共查询到20条相似文献,搜索用时 46 毫秒
1.
J. Sternfeld 《Israel Journal of Mathematics》1975,20(3-4):300-320
The main result of this paper is the following: IfX is a compact two dimensional metric space, and {φ i} i = 1/4 are four functions inC(X), then there exists a functionf inC(X) which cannot be represented in the form: $$f(x) = \sum\limits_{i = 1}^4 {g_\iota (\varphi _i (x))} $$ , with $$g_\iota \in C(R)$$ . 相似文献
2.
A. A. Fora 《Periodica Mathematica Hungarica》1985,16(2):97-113
In this paper, we definen-segmentwise metric spaces and then we prove the following results:
- (i)|Let (X, d) be ann-segmentwise metric space. ThenX n has the fixed point property with respect to uniformly continuous bounded functions if and only if, for any continuous functionF: C *(X) → C*(X) and for anyn-tuple of distinct points x1, x2, ?, xn ∈X, there exists anh ∈C *(X) such that $$F(h)(x_1 ) = h(x_1 ),i = 1,2,...,n;$$ whereC *(X) has either the uniform topology or the subspace product (Tychonoff) topology \((C^ * (X) \subseteq X^X )\) .
- LetX i (i = 1, 2, ?) be countably compact Hausdorff spaces such thatX 1 × ? × Xn has the fixed point property for alln ∈N Then the product spaceX 1 × X2 × ? has the fixed point property. We shall also discuss several problems in the Fixed Point Theory and give examples if necessary. Among these examples, we have:
- There exists a connected metric spaceX which can be decomposed as a disjoint union of a closed setA and an open setB such thatA andB have the fixed point property andX does not have.
- There exists a locally compact metrizable spaceX which has the fixed point property but its one-point compactificationX + does not have the fixed point property.
3.
A. Nissenzweig 《Israel Journal of Mathematics》1975,22(3-4):266-272
LetX be an infinite dimensional Banach space, andX* its dual space. Sequences {χ n * } n=1 ∞ ?X* which arew* converging to 0 while inf n ‖x* n ‖>0, are constructed. 相似文献
4.
Jiří Matoušek 《Israel Journal of Mathematics》1996,93(1):333-344
We investigate the minimum dimensionk such that anyn-point metric spaceM can beD-embedded into somek-dimensional normed spaceX (possibly depending onM), that is, there exists a mappingf: M→X with $$\frac{1}{D}dist_M (x,y) \leqslant \left| {f(x) - f(y)} \right| \leqslant dist_M (x,y) for any$$ Extending a technique of Arias-de-Reyna and Rodríguez-Piazza, we prove that, for any fixedD≥1,k≥c(D)n 1/2D for somec(D)>0. For aD-embedding of alln-point metric spaces into the samek-dimensional normed spaceX we find an upper boundk≤12Dn 1/[(D+1)/2]lnn (using thel ∞ k space forX), and a lower bound showing that the exponent ofn cannot be decreased at least forD?[1,7)∪[9,11), thus the exponent is in fact a jumping function of the (continuously varied) parameterD. 相似文献
5.
E. N. Chukwu 《Journal of Optimization Theory and Applications》1984,42(2):181-199
A system is totallyG-controllable if every pointx 0 of the state spaceE n can be steered to the targetG in finite time and can be held inG forever afterward. Sufficient conditions are developed for the totalG-controllability of the linear system (a) $$\dot x(t) = A(t)x(t) + B(t)u(t)$$ and its perturbation (b) $$\dot x(t) = A(t)x(t) + B(t)u(t) + F(t,x(t),u(t)),$$ where the targetG is an affine manifold inE n. We state conditions on the perturbation functionF which guarantee that, if (a) is totallyG-controllable, then so is (b). These conditions onF are natural and are obtained by solving a system of nonlinear integral equations by the Leray-Schauder fixed-point theorem. 相似文献
6.
Patrice Assouad 《Israel Journal of Mathematics》1978,31(1):97-100
We give a purely metric proof of the following result: let (X,d) be a separable metric space; for all ?>0 there is an injectionf ofX inC 0 + such that: $$\forall x,y \in X,d(x, y) \leqq \parallel f(x) - f(y)\parallel _\infty \leqq (3 + \varepsilon )d(x, y).$$ It is a more precise version of a result of I. Aharoni. We extend it to metric space of cardinal α+ (for infinite α). 相似文献
7.
