigroup Forum》1992,44(1):149-156
A pair (S, P) of a regular semigroupsS and a subsetP ofE
s
whereE
s
is the set of all idempotent elements ofS is called aP-regular semigroupS(P) if it satisfies the following:
The class of orthodox semigroups and the class of regular *-semigroups are within the class ofP-regular semigroups. This paper gives a characterisation of theP-kernel of aP-congruence. 相似文献
| (1) | P 2 ⊆E S |
| (2) | qPq⊆P for allq∈P |
| (3) | for anyx∈S there existsx †∈V(x) (the set of inverses ofx), such thatxP 1 x †⊆P andx † P 1 x⊆P whereP 1=P∩{1}. |
16.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2). 相似文献
| (1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
| (2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
17.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
| (1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
| (2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
| (3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
| (4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |
18.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
| – | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
| – | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
| – | • is prime; |
| – | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
| – | • is recursively presented; |
| – | • satisfies no identity; |
| – | • contains a transcendental, invertible element; |
| – | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
| – | • is graded if % MathType!End!2!1! has characteristic 2; |
| – | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
| – | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
19.
Let G be a 2-edge-connected simple graph with girth g, independence number α(G), and if one of the following two conditions holds
then G is upper embeddable and the lower bound v − 3g + 7 is best possible. Similarly the result for 3-edge-connected simple graph with girth g and independence number α(G) is also obtained.
Huang Yuanqiu: Partially supported by National Science Foundation of China (No. 10771062) and Program for New Century Excellent
Talents in University (No. NCET-07-0276). 相似文献
| (1) | α(G) ≤ 2; | |
| (2) | α(G) ≥ 3, and for any three nonadjacent vertices v
i
(i = 1,2,3), it has
|
20.
A. S. Sivatski 《Journal of Mathematical Sciences》2007,145(1):4823-4830
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose
that elements
are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
In particular, the algebra A provides an example of an indecomposable algebra of index 2n+1 over a field, the u-invariant and the 2-cohomological dimension of which equal 2n+3 and n + 3, respectively. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 227–241. 相似文献
| (1) | the field K has no proper extension of odd degree |
| (2) | the u-invariant of K equals 4 |
| (3) | the multiquadratic extension is not 4-excellent, and the quadratic form 〈uv,-u,-v, a〉 provides a relevant counterexample |
| (4) | the central division algebra A = D ⊗E (a, t0) ⊗E (b1, t1) ⋯ ⊗E (bn, tn) does not decompose into a tensor product of two nontrivial central simple algebras over E, where E = K ((t0))((t1)) … ((tn)) is the Laurent series field in the variables t0, t1, …, tn |
| (5) | ind A = 2n+1. |