On goodness-of-fit testing for ergodic diffusion process with shift parameter

A problem of goodness-of-fit test for ergodic diffusion processes is presented. In the null hypothesis the drift of the diffusion is supposed to be in a parametric form with unknown shift parameter. Two Cramer–von Mises type test statistics are studied. The first test uses the local time estimator of the invariant density, the second one uses the empirical distribution function. The unknown parameter is estimated via the maximum likelihood estimator. It is shown that the limit distribution of the two test statistics does not depend on the unknown parameter, thus both the tests are asymptotically parameter free. Some considerations on the consistency of the proposed tests and some simulation studies are also given.     

Fundamental domains for properly discontinuous affine groups

We construct a fundamental region for the action on the \(2d+1\) -dimensional affine space of some free, discrete, properly discontinuous groups of affine transformations preserving a quadratic form of signature \((d+1, d)\) , where \(d\) is any odd positive integer.     

Novel pincer complexes of Ag(I), coordination of toluene and their comparison with indium analogues

The bis(imino)pyridine scaffold provides for the synthesis and characterization of the unique Ag(I) pincer complexes [{ArN=CPh}(2)(NPh)]Ag(+)(OTf)(-) (Ar = 2,5-(t)Bu(2)C(6)H(3); 2,6-(i)Pr(2)C(6)H(3)). The similar covalent radii of Ag(I) and In(I), prompted a bonding comparison of these species with their In(I) analogues. Coordination of toluene to the Ag center revealed the stronger Lewis acidity of the metal site in these compounds relative to In(I) analogues.     

An EMF cell with a nitrogen solid electrolyte--on the transference of nitrogen ions in yttria-stabilized zirconia

The mobility and electrochemical activity of nitrogen inside and/or at the surface of ionic compounds is of fundamental, as well as of possibly practical, relevance. In order to better understand the role of nitrogen anions in solid electrolytes, we measured the transference number of nitrogen in yttria-stabilized zirconia (YSZ) by a concentration cell technique as a function of oxygen activity at different temperatures in the range of 1023 ≤T/K≤ 1123. YSZ doped with 1.9 wt% of N (YSZ:N) turned out to have an appreciable nitrogen transference number, which increased from 0 to 0.1 with decreasing oxygen activity in the range of -20 < log a(O(2)) < -14. The stability of N in YSZ:N, however, has yet to be elucidated under oxidizing conditions.     

Method for fractional solid-waste sampling and chemical analysis

Chemical characterization of solid waste is a demanding task due to the heterogeneity of the waste. This article describes how 45 material fractions hand-sorted from Danish household waste were subsampled and prepared for chemical analysis of 61 substances. All material fractions were subject to repeated particle-size reduction, mixing, and mass reduction until a sufficiently small but representative sample was obtained for digestion prior to chemical analysis. The waste-fraction samples were digested according to their properties for maximum recognition of all the studied substances. By combining four subsampling methods and five digestion methods, paying attention to the heterogeneity and the material characteristics of the waste fractions, it was possible to determine 61 substances with low detection limits, reasonable variance, and high accuracy. For most of the substances of environmental concern, the waste-sample concentrations were above the detection limit (e.g. Cd?>?0.001?mg?kg^?1, Cr?>?0.01?mg?kg^?1, Hg?>?0.002?mg?kg^?1, Pb?>?0.005?mg?kg^?1). The variance was in the range of 5–100%, depending on material fraction and substance as documented by repeated sampling of two highly different material fractions (‘Vegetable food’ and ‘Shoes, leather, etc.’). Statistical analysis showed for the ‘Vegetable food’ that the variance could not be attributed to a single step in the procedure, whereas in the case of ‘Shoes, leather, etc.’, the first coarse shredding was the main source of variance (20–85% of the overall variation). Only by increasing the sample size significantly can this variance be reduced. The accuracy and short-term reproducibility of the chemical characterization were good, as determined by the analysis of several relevant certified reference materials. Typically, six to eight different certified reference materials representing a range of concentrations levels and matrix characteristics were included. Based on the documentation provided, the methods introduced were considered satisfactory for characterization of the chemical composition of waste-material fractions.     

THE CONDENSED PHOSPHATES AS INHIBITORS OF THE ZINC-ENZYME CARBONIC ANHYDRASE II

The mobilization of the zinc ion from the zinc enzyme BCA II by the condensed phosphates pyrophosphate (PP), tripolyphosphate (TPP), and higher polyphosphate (HPP) induces the inhibition of the enzymatic activity. The chelating capacity increases with the ligand concentration and with the length of the polyphosphatic chain. The activity is restored when the polyphosphate is hydrolyzed, becoming incapable of chelating the zinc ion, which is able to reform the zinc enzyme.     

Importance of out-of-state spin-orbit coupling for slow magnetic relaxation in mononuclear Fe(II) complexes

Two mononuclear high-spin Fe(II) complexes with trigonal planar ([Fe(II)(N(TMS)(2))(2)(PCy(3))] (1) and distorted tetrahedral ([Fe(II)(N(TMS)(2))(2)(depe)] (2) geometries are reported (TMS = SiMe(3), Cy = cyclohexyl, depe = 1,2-bis(diethylphosphino)ethane). The magnetic properties of 1 and 2 reveal the profound effect of out-of-state spin-orbit coupling (SOC) on slow magnetic relaxation. Complex 1 exhibits slow relaxation of the magnetization under an applied optimal dc field of 600 Oe due to the presence of low-lying electronic excited states that mix with the ground electronic state. This mixing re-introduces orbital angular momentum into the electronic ground state via SOC, and 1 thus behaves as a field-induced single-molecule magnet. In complex 2, the lowest-energy excited states have higher energy due to the ligand field of the distorted tetrahedral geometry. This higher energy gap minimizes out-of-state SOC mixing and zero-field splitting, thus precluding slow relaxation of the magnetization for 2.     

An organometallic sandwich lanthanide single-ion magnet with an unusual multiple relaxation mechanism

A dysprosium(III) sandwich complex, [Dy(III)(COT″)(2)Li(THF)(DME)], was synthesized using 1,4-bis(trimethylsilyl)cyclooctatetraenyl dianion (COT″). The complex behaves as a single-ion magnet and demonstrates unusual multiple relaxation modes. The observed relaxation pathways strongly depend on the applied static dc fields.     

Preparation and characterization of a reduced chromium complex via vinyl oxidative coupling: formation of a self-activating catalyst for selective ethylene trimerization

Reaction of the divalent [(t-Bu)NP(Ph)(2)N(t-Bu)]CrCl(2)Li(THF)(2) (1) with 1 equiv of vinyl Grignard (CH(2)=CH)MgCl reproducibly afforded the triangulo {π-[(t-Bu)N-P(Ph)(2)-N(t-Bu)]Cr}(2)(μ,μ',η(4),η(4)'-C(4)H(4)){σ-[(t-Bu)N-P(Ph)(2)-N(t-Bu)]Cr} (2) containing a σ-/π-bonded butadiene-diyl unit. The diene-diyl moiety was generated by an oxidative coupling and deprotonation of two vinyl anions. The crystal structure revealed that of the three chromium atoms, each bearing one NPN ligand, two are perpendicularly bonded to the two sides of the π-system of the butadiene-diyl residue in a sort of inverted sandwich type of structure. The third is instead coplanar with the doubly deprotonated C(4) unit and σ-bonded to the two terminal carbon atoms. Despite the appearance as a Cr(II)/Cr(I) mixed valence species, DFT calculations have revealed that the structure of 2 consists of three divalent chromium atoms, while the additional electron resides on the π-system of the bridging organic residue. Complex 2 behaves as a single component selective catalyst for ethylene trimerization.