Hermano Frid Neto 《Bulletin of the Brazilian Mathematical Society》1988,19(1):39-59
In this paper we prove an uniqueness and stability theorem for the solutions of Cauchy problem for the systems $$\frac{\partial }{{\partial t}}u + \sum\limits_{i = 1}^n { \frac{\partial }{{\partial x_i }} } f^i (x,t,u) = g(x,t,u),$$ whereu is a vector function (u 1 (x, t),..., u r (x, t)),f i =(a 1 i (x, t, u),..., a r i (x, t, u)), i=1,...,n, g=(g 1 (x, t, u),...,g r (x, t, u),i G ? n and t≥0. We use the concept of entropy solution introduced by Kruskov and improved by Lax, Dafermos and others autors. We assume that the Jacobian matricesf u i are symmetric and the Hessian(a j i ) uu (i=1,...,n; j=1,...,r) are positive. We obtain uniqueness and stability inL loc 2 within the class of those entropy solutions which satisfy $$\frac{{u_j (---,x_i ,---,t)---u_j (---,y_i ,---,t)}}{{x_i - y_i }} \geqslant - K(t),$$ (i=1,...,n; j=1,...,r) for (?,x i ,?,t), (?,y i ,?,t) on a compact setD ? ? n x (0, ∞) and a functionK(t)∈L loc 1 ([0, ∞)) depending onD. Here we denote by (?,x i ,?,t) and (?,y i ,?,t) two points whose coordinates only differ in thei-th space variable. At the end we relax the hypotheses of symmetry and convexity on the system and give a theorem of uniqueness and stability for entropy solutions which are locally Lipschitz continuous on a strip ? n x [0,T]. 相似文献
8.
Let T be a torus (not assumed to be split) over a field F, and denote by nH et 2 (X,{ie375-1}) the subgroup of elements of the exponent dividing n in the cohomological Brauer group of a scheme X over the field F. We provide conditions on X and n for which the pull-back homomorphism nH et 2 (T,{ie375-2}) → n H et 2 (X × F T, {ie375-3}) is an isomorphism. We apply this to compute the Brauer group of some reductive groups and of non-singular affine quadrics. Apart from this, we investigate the p-torsion of the Azumaya algebra defined Brauer group of a regular affine scheme over a field F of characteristic p > 0. 相似文献
9.
Michael Iltis 《Journal of Theoretical Probability》1995,8(3):501-522
Given a sequence {X1}i=1,2,3,... of i.i.d. random variables taking values in ? d ,d≥2, letS n =Σ i=1 n X t=1. For Λ a Borel set in ? d having smooth boundary, witha=infx∈ΛI(x) the minimal value of the large deviation rate functionI(x) over Λ, we find, under suitable hypotheses, asymptotic results asn→∞, of the form $$P(S_n \in n\Gamma ) = n^\gamma e^{ - na} (d_0 + o(1))$$ where the constant γ depends sensitively on the geometry of Λ and the dimensiond, and takes values ?∞<γ≤(d?2/2). For fixeda=infx∈ΛI(x), we construct examples having any specific γ in this range. 相似文献
10.
We introduce the counting function π 2,8 * (x) of the primes with difference 8 between consecutive primes ( ****p n,pn+1 =p n + 8) can be approximated by logarithm integralLi 2,8 * . We calculate the values of π 2,8 * (x) and the sumC 2,8(x) of reciprocals of primes with difference 8 between consecutive primes (p n,pn+1 =p n +8)) wherex is counted up to 7 x 1010. From the results of these calculations, we obtain π 2,8 * (7 x 1010) = 133295081 andC 2,8(7 x 1010) = 0.3374 ±2.6 x 10-4. 相似文献
11.
Rongmu Yan 《Archiv der Mathematik》2006,86(5):458-463
We prove that the volume of PT z 1, 0 M, calculated with respect to a Kähler metric induced by a complex Finsler structure, is a constant. This contrasts sharply with the situation in real Finsler geometry, where the volume of unit tangent sphere at each point x in a real Finsler manifold is in general a function of x. Furthermore, we point out that different metrics have different constants in general. 相似文献
12.
We consider a Markov chain X = {Xi,i = 1,2,...} with the state space {0,1},and define W =∑i=1n XiXi+1,which is the number of 2-runs in X before time n + 1.In this paper,we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW.The error estimate obtained herein improves the corresponding result in previous literatures. 相似文献
13.
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
14.
LetL be the space of rapidly decreasing smooth functions on ? andL * its dual space. Let (L 2)+ and (L 2)? be the spaces of test Brownian functionals and generalized Brownian functionals, respectively, on the white noise spaceL * with standard Gaussian measure. The Donsker delta functionδ(B(t)?x) is in (L 2)? and admits the series representation $$\delta (B(t) - x) = (2\pi t)^{ - 1/2} \exp ( - x^2 /2t)\sum\limits_{n = 0}^\infty {(n!2^n )^{ - 1} H_n (x/\sqrt {2t} )} \times H_n (B(t)/\sqrt {2t} )$$ , whereH n is the Hermite polynomial of degreen. It is shown that forφ in (L 2)+,g t,φ(x)≡〈δ(B(t)?x), φ〉 is inL and the linear map takingφ intog t,φ is continuous from (L 2)+ intoL. This implies that forf inL * is a generalized Brownian functional and admits the series representation $$f(B(t)) = (2\pi t)^{ - 1/2} \sum\limits_{n = 0}^\infty {(n!2^n )^{ - 1} \langle f,\xi _{n, t} \rangle } H_n (B(t)/\sqrt {2t} )$$ , whereξ n,t is the Hermite function of degreen with parametert. This series representation is used to prove the Ito lemma forf inL *, $$f(B(t)) = f(B(u)) + \int_u^t {\partial _s^ * } f'(B(s)) ds + (1/2)\int_u^t {f''} (B(s)) ds$$ , where? s * is the adjoint of \(\dot B(s)\) -differentiation operator? s . 相似文献
15.
