Theory of Valuations on Manifolds: A Survey

This is a non-technical survey of a recent theory of valuations on manifolds constructed in [A10], [A11], [AF] and [A12], and actually a guide to this series of articles. We also review some recent related results obtained by a number of people. Received: February 2006, Revision: June 2006, Accepted: June 2006     

Inequalities for the moments of v-infinitely divisible laws and the characterization of probability distributions

Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 93–103.     

On the location parameter confidence intervals based on a random size sample from a partially known population

The problem of constructing confidence intervals of a fixed length for the location parameter based on a random size sample is considered. It is proposed to use the confidence interval $$\theta _p^* - u\sqrt p /\sigma< \theta< \theta _p^* + u\sqrt p /\sigma $$ , whereθ _p ^* is an adaptive estimator,σ ² is the Fisher information, and p^?1 is the mean of the sample size. Nonparametric bounds are given for the limit as p → 0 confidence probability. Bibliography: 5 titles.     

Inhibiting activity of complexes of urethanes with variable valency metals

Conclusions The powerful inhibiting action of complexes of variable valency metals with urethanes in the oxidation of ethylbenzene has been revealed.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, pp. 479–482, February, 1970.     

Towards a new edition of the “Guide to the expression of uncertainty in measurement”

The “Guide to the expression of uncertainty in measurement” (GUM) is an extremely important document. It unifies methods for calculating measurement uncertainty and enables the consistent interpretation and comparison of measurement results, regardless of who obtained these measurements and where they were obtained. Since the document was published in 1995, it has been realised that its recommendations do not properly address an important class of measurements, namely, non-linear indirect measurements. This drawback prompted the initiation of the revision of the GUM in the Working Group 1 of the Joint Committee for Guides in Metrology, which commenced in October 2006. The upcoming revision of the GUM provides the metrological community with an opportunity to improve this important document, in particular, to reflect developments in metrology that have occurred since the first GUM publication in 1995. Thus, a discussion of the directions for this revision is important and timely. By identifying several shortcomings of the GUM and proposing directions for its improvement, we hope this article will contribute to this discussion. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Synthesis, binding affinity, and relaxivity of target-specific MRI contrast agents

Although magnetic resonance imaging (MRI) is one of the most important imaging modalities of the central nervous system (CNS), one of the main drawbacks of MRI is its limited specificity. This can potentially be partially alleviated by target-specific contrast agents. In the present paper we describe a simple high yield synthesis of two such gadolinium-based spiperone targeted MRI contrast agents, 1a and 1b. The R₁ relaxivities of 1a and 1b were evaluated and found to be 5.94 and 8.31 mM⁻¹ s⁻¹, respectively at 9.4T, while their R₂ relaxivities at the same magnetic field were found to be 18.05 and 22.60 mM⁻¹ s⁻¹, respectively. In addition and very importantly compound 1a, which is a gadolinium-based, spiperone-targeted MRI contrast agent, was found to preserve some of the spiperone affinity toward the dopamine D2 receptor. Compounds 1a and 1b thus represent potential agents for in vitro dopamine receptor imaging using MRI in experimental models. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Asymptotic ɛ -admissibility of the sample variance as an estimator of the population variance

A quantitative estimate is given of the robustness of the characterization of the distribution with a density by the property of asymptotic -admissibility of the sample variance as an estimator of the population variance with a quadratic loss function.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 61, pp. 75–83, 1976.     

Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole

We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of \mathbb C{\mathbb C} . As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.     

Nonnegative Fourier–Jacobi Coefficients and Some Classes of Functions

Fourier–Jacobi series with nonnegative Fourier–Jacobi coefficients are considered. Under special restrictions on the Jacobi weight function, we establish in terms of Fourier–Jacobi coefficients a necessary and sufficient condition in order that the sum of the Fourier–Jacobi series should possess certain structural properties.