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1.
Much of General Topology addresses this issue: Given a function fC(Y,Z) with YY′ and ZZ′, find , or at least , such that ; sometimes Z=Z′ is demanded. In this spirit the authors prove several quite general theorems in the context Y′=(XI)κ=∏iIXi in the κ-box topology (that is, with basic open sets of the form ∏iIUi with Ui open in Xi and with Ui≠Xi for <κ-many iI). A representative sample result, extending to the κ-box topology some results of Comfort and Negrepontis, of Noble and Ulmer, and of Hušek, is this. Theorem Let ωκα (that means: κ<α, and [β<α and λ<κ]βλ<α) with α regular, be a set of non-empty spaces with each d(Xi)<α, π[Y]=XJ for each non-empty JI such that |J|<α, and the diagonal in Z be the intersection of <α-many regular-closed subsets of Z×Z. Then (a) Y is pseudo-(α,α)-compact, (b) for every fC(Y,Z) there is J[I]<α such that f(x)=f(y) whenever xJ=yJ, and (c) every such f extends to . 相似文献
2.
We investigate the diagonal sequence property in Banach spaces with weaker topologies. In particular, we present examples of Banach spaces with weaker locally convex topologies which have the diagonal sequence property but are not Fréchet–Urysohn. The examples answer negatively a question of Averbukh and Smolyanov. We give also a very simple proof of the fact that each Banach space contains a subset A whose weak closure includes 0, but 0 is not contained in the weak closure of any bounded subset of A. 相似文献
3.
The estimation of the location parameter of an ℓ1-symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the ℓ1-sphere, we investigate a general class of estimators of the form δ=X+g. Under the usual quadratic loss, domination of δ over X is obtained through the partial differential inequality 4 div g+2X
∂2g+ g20 and a new superharmonicity-type-like notion adapted to the ℓ1-context. Specifically the condition of ℓ1-superharmonicity is that 2Δf+X
3f0 and div 3f0 as compared to the usual (ℓ2) condition Δf0. 相似文献
4.
J.C. FERRANDO S. MOLL 《数学学报(英文版)》2007,23(9):1593-1600
In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc (X) has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc (X) contains a dense (LM) subspace and if and only if X is a-compact. 相似文献
5.
Vincent Vigon 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2003,39(6):993-1011
Soit (Y,Z) un subordinateur bivarié. Nous donnons une condition suffisante pour que Yt/Zt converge vers zéro quand t tend vers 0 ou +∞. Ceci généralise partiellement des résultats de Bertoin et de Kesten–Erickson.Soit X un processus de Lévy et St=sup{Xs: st}. Soit f une fonction sous-additive. En appliquant le résultat précédent au subordinateur bivarié d'échelle, nous donnons des conditions nécéssaires et suffisantes pour que
et
égalent 0 ou +∞.Let (Y,Z) be a bivariate subordinator. Generalizing theorems of Bertoin and Kesten–Erickson, we give a sufficient condition for Yt/Zt to converge to 0 when t tends either to 0 or +∞.Let X be a Lévy process. Denote by St=sup{Xs: st} and let f be any sub-additive function. Applying our first result to the bivariate ladder process, we give necessary and sufficient conditions for
and
to be either 0 or +∞. 相似文献
6.
Lα (0 α 1) is a class of infinitely divisible distributions defined by restricting the measure in the Levy-Khinchin formula to a special form. When α = 1, Lα is just the classical class L. Several properties for Lα classes, which are similar to the most important properties for the class L, are established. Also, a conjecture of Wolfe about unimodality of some Lα distributions is disproved by giving a counterexample. 相似文献
7.
In this paper, by means of a series of counterexamples, we study in a systematic way the relationships among (pseudo, quasi) α-preinvexity, (strict, strong, pseudo, quasi) α-invexity and (strict, strong, pseudo, quasi) αη-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of Noor and Noor [M.A. Noor, K.I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Appl. 316 (2006) 697–706]. 相似文献
8.
For a compact Lie group G we prove that every free (resp., semifree) G-space admits a based-free (resp., semifree) G-compactification. Examples of finite- and infinite-dimensional G-spaces are presented that do not admit a free or based-free G-compactification. We give several characterizations of the maximal G-compactification βGX that are further applied to prove the formula (βGX)/H=βG/H(X/H) for arbitrary closed normal subgroup H⊂G. Mathematics Subject Classification (2000) 54H15, 54D35 相似文献
9.
In this paper we introduce partial diamond-α dynamic derivatives for two-variable functions and the double integral calculus via the diamond-α dynamic integral on time scales. Also we establish a two-dimensional weighted Hardy–Knopp type integral inequality on time scales. 相似文献
10.
11.
