Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

Determination of uranium and thorium isotopes in soil samples by coprecipitation

Summary The paper presents a procedure to prepare soil samples for U and Th isotope measurement by alpha-spectrometry after coprecipitation with LaF₃. In this procedure the reduction of U(VI) to U(IV) was performed by Zn metal in 4M HCl solution. The recoveries of chemical separation equal to e_U-chemistry = 78±4% for uranium and e_Th-chemistry = 82±4% for thorium. Canberra alpha-spectrometer was used with PIPS detectors of A-1200-37-AM Model of 1200 mm² active area. The counting efficiency of the measuring system equals to e_counting = 18% and the total efficiencies were e_U = e_counting ^.e_U-chemistry = 14.0±0.7% for uranium and e_Th = e_counting ^.e_Th-chemistry = 14.7±0.7% for thorium. The recoveries of chemical separation were rather high (about 80%), that leads to the use of a small weight of soil sample (about 0.5 g). The efficiencies were also stable, that allows analyzing the soil sample without using radiotracers. They are advantages of the sample preparation procedure of this work.     

Graphitized carbon black in quartz tubes for the sampling of indoor air nicotine and analysis by microwave thermal desorption-capillary gas chromatography

Nicotine in a smoky indoor air environment can be determined using graphitized carbon black as a solid sorbent in quartz tubes. The temperature stability, high purity, and heat absorption characteristics of the sorbent, as well as the permeability of the quartz tubes to microwaves, enable the thermal desorption by means of microwaves after active sampling. Permeation and dynamic dilution procedures for the generation of nicotine in the vapor phase at low and high concentrations are used to evaluate the performances of the sampler. Tube preparation is described and the microwave desorption temperature is measured. Breakthrough volume is determined to allow sampling at 0.1-1 L/min for definite periods of time. The procedure is tested for the determination of gas and paticulate phase nicotine in sidestream smoke produced in an experimental chamber.     

Determination of geosmin and 2-methylisoborneol in water using solid-phase microextraction and gas chromatography-chemical ionisation/electron impact ionisation-ion-trap mass spectrometry

A method for the determination of geosmin and 2-methylisoborneol (MIB) in water by solid-phase microextraction (SPME) is presented. Various SPME fibre chemistries have been compared for their efficiency in extracting MIB from water. Extraction conditions including the extraction time and temperature have been optimised. A 30 ml water sample is extracted for 20 min at 60 degrees C using a divinylbenzene fibre, and the extract analysed by gas chromatography with ion-trap mass spectrometry detection. d5-Geosmin and d3-MIB are added as internal standards to compensate for any variability in the SPME process which is not carried out to equilibrium. Chemical ionisation, using acetonitrile as the reagent gas, was found to give superior sensitivity to electron impact ionisation (EI) for the detection of MIB. EI was used as the ionisation mode for detection of geosmin. The method shows good linearity over the concentration range 5-40 ng l-1 and gives detection limits of 1 ng l-1 for both geosmin and MIB. Recovery (93-110%) and precision (3-12%) over this concentration range, for both raw and treated drinking waters, are comparable to currently employed methods such as closed-loop stripping analysis (CLSA). The method offers the advantage of being simple to use, with much shorter analysis times in comparison to CLSA.     

The insertion of the dioxides of carbon and sulphur into the palladium-carbon bond