共查询到20条相似文献,搜索用时 15 毫秒
1.
Hai-yan Wu Chong-guang Cao Wei Zhang 《Journal of Applied Mathematics and Computing》2008,26(1-2):475-487
Suppose F is a field of characteristic not 2. Let n and m be two arbitrary positive integers with n≥2. We denote by M n (F) and S n (F) the space of n×n full matrices and the space of n×n symmetric matrices over F, respectively. All linear maps from S n (F) to M m (F) preserving M–P inverses of matrices are characterized first, and thereby all linear maps from S n (F) (M n (F)) to S m (F) (M m (F)) preserving M–P inverses of matrices are characterized, respectively. 相似文献
2.
Paul Feit 《Israel Journal of Mathematics》1990,69(3):289-320
Letf(X; T 1, ...,T n) be an irreducible polynomial overQ. LetB be the set ofb teZ n such thatf(X;b) is of lesser degree or reducible overQ. Let ?={F j}{F j } j?1 ∞ be a Følner sequence inZ n — that is, a sequence of finite nonempty subsetsF j ?Z n such that for eachvteZ n , $\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap (F_j + \upsilon )} \right|}}{{\left| {F_j } \right|}} = 1$ Suppose ? satisfies the extra condition that forW a properQ-subvariety ofP n ?A n and ?>0, there is a neighborhoodU ofW(R) in the real topology such that $\mathop {lim sup}\limits_{j \to \infty } \frac{{\left| {F_j \cap U} \right|}}{{\left| {F_j } \right|}}< \varepsilon $ whereZ n is identified withA n (Z). We prove $\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap B} \right|}}{{\left| {F_j } \right|}} = 0$ . 相似文献
3.
We give a necessary and sufficient condition for a double indexed sequence {h m n } of vectors in a Hilbert space such that it can be represented in the form h m n = T m S n h 0 0 , (?)m, n ∈ N, where (T,S) is a pair of commuting contractions having regular unitary dilation. 相似文献
4.
Let {W i (t), t ∈ ?+}, i = 1, 2, be two Wiener processes, and let W 3 = {W 3(t), t ∈ ? + 2 } be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower bounds for the boundary noncrossing probability P f = P{W 1(t 1) + W 2(t 2) + W 3(t) + f(t) ≤ u(t), t ∈ ? + 2 }, where f, u : ? + 2 → ? are two general measurable functions. We further show that, for large trend functions γf > 0, asymptotically, as γ → ∞, P γf is equivalent to \( {P}_{\gamma}\underset{\bar{\mkern6mu}}{{}_f} \) , where \( \underset{\bar{\mkern6mu}}{f} \) is the projection of f onto some closed convex set of the reproducing kernel Hilbert space of the field W(t) = W 1(t 1) + W 2(t 2) + W 3(t). It turns out that our approach is also applicable for the additive Brownian pillow. 相似文献
5.
In this paper we consider systems with n degrees of freedom given by the natural Hamiltonian function of the form $$ H = \frac{1} {2}p^T Mp + V(q), $$ where q = (q 1, …, q n ) ∈ ? n , p = (p 1, …, p n ) ∈ ? n , are the canonical coordinates and momenta, M is a symmetric non-singular matrix, and V (q) is a homogeneous function of degree k ∈ ?*. We assume that the system admits 1 ? m < n independent and commuting first integrals F 1, … F m . Our main results give easily computable and effective necessary conditions for the existence of one more additional first integral F m+1 such that all integrals F 1, … F m+1 are independent and pairwise commute. These conditions are derived from an analysis of the differential Galois group of variational equations along a particular solution of the system. We apply our result analysing the partial integrability of a certain n body problem on a line and the planar three body problem. 相似文献
6.
Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves LetA denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and letP denote the orthogonal projection ofL 2(Ω,dA) ontoA. A functionb inA induces a Hankel operator (densely defined) onA by the ruleH b (g)=(I?P)bg. This paper continues earlier investigations of the authors and others by determining conditions under whichH b is bounded, compact, or lies in the Schatten-von Neumann idealS p , 1<p<∞ 相似文献
7.