L. P. Vlasov 《Mathematical Notes》1995,58(2):785-793
Generalizing the result of A. L. Garkavi (the caseX = ?) and his own previous result concerningX = ?), the author characterizes the existence subspaces of finite codimension in the spaceC(Q, X) of continuous functions on a bicompact spaceQ with values in a Banach spaceX, under some assumptions concerningX. Under the same assumptions, it is proved that in the space of uniform limits of simple functions, each subspace of the form $$\left\{ {g \in B:\smallint _Q \left\langle {g(t),d\mu _i } \right\rangle = 0,i = 1,...,n} \right\},$$ whereμ i ∈ C(Q, X)* are vector measures of regular bounded variation, is an existence subspace (the integral is understood in the sense of Gavurin). 相似文献
16.
Wei-Bin Zeng 《Journal of Theoretical Probability》1995,8(1):1-15
LetX 1,X 2, ...,X n be independent and identically distributed random vectors inR d , and letY=(Y 1,Y 2, ...,Y n )′ be a random coefficient vector inR n , independent ofX j /′ . We characterize the multivariate stable distributions by considering the independence of the random linear statistic $$U = Y_1 X_1 + Y_2 X_2 + \cdot \cdot \cdot + Y_n X_n $$ and the random coefficient vectorY. 相似文献
17.
Suppose that D ? ?n is a domain with smooth boundary ?D, E ? ?D is a boundary subset of positive Lebesgue measure mes(E) > 0, and F ? G is a nonpluripolar compact set in a strongly pseudoconvex domain G ? ?m. We prove that, under some additional conditions, each function separately analytic on the set X = (D×F)∪(E× G) can be holomorphically continued into the domain where ω* is the P-measure and ω in * is the inner P-measure. 相似文献
18.
D. V. Gorbachev 《Mathematical Notes》1997,62(2):160-171
On the multidimensional classW 0 r H ω (n) of continuous periodic functionsF with therth derivativeD r F from $$H_\omega ^{(n)} = \left\{ {f \in C| |f(x) - f(y)| \leqslant \sum\limits_{i = 1}^n {\omega _i } (|x_i - y_i |)\forall x, y \in \mathbb{R}^n } \right\}$$ (where the ω i (x i ) are the convex moduli of continuity) and zero mean with respect to each variable, we obtain the exact value of $$M_r (\omega ) = \mathop {\sup }\limits_{F \in W_0^r H_\omega ^{(n)} } \left\| F \right\|c$$ . 相似文献
19.
Let (X 1,Y 1),...(X n ,Y n ) be a random sample from the (k+1)-dimensional multivariate density functionf *(x,y). Estimates of thek-dimensional density functionf(x)=∫f *(x,y)dy of the form $$\hat f_n (x) = \frac{1}{{nb_1 (n) \cdots b_k (n)}}\sum\limits_{i = 1}^n W \left( {\frac{{x_1 - X_{i1} }}{{b_1 (n)}}, \cdots ,\frac{{x_k - X_{ik} }}{{b_k (n)}}} \right)$$ are considered whereW(x) is a bounded, nonnegative weight function andb 1 (n),...,b k (n) and bandwidth sequences depending on the sample size and tending to 0 asn→∞. For the regression function $$m(x) = E(Y|X = x) = \frac{{h(x)}}{{f(x)}}$$ whereh(x)=∫y(f) * (x, y)dy , estimates of the form $$\hat h_n (x) = \frac{1}{{nb_1 (n) \cdots b_k (n)}}\sum\limits_{i = 1}^n {Y_i W} \left( {\frac{{x_1 - X_{i1} }}{{b_1 (n)}}, \cdots ,\frac{{x_k - X_{ik} }}{{b_k (n)}}} \right)$$ are considered. In particular, unform consistency of the estimates is obtained by showing that \(||\hat f_n (x) - f(x)||_\infty \) and \(||\hat m_n (x) - m(x)||_\infty \) converge completely to zero for a large class of “good” weight functions and under mild conditions on the bandwidth sequencesb k (n)'s. 相似文献