Making Use of Incomplete Observations for Regression in Bivariate Normal Model

Two estimates of the regression coefficient in bivariate normal distribution are considered: the usual one based on a sample and a new one making use of additional observations of one of the variables. They are compared with respect to variance. The same is done for two regression lines. The conclusion is that the additional observations are worth using only when the sample is very small.     

How to Exhibit Toroidal Maps in Space

Steinitz's theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of the embedded graph. Its faces are bounded by convex polygons whose points are coplanar. A map on the torus does not necessarily have such a geometric realization. In this paper we relax the condition that faces are the convex hull of coplanar points. We require instead that the convex hull of the points on a face can be projected onto a plane so that the boundary of the convex hull of the projected points is the image of the boundary of the face. We also require that the interiors of the convex hulls of different faces do not intersect. Call this an exhibition of the map. A map is polyhedral if the intersection of any two closed faces is simply connected. Our main result is that every polyhedral toroidal map can be exhibited. As a corollary, every toroidal triangulation has a geometric realization.     

Synthesis and structure of Ca(18)Li(5)In(25.07): a novel intergrowth of Li-centered in(12) icosahedral clusters and electron-precise Zintl layers

A new ternary polar intermetallic, Ca(18)Li(5)In(25.07), was obtained from high-temperature reactions of the elements in welded Nb tubes. Its crystal structure, established by single-crystal X-ray diffraction, was found to crystallize in the orthorhombic space group Cmmm (No. 65). Unit cell parameters are a = 9.9151(6) A, b = 26.432(2) A, and c = 10.2116(6) A; Z = 2. The structure of Ca(18)Li(5)In(25.07) features two distinct types of indium anionic layers. An "electron-deficient" layer is made up of Li-centered In(12) icosahedra that are interconnected by bridging planar In(4) units and In atoms. A second In(3)(5-) layer is an electron-precise Zintl layer formed by fused four-, five-, and six-membered rings of three- and four-bonded indium atoms. The two distinct layers are alternately stacked and linked into a complex three-dimensional network. Vacancies are observed to occur only at the In(12) icosahedral and the bridging indium units within the "electron-deficient" layers. Magnetic property measurements indicate that Ca(18)Li(5)In(25.07) exhibits temperature-independent paramagnetism consistent with metallic behavior. Band structure calculations were performed to elucidate the role of defects and vacancies in the electronic structure of the electron-deficient "metallic" Zintl phase.     

The effect of electron detachment on the structure and properties of the chlorine-acetonitrile anionic complex

The results of the theoretical study of ground state potential energy surfaces for the chlorine-acetonitrile anion and its photodetachment product are presented. The shallow potential surfaces allow for the nondefinitive position of the chlorine within the complex. The dissociation energy of the neutral complex, estimated through the thermodynamic cycle, indicates significant structural changes due to the photodetachment process. The excess negative charge is localized mostly on the chlorine atom, and the electron detachment proceeds as an electron is removed from chlorine. The process leads to drastic changes in the electrostatic interactions within the complex. The first electronic excited state corresponds to the excess electron transfer from chlorine to acetonitrile fragment. This state is a precursor of the observed charge-transfer-to-solvent state.     

Accurate and efficient method for predicting thermochemistry of polycyclic aromatic hydrocarbons - bond-centered group additivity

A self-consistent estimation method for the thermochemical properties of polycyclic aromatic hydrocarbons (PAH) is presented. This method is based on enthalpies of formation (DeltaHf(degrees), entropies (S(degrees)298, and heat capacities (C(degrees)p obtained from B3LYP/6-31G(d) calculations of the total energies and frequencies for 139 PAHs, including C(60) and C(70) fullerenes. The enthalpies of formation were calculated using an optimized set of homodesmic reactions given the available experimental DeltaHf(degrees) of PAHs. The theoretical entropies were compared with the existing experimental entropies, and some inconsistencies in the experimental data were identified. The estimation method presented here is a systematic extension of the widely employed atom-centered group additivity method originally proposed by Benson. This new method is based on bond-centered groups that define bonds linking two atom-centered groups and specify the size of the rings to which they belong. In addition, a term to describe the resonance energy is included. The thermochemical properties of PAHs up to C(70) fullerene are estimated with a mean average deviation of 2.8 kcal mol(-1) in DeltaHf(degrees), 0.7 cal K(-1) mol(-1) in S(degrees)298, and about 0.5 cal K(-1) mol(-1) in the C(degrees)p. This bond-centered group additivity method for the thermochemical properties of PAHs significantly expands both the range of systems that can be estimated and the accuracy of the estimations. The results of this work also allow us to assess the quality of available experimental data. For example, there are strong indications that the literature DeltaHf(degrees)of benzo[k]fluoranthene is about 10 kcal mol(-1) too low.     