Under certain conditions, the contraction mapping fixed point theorem guarantees the convergence of the iterationx i+1=f(x i ) toward a fixed point of the functionf:R n →R n. When an interval extensionF off is used in a similar iteration scheme to obtain a sequence of interval vectors these conditions need not provide convergence to a degenerate interval vector representing the fixed point, even if the width of the initial interval vector is chosen arbitrarily small. We give a sufficient condition on the extensionF in order that the convergence is guaranteed. The centered form of Moore satisfies this condition. 相似文献
8.
Björn G. Walther 《Arkiv f?r Matematik》1999,37(2):381-393
For Ξ∈R n ,t∈R andf∈S(R n ) define $\left( {S^2 f} \right)\left( t \right)\left( \xi \right) = \exp \left( {it\left| \xi \right|^2 } \right)\hat f\left( \xi \right)$ . We determine the optimal regularitys 0 such that $\int_{R^n } {\left\| {(S^2 f)[x]} \right\|_{L^2 (R)}^2 \frac{{dx}}{{(1 + |x|)^b }} \leqslant C\left\| f \right\|_{H^s (R^n )}^2 ,s > s_0 } ,$ holds whereC is independent off∈S(R n ) or we show that such optimal regularity does not exist. This problem has been treated earlier, e.g. by Ben-Artzi and Klainerman [2], Kato and Yajima [4], Simon [6], Vega [9] and Wang [11]. Our theorems can be generalized to the case where the exp(it|ξ|2) is replaced by exp(it|ξ|a),a≠2. The proof uses Parseval's formula onR, orthogonality arguments arising from decomposingL 2(R n ) using spherical harmonics and a uniform estimate for Bessel functions. Homogeneity arguments are used to show that results are sharp with respect to regularity. 相似文献
9.
Alexandr Kuzminykh 《Journal of Geometry》2009,94(1-2):143-150
We prove the existence of a family Ω(n) of 2 c (where c is the cardinality of the continuum) subgraphs of the unit distance graph (E n , 1) of the Euclidean space E n , n ≥ 2, such that (a) for each graph G ? Ω(n), any homomorphism of G to (E n , 1) is an isometry of E n ; moreover, for each subgraph G 0 of the graph G obtained from G by deleting less than c vertices, less than c stars, and less than c edges (we call such a subgraph reduced), any homomorphism of G 0 to (E n , 1) is an isometry (of the set of the vertices of G 0); (b) each graph G ? Ω(n) cannot be homomorphically mapped to any other graph of the family Ω(n), and the same is true for each reduced subgraph of G. 相似文献
10.
We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH ? n . We show that there exists a Γ-invariant real hypersurfaceF ?H ? n such that the Dirichlet fundamental polyhedron for Γ centered at z0 has two sides (resp. infinitely many sides) if and only ifz 0 ∈F (resp.z 0 ?F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH ? n is developed in terms of these horospherical coordinates. 相似文献
11.
Wolfgang Luh 《Constructive Approximation》1986,2(1):179-187
Let Ω ?C be an open set with simply connected components and suppose that the functionφ is holomorphic on Ω. We prove the existence of a sequence {φ (?n)} ofn-fold antiderivatives (i.e., we haveφ (0)(z)∶=φ(z) andφ (?n)(z)=dφ (?n?1)(z)/dz for alln ∈ N0 and z ∈ Ω) such that the following properties hold:
- For any compact setB ?Ω with connected complement and any functionf that is continuous onB and holomorphic in its interior, there exists a sequence {n k} such that {φ?nk} converges tof uniformly onB.
- For any open setU ?Ω with simply connected components and any functionf that is holomorphic onU, there exists a sequence {m k} such that {φ?mk} converges tof compactly onU.
- For any measurable setE ?Ω and any functionf that is measurable onE, there exists a sequence {p k} such that {φ (-Pk)} converges tof almost everywhere onE.
12.
