Correction to: On the strong universal consistency of local averaging regression estimates

A general result concerning the strong universal consistency of local averaging regression estimates is presented, which is used to extend previously known results on the strong universal consistency of kernel and partitioning regression estimates. The proof is based on ideas from Etemadi’s proof of the strong law of large numbers, which shows that these ideas are also useful in the context of strong laws of large numbers for conditional expectations in \(L_2\).

     

The Table of Standard Atomic Weights—An exercise in consensus

The present Table of Standard Atomic Weights (TSAW) of the elements is perhaps one of the most familiar data sets in science. Unlike most parameters in physical science whose values and uncertainties are evaluated using the “Guide to the Expression of Uncertainty in Measurement” (GUM), the majority of standard atomic-weight values and their uncertainties are consensus values, not GUM-evaluated values. The Commission on Isotopic Abundances and Atomic Weights of the International Union of Pure and Applied Chemistry (IUPAC) regularly evaluates the literature for new isotopic-abundance measurements that can lead to revised standard atomic-weight values, A_r°(E) for element E. The Commission strives to provide utmost clarity in products it disseminates, namely the TSAW and the Table of Isotopic Compositions of the Elements (TICE). In 2016, the Commission recognized that a guideline recommending the expression of uncertainty listed in parentheses following the standard atomic-weight value, for example, A_r°(Se) = 78.971(8), did not agree with the GUM, which suggests that this parenthetic notation be reserved to express standard uncertainty, not the expanded uncertainty used in the TSAW and TICE. In 2017, to eliminate this noncompliance with the GUM, a new format was adopted in which the uncertainty value is specified by the “±” symbol, for example, A_r°(Se) = 78.971 ± 0.008. To clarify the definition of uncertainty, a new footnote has been added to the TSAW. This footnote emphasizes that an atomic-weight uncertainty is a consensus (decisional) uncertainty. Not only has the Commission shielded users of the TSAW and TICE from unreliable measurements that appear in the literature as a result of unduly small uncertainties, but the aim of IUPAC has been fulfilled by which any scientist, taking any natural sample from commerce or research, can expect the sample atomic weight to lie within A_r°(E) ± its uncertainty almost all of the time.     

Nonparametric quantile estimation using importance sampling

Nonparametric estimation of a quantile of a random variable m(X) is considered, where \(m: \mathbb {R}^d\rightarrow \mathbb {R}\) is a function which is costly to compute and X is a \(\mathbb {R}^d\)-valued random variable with a given density. An importance sampling quantile estimate of m(X), which is based on a suitable estimate \(m_n\) of m, is defined, and it is shown that this estimate achieves a rate of convergence of order \(\log ^{1.5}(n)/n\). The finite sample size behavior of the estimate is illustrated by simulated data.     

Comparison of some properties of 2,3- and 3,5-dimethoxybenzoates of light lanthanides

The physico-chemical properties and thermal stability in air of the light lanthanide 2,3- and 3,5-dimethoxybenzoates were studied and compared in order to observe if there is influence of the position of -OCH₃ substituents in benzene ring on their properties, mainly on their thermal stability. The complexes of both of two series are crystalline, hydrated or anhydrous salts with colours typical of Ln³⁺ ions. The carboxylate group shows the different coordination modes. It may coordinate as a bidentate, chelating or tridentate chelating-bridging ligand. The thermal stabilities of 2,3- and 3,5-dimethoxybenzoates of light lanthanides were studied in the temperature range 293-1173 K. The solubilities of 2,3- and 3,5-dimethoxybenzoates of these elements in water at room temperature are in the orders of 10^-3-10^-2 mol dm^-3 and 10^-4 mol dm^-3, respectively. The various positions of -OCH₃ groups in benzene ring influences some physico-chemical properties of these compounds. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal Stability of 4-chloro-2-nitro- and 4-chloro-3-nitrobenzoates of Rare Earth Elements: Influence of substituent positions

The physico-chemical properties and thermal stability in air of rare earth element 4-chloro-2-nitro- and 4-chloro-3-nitrobenzoates of the general formulae Ln(C₇H₃NO₄Cl)₃2H₂O were compared and the influence of the position of the Cl and NO₂ substituents on their thermal stabilities was investigated. The complexes of both series are crystalline, hydrated salts with colours typical of Ln³⁺. The carboxylate group in these complexes is a bidentate, chelating ligand. The NO₂ group in the chloronitro complexes does not undergo isomerization. The thermal stabilities of the 4-chloro-3-nitrobenzoates of rare earth elements were studied in the temperature range 293–1173 K, but those of 4-chloro-2-nitrobenzoates of those elements were studied only at 293–523 K because they decompose explosively above 523 K. The positions of the Cl and NO₂ substituents on the benzene ring influence the thermal properties of the complexes and their decomposition mechanisms. The different thermal stabilities of the complexes are connected with various inductive and mesomeric effects of the Cl and NO₂ substituents on the electron density in benzene ring.This revised version was published online in November 2005 with corrections to the Cover Date.     

ESI Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (ESI-FT-ICR-MS): A Rapid High-Resolution Analytical Method for Combinatorial Compound Libraries

The direct determination of the elemental compositions of the components of compound collections from combinatorial chemistry is achieved by ESI-FT-ICR mass spectrometry. Coupling with HPLC opens up a new dimension in high-resolution, informative analysis. The improved resolution of ESI-FT-ICR mass spectrometry in comparison to quadrupole mass spectrometry in the measurement of a compound obtained by solid-phase synthesis is illustrated.     

Strong Laws of Large Numbers by Elementary Tauberian Arguments

For Kolmogorovs strong law of large numbers an alternative short proof is given which weakens Etemadis condition of pairwise independence. The argument uses the known – and elementary – equivalence of (Cesàro) C₁- and C₂-summability for one-sided bounded sequences. Also other strong laws of large numbers are established, in part via Borel summability.