SrInGe and EuInGe: new Zintl phases with an unusual anionic network derived from the ThSi(2) structure

Two new isostructural Zintl phases, EuInGe and SrInGe, are obtained from high-temperature reactions of the pure elements in welded Ta tubes. Both ternary phases crystallize in a new structure type in space group Pnma (No. 62), with a = 4.921(1) A, b = 3.9865(9) A, and c = 16.004(3) A for EuInGe; and a = 5.021(1) A, b = 4.0455(9) A, and c = 16.188(4) A for SrInGe. The crystal structures established by single-crystal X-ray diffraction feature zigzag chains of 3-bonded Ge atoms and puckered layers of 4-bonded In atoms. The two structural units are linked into an anionic network with channels composed of 5-membered and 7-membered rings. The channels are filled by the respective divalent cations. The chemical bonding of the anionic [InGe](2)(-) network, derived from a one-electron oxidative distortion of the alpha-ThSi(2) structure, is explained using extended-Hückel band structure calculations. Magnetic measurements indicate that EuInGe exhibits Curie-Weiss paramagnetic behavior above 35 K and antiferromagnetic behavior below 35 K. The calculated effective moment, mu(eff) = 8.11 mu(B), of EuInGe and the diamagnetic behavior of SrInGe are consistent with the oxidation states of Eu(II) and Sr(II), respectively.     

Determination of the total nitrogen content of hard, semihard, and processed cheese by the Kjeldahl method: collaborative study

The objective of this collaborative study was to determine interlaboratory performance statistics for a modified and optimized version of AOAC Method 920.123 for the determination of the total nitrogen content of hard, semihard, and processed cheese by Kjeldahl analysis. Details included addressing the issues of material homogeneity, test portion size (1 g), quantitative transfer (weighing on to filter paper), ensuring system suitability (nitrogen recoveries), and using AOAC Method 991.20 as the basis for nitrogen analysis. Fifteen laboratories tested 18 pairs of blind duplicate cheese materials with a crude protein content between 18 and 36%. Materials represented hard, semihard, and processed commercial cheeses with a wide range of composition. Statistical performance parameters expressed as crude protein (nitrogen x 6.38), g/100 g, with invalid and outlier data removed were mean = 26.461, repeatability standard deviation (Sr) 0.111, reproducibility standard deviation (S(R)) = 0.153, repeatability relative standard deviation (RSDr) = 0.42%, reproducibility relative standard deviation (RSDR) = 0.58%, repeatability (r) = 0.312, and reproducibility (R) = 0.428. The interlaboratory study results were acceptable and comparable to those for the milk Kjeldahl nitrogen method on a relative nitrogen basis. The Study Directors recommend that this modified method for the determination of total nitrogen in hard, semihard, and processed cheese by Kjeldahl analysis be adopted First Action as an improved method to replace Method 920.123.     

Optimized conditions for hydrocarbon group type analysis of base oils by thin-layer chromatography-flame ionisation detection

The results of research on the optimization of the thin-layer chromatography-flame ionisation detection for the determination of group composition of natural base oils, including separation of the aromatics into subgroups, are presented. Neutral base oils obtained in several steps of refining from vacuum distillation petroleum fractions are the most difficult to analyze by hydrocarbon group type analysis (HGTA) because of the high content of aliphatic fragments in their molecules. Factors affecting the accuracy and precision of the results were identified. The paper presents the analytical procedure, including two different calibration methods, as well as the results of studies on the reproducibility of HGTA of typical base oils of different viscosity classes under the optimized conditions. The same conditions were found suitable for HGTA of other high-boiling petroleum fractions by TLC with flame ionisation detection. The paper also introduces a new procedure for reproducible determination of polar fractions in base oils utilizing solid-phase extraction columns, and presents a corrected procedure for the determination of saturated compounds and aromatics (mono-, bi- and polycyclic) in base oils by column liquid chromatography.     

The analysis of the zero-order and the second derivative spectra of retinol acetate, tocopherol acetate and coenzyme Q10 and estimation of their analytical usefulness for their simultaneous determination in synthetic mixtures and pharmaceuticals

The aim of the present work was to develop a simple and rapid method of retinol acetate, tocopherol acetate and coenzyme Q(10) determination in pharmaceuticals without involving any preparation operations like separation or masking. The values of second derivative amplitude at 212 nm for tocopherol, 351 nm for retinol and 222 nm for coenzyme were used for construction of calibration graphs. Beer's law is obeyed in the concentration range 0.5-20, 0.5-7.5 and 0.5-30 microg ml(-1) for retinol acetate, tocopherol acetate and coenzyme, respectively. The elaborated procedures were successfully applied to the simultaneous determination of studied compounds in their binary synthetic mixtures and in commercial preparations with high reliability and repeatability. Spectral properties of retinol acetate allows to determine its contents in ternary mixture which includes Vitamin E and coenzyme Q(10).     

Direct asymmetric aldol-Tishchenko reaction of aliphatic ketones catalyzed by syn-aminoalcohol-Yb(III) complexes

The asymmetric direct aldol condensation of aldehydes with ethyl- and propylketones is catalyzed by syn-alpha-aminoalcohol-Yb(OTf)3 complexes, yielding the anti-1,3-diol monoesters with high diastereocontrol and good enantioselectivity. Three adjacent stereogenic centers are created in a simultaneous aldol condensation and Evans-Tishchenko reduction in an acyclic system.