We obtain some integro-local and integral limit theorems for the sums S(n) = ξ(1) + ? + ξ(n) of independent random variables with general semiexponential distribution (i.e., a distribution whose right tail has the form $P(\xi \ge t) = e^{ - t^\beta L(t)} $ , where β ∈ (0, 1) and L(t) is a slowly varying function with some smoothness properties). These theorems describe the asymptotic behavior as x → ∞ of the probabilities P(S(n) ∈ [x, x + Δ)) and P(S(n) ≥ x) in the zone of normal deviations and all zones of large deviations of x: in the Cramér and intermediate zones, and also in the “extreme” zone where the distribution of S(n) is approximated by that of the maximal summand. 相似文献
13.
LetR be a ring. For the setF of all nonzero ideals ofR, we introduce an equivalence relation inF as follows: For idealsI andJ, I~J if and only ifV R (I)=V R(J), whereV R() is the centralizer inR. LetI R=F/~. Then we can see thatn(I R), the cardinality ofI R, is 1 if and only ifR is either a prime ring or a commutative ring (Theorem 1.1). An idealI ofR is said to be a commutator ideal ifI is generated by{st?ts; s∈S, t∈T} for subsetS andT ofR, andR is said to be a ring with (N) if any commutator ideal contains no nonzero nilpotent ideals. Then we have the following main theorem: LetR be a ring with (N). Thenn(I R) is finite if and only ifR is isomorphic to an irredundant subdirect sum ofS⊕Z whereS is a finite direct sum of non commutative prime rings andZ is a commutative ring (Theorem 2.1). Finally, we show that the existence of a ringR such thatn(I R)=m for any given natural numberm. 相似文献
14.
A non-zero vector-valued sequence u ∈ ?q(X′) is a cover for a subset M of ?P(X) if, for some 0 < α ≤ 1, ∥u * h∥ ∞ ≥ α ∥u∥q ∥h∥p for all h ∈ M. Covers of ?1 = ?1(R) are important in worst case system identification in ?1 and in the reconstruction of elements in a normed space from corrupted functional values. We investigate the existence of covers for certain naturally occurring subspaces of ?p(X). We show that there exist finitely supported covers for some subspaces, and obtain lower bounds for their ’lengths’. We also obtain similar results for covers associated with convolution products for spaces of measurable vector-valued functions defined on the positive real axis. 相似文献
15.
P. Burmeister 《Algebra Universalis》1973,3(1):271-279
Let U be any nontrivial primitive class of partial algebras, i.e. there existsA ∈ U with |A|≥2, and U is closed with respect to homomorphic images (in the weak sense), subalgebras (on closed subsets) and cartesian products of U-algebras, and let U f denote the—also nontrivial and primitive—class of all full U-algebras. Then every U-algebra with at least two elements is a relative algebra of some U f -algebra. For any U-algebraAsetU A =U i εI({i}×(A K i—domf i A )), where (K i) i εI is the type under consideration. Furthermore let F(N, U) denote any U-algebra U-freely generated by some setN (and let F (M, U f ) be similarly defined). Then for every nonempty setM there exists a setN satisfyingM ?N such that there exists a bijective mapping σ:U F(N, U) →N ?M satisfying σ((i, α)) ? α(K i ) for all (i, α) ∈U F (N, U), and, for the structureg=(g i)iεI defined by ,g i : =f i F(N, U) ∪ {(α, σ((i, α))) | (i, α ∈U F(N, U)} id M induces an isomorphism betweenF(M, U f ), and (F(N, U)g). 相似文献
16.
Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619–655 (1990)] are used to prove the following: Let P ∈ ?[z1,...,z n ] and denote by P m its principal part. If P ? Pm is dominated by P m then the following assertions for the partial differential operators P(D) and P m(D) are equivalent for N ∈ S n?1:
- P(D) and/or Pm D)admit a continuous linear right inverse on C ∞(H +(N)).
- P(D) admits a continuous linear right inverse on C ∞ (? n ) and a fundamental solution E ∈ C ∞(?n) satisfying Supp $E \subset \overline {H - (N)} $
17.
F. Peherstorfer 《Constructive Approximation》1996,12(4):481-488
LetW N(z)=aNzN+... be a complex polynomial and letT n be the classical Chebyshev polynomial. In this article it is shown that the polynomials (2aN)?n+1Tn(WN), n ∈N, are minimal polynomials on all equipotential lines for {z∈C:|W N(z)|≤1 Λ ImW N(z)=0} 相似文献
18.
19.
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
20.