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91.
92.
Simeon M. Berman 《纯数学与应用数学通讯》2007,60(8):1238-1259
Let f(x), x ∈ ?M, M ≥ 1, be a density function on ?M, and X1, …., Xn a sample of independent random vectors with this common density. For a rectangle B in ?M, suppose that the X's are censored outside B, that is, the value Xk is observed only if Xk ∈ B. The restriction of f(x) to x ∈ B is clearly estimable by established methods on the basis of the censored observations. The purpose of this paper is to show how to extrapolate a particular estimator, based on the censored sample, from the rectangle B to a specified rectangle C containing B. The results are stated explicitly for M = 1, 2, and are directly extendible to M ≥ 3. For M = 2, the extrapolation from the rectangle B to the rectangle C is extended to the case where B and C are triangles. This is done by means of an elementary mapping of the positive quarter‐plane onto the strip {(u, v): 0 ≤ u ≤ 1, v > 0}. This particular extrapolation is applied to the estimation of the survival distribution based on censored observations in clinical trials. It represents a generalization of a method proposed in 2001 by the author [2]. The extrapolator has the following form: For m ≥ 1 and n ≥ 1, let Km, n(x) be the classical kernel estimator of f(x), x ∈ B, based on the orthonormal Legendre polynomial kernel of degree m and a sample of n observed vectors censored outside B. The main result, stated in the cases M = 1, 2, is an explicit bound for E|Km, n(x) ? f(x)| for x ∈ C, which represents the expected absolute error of extrapolation to C. It is shown that the extrapolator is a consistent estimator of f(x), x ∈ C, if f is sufficiently smooth and if m and n both tend to ∞ in a way that n increases sufficiently rapidly relative to m. © 2006 Wiley Periodicals, Inc. 相似文献
93.
94.
The calibration of Karl Fischer instruments and reagents and the compensation for instrumental bias are essential to the accurate measurement of trace levels of water in organic and inorganic chemicals. A stable, non-hygroscopic standard, Water Saturated Octanol, which is compatible with the Karl Fischer reagents, has been prepared. This material, Standard Reference Material (SRM) 2890, is homogeneous and is certified to contain 39.24 ± 0.85 mg water/mL (expanded uncertainty) of solution (47.3 ± 1.0 mg water/g solution, expanded uncertainty) at 21.5?°C. The solubility of water in 1-octanol has been shown to be nearly constant between 10?°C and 30?°C (i.e., within 1% of the value at 21.5?°C). The results of an interlaboratory comparison exercise illustrate the utility of SRM 2890 in assessing the accuracy and bias of Karl Fischer instruments and measurements. 相似文献
95.
We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finii e semigroups are irreducible for join, for semidirect product and for Mal’cev product. In particular, these pseudovarieties do not admit maximal proper subpseudovarieties. More generally, analogous results are proved for the pseudovariety of all finite semigroups all of whose subgroups are in a fixed pseudovariety of groups H, provided th.it H is closed under semidirect product. 相似文献
96.
Let f be a function from a finite field with a prime number p of elements, to . In this article we consider those functions f(X) for which there is a positive integer with the property that f(X)i, when considered as an element of , has degree at most p−2−n+i, for all i=1,…,n. We prove that every line is incident with at most t−1 points of the graph of f, or at least n+4−t points, where t is a positive integer satisfying n>(p−1)/t+t−3 if n is even and n>(p−3)/t+t−2 if n is odd. With the additional hypothesis that there are t−1 lines that are incident with at least t points of the graph of f, we prove that the graph of f is contained in these t−1 lines. We conjecture that the graph of f is contained in an algebraic curve of degree t−1 and prove the conjecture for t=2 and t=3. These results apply to functions that determine less than directions. In particular, the proof of the conjecture for t=2 and t=3 gives new proofs of the result of Lovász and Schrijver [L. Lovász, A. Schrijver, Remarks on a theorem of Rédei, Studia Sci. Math. Hungar. 16 (1981) 449–454] and the result in [A. Gács, On a generalization of Rédei’s theorem, Combinatorica 23 (2003) 585–598] respectively, which classify all functions which determine at most 2(p−1)/3 directions. 相似文献
97.
Simeon Zamkovoy 《Annals of Global Analysis and Geometry》2009,36(1):37-60
The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold
to be paraSasakian. A -homothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is proved
that their scalar curvature is a constant, and it is shown that in the paraSasakian case these spaces can be obtained from
Einstein paraSasakian manifolds with -homothetic transformations. It is shown that an almost paracontact structure admits a connection with totally skew-symmetric
torsion if and only if the Nijenhuis tensor of the paracontact structure is skew-symmetric and the defining vector field is
Killing.
相似文献
98.
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is
shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric
of neutral signature iff the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved
through employing a certain symmetric (0,2) tensor. The well known result of Cartan–Chern–Moser giving necessary and sufficient
condition a CR-structure to be CR equivalent to a hyperquadric in
\mathbbCn+1{\mathbb{C}^{n+1}} is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic
Yamabe equation on the hyperbolic Heisenberg group is shown. 相似文献
99.
100.
Grigor'eva N. V. Margolis N. V. Tselinskii I. V. 《Journal of Structural Chemistry》1970,11(3):525-527
Journal of Structural Chemistry - 相似文献