Shashikala Sukhatme 《Journal of multivariate analysis》1983,13(4):539-549
Let Y1,…, Yn be independent identically distributed random variables with distribution function F(x, θ), θ = (θ′1, θ′2), where θi (i = 1, 2) is a vector of pi components, p = p1 + p2 and for θI, an open interval in
p, F(x, θ) is continuous. In the present paper the author shows that the asymptotic distribution of modified Cramér-Smirnov statistic under Hn: θ1 = θ10 + n−1/2γ, θ2 unspecified, where γ is a given vector independent of n, is the distribution of a sum of weighted noncentral χ12 variables whose weights are eigenvalues of a covariance function of a Gaussian process and noncentrality parameters are Fourier coefficients of the mean function of the Gaussian process. Further, the author exploits the special form of the covariance function by using perturbation theory to obtain the noncentrality parameters and the weights. The technique is applicable to other goodness-of-fit statistics such as U2 [G. S. Watson, Biometrika 48 (1961), 109–114]. 相似文献
12.
The larger project broached here is to look at the generally sentence “if X is well-ordered then f(X) is well-ordered”, where f is a standard proof-theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded ω-models for a particular theory Tf whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function f. To illustrate this theme, we prove in this paper that the statement “if X is well-ordered then εX is well-ordered” is equivalent to . This was first proved by Marcone and Montalban [Alberto Marcone, Antonio Montalbán, The epsilon function for computability theorists, draft, 2007] using recursion-theoretic and combinatorial methods. The proof given here is principally proof-theoretic, the main techniques being Schütte’s method of proof search (deduction chains) [Kurt Schütte, Proof Theory, Springer-Verlag, Berlin, Heidelberg, 1977] and cut elimination for a (small) fragment of . 相似文献
13.
Let {Zi,i≥1} be a linear process defined by with {dj,j≥0} being a regular varying sequence of real numbers and {ξt,−∞<t<∞} being a sequence of -mixing random variables. The present paper studies the asymptotic behavior of the quadratic form under some mild assumptions on dj and ξt. Meanwhile, the similar results of α-mixing random variables are presented. 相似文献
14.
Tilmann Gneiting 《Journal of multivariate analysis》1998,64(2):131-147
Ann-dimensional random vector is said to have anα-symmetric distribution,α>0, if its characteristic function is of the form((|u1|α+…+|un|α)1/α). We study the classesΦn(α) of all admissible functions: [0, ∞)→
. It is known that members ofΦn(2) andΦn(1) are scale mixtures of certain primitivesΩnandωn, respectively, and we show thatωnis obtained fromΩ2n−1byn−1 successive integrations. Consequently, curious relations between 1- and 2- (or spherically) symmetric distributions arise. An analogue of Askey's criterion gives a partial solution to a question of D. St. P. Richards: If(0)=1,is continuous, limt→∞ (t)=0, and(2n−2)(t) is convex, thenΦn(1). The paper closes with various criteria for the unimodality of anα-symmetric distribution. 相似文献
15.
Bernhard Beckermann Ana C. Matos Franck Wielonsky 《Journal of Computational and Applied Mathematics》2008,219(2):329
Recently, Brezinski has proposed to use Wynn's ε-algorithm in order to reduce the Gibbs phenomenon for partial Fourier sums of smooth functions with jumps, by displaying very convincing numerical experiments. In the present paper we derive analytic estimates for the error corresponding to a particular class of hypergeometric functions, and obtain the rate of column convergence for such functions, possibly perturbed by another sufficiently differentiable function. We also analyze the connection to Padé–Fourier and Padé–Chebyshev approximants, including those recently studied by Kaber and Maday. 相似文献
16.
Ken-ichi Yoshihara 《Journal of multivariate analysis》1978,8(4):584-588
In 1974, Sen proved weak convergence of the empirical processes (in the J1-topology on Dp[0, 1]) for a stationary φ-mixing sequence of stochastic p( 1)-vectors. In this note, we show that Sen's theorem on weak convergence of the multidimensional empirical process for a stationary φ-mixing sequence of stochastic vectors remains true under a less restrictive condition on the mixing constants {φn}, i.e., φn = O(n−1−δ) for some δ > 0. 相似文献
17.
18.
Wolfgang zu Castell 《Journal of multivariate analysis》2000,75(2):71
T. Gneiting (1998, J. Multivariate Analysis64, 131–147) proved a relation between the primitives of the classes Φd(2) and Φd(1) of 2- and 1-symmetric characteristic functions on
d, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the calculus of generalized hypergeometric functions. 相似文献
19.
The ω-problem on a topological space X consists in finding out whether there exists a function whose oscillation is equal to a given upper semi-continuous (USC) function f:X→[0,∞] vanishing at isolated points of X. If such F exists, we call it an ω-primitive for f. Unlike the case of metrizable spaces, an ω-primitive need not exist if X is not metrizable. We study the ω-problem for f taking the value ∞ in the case of ordinal space, products of regular “constancy” spaces and the wedge sums of such spaces. Some open problems are formulated. 相似文献
20.
Farhat Usman Suhel Ahmad Khan 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5354-5362
In this paper, we introduce relaxed η-α-P-monotone mapping, and by utilizing KKM technique and Nadler’s Lemma we establish some existence results for the generalized mixed vector variational-like inequality problem. Further, we give the concepts of η-complete semicontinuity and η-strong semicontinuity and prove the solvability for generalized mixed vector variational-like inequality problem without monotonicity assumption by applying the Brouwer’s fixed point theorem. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature. 相似文献