Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

A Safe Way of Performing Some Dangerous Experiments. II. Construction of a Safety Dropper

Due to the high safety risks, chemistry instructors avoid demonstrating many remarkable experiments based on the addition of a liquid to a solid. Well-known examples of such demonstrations are various pyrotechnic mixtures of potassium chlorate and sugar (sucrose), which are usually activated with a drop of concentrated sulfuric acid. Other attractive demonstrations are the addition of water to freshly prepared magnesium phosphide and addition of water to burning magnesium. In all of these demonstrations the reaction that takes place immediately is very vigorous and can be hazardous for the instructor. Because chemistry teachers and instructors usually try to avoid performing experiments that include a hazard, a number of highly attractive experiments may remain unknown to the public. Using a simple homemade device called a safety dropper, one can perform all of these experiments with complete safety, both for the audience and the demonstrator. Details for performing some of these experiments as well as for the construction of the safety dropper are given in this paper. Video clips of demonstrations are included as an aid for inexperienced instructors.     

Generation of C6H4+* by laser vaporization of magnesium with o-C6H4F2 in argon carrier gas

A route to efficient generation of C6H4+*, potentially the benzyne radical cation, is presented. Laser vaporization of Mg+* and supersonic expansion in helium doped with o-, m-, or p-C6H4F2 yields, among other ions, o-, m-, p-C6H4F2Mg+* complexes, but no C6H4+*. Collision-induced dissociation experiments show that the o-C6H4F2Mg+* complex can be converted into C6H4+* in a mildly energetic collision, with a center-of-mass energy around 1-2 eV. These conditions can also be reached in the ion source when argon is used as a carrier gas. In this way, mass spectra containing the desired m/z 76 peak, i.e. C6H4+*, are obtained.     

Removal of zinc ions as zinc chloride complexes from strongly acidic aqueous solutions by ionic exchange

The aim of this study was to compare several anion exchangers and to investigate the capacity of Amberlite IRA410 to remove zinc as chloride [ZnCl₃]^? from hydrochloric solutions (1 M). Influence of the process parameters such as stirring rate, resin quantity and zinc initial concentration over the removal process, was considered. The highest experimental ionic exchange capacity between the considered anionic exchangers, in the same working conditions (500 rpm, 5 g resin and 500 mg L^?1), was obtained for Amberlite IRA410, 8.34 mg g^?1. With an increase of zinc ions concentration, ionic exchange capacity increased up to 19.31 mg g^?1 (1100 mg L^?1). The experimental data were analysed using Langmuir, Freundlich, Temkin and Dubinin-Radushkevich isotherm models. The results were also analyzed using sorption kinetics models, pseudo-first-, pseudo-second-order, intra-particle and film diffusion models. From the Dubinin-Radushkevich and Temkin isotherm models the mean free energy and heat of sorption were calculated to be 7.45 kJ mol^?1, respectively 1×10^?4 kJ mol^?1, which indicates that zinc sorption is characterized by a physisorption process. Kinetic studies showed that the adsorption followed a pseudo-second-order kinetic model.     

A Simple Home-built Gas Liquefaction Cell

Liquefaction of gases offers deeper insight into the properties of various substances that are gaseous under normal conditions; however, the boiling temperatures of a number of gases are very low, preventing their liquefaction by means of standard laboratory techniques. A simple gas-liquefaction cell (designed by the authors) that can operate down to liquid-nitrogen temperature (77 K) is described in this paper. The properties of several liquefied (condensed) gases (e.g., ammonia, chlorine, nitric oxide, oxygen, and ozonized oxygen) are studied using this cell. The cell is also suitable for demonstration experiments.     

Thermal analysis of two types of dextran-coated magnetite

The thermal stability of two kinds of dextran-coated magnetite (dextran with molecular weight of 40,000 (Dex40) and 70,000 (Dex70)), obtained by dextran adsorption onto the magnetite surface is investigated in comparison with free dextran in air and argon atmosphere. The thermal behavior of the two free dextran types and corresponding coated magnetites is similar, but atmosphere dependent. The magnetite catalyzes the thermal decomposition of dextran, the adsorbed dextran displaying lower initial decomposition temperatures comparative with the free one in both working atmospheres. The dextran adsorbed onto the magnetite surface decomposes in air through a strong sharp exothermic process up to ~450 °C while in argon atmosphere two endothermic stages are identified, one in the temperature range 160–450 °C and the other at 530–800 °C.     

Structure of sodiated octa-glycine: IRMPD spectroscopy and molecular modeling

The structure of the sodiated peptide GGGGGGGG-Na⁺ or G₈-Na⁺ was investigated by infrared multiple photon dissociation (IRMPD) spectroscopy and a combination of theoretical methods. IRMPD was carried out in both the fingerprint and N—H/O—H stretching regions. Modeling used the polarizable force field AMOEBA in conjunction with the replica-exchange molecular dynamics (REMD) method, allowing an efficient exploration of the potential energy surface. Geometries and energetics were further refined at B3LYP-D and MP2 quantum chemical levels. The IRMPD spectra indicate that there is no free C-terminus OH and that several N—Hs are free of hydrogen bonding, while several others are bound, however not very strongly. The structure must then be either of the charge solvation (CS) type with a hydrogen-bound acidic OH, or a salt bridge (SB). Extensive REMD searches generated several low-energy structures of both types. The most stable structures of each type are computed to be very close in energy. The computed energy barrier separating these structures is small enough that G₈-Na⁺ is likely fluxional with easy proton transfer between the two peptide termini. There is, however, good agreement between experiment and computations in the entire spectral range for the CS isomer only, which thus appears to be the most likely structure of G₈-Na⁺ at room temperature.     

Numerical solutions to singular ϕ-Laplacianwith Dirichlet boundary conditions

In this note we are concerned with numerical solutions to Dirichlet problem $$[\phi(u')]' =f(x) \quad \mbox{in} [\alpha, \beta]; \quad u(\alpha)=A, \; u(\beta)=B, $$ where \(\phi :(-\eta , \eta ) \to \mathbb {R}\) \((\eta <+ \infty )\) is an increasing diffeomorphism with \(\phi '(y)\geq d >0\) for all \(y\in (-\eta , \eta )\) . The obtained algorithm combines the shooting method with Euler’s method and it is convergent whenever the problem is solvable. We provide numerical experiments confirming the theoretical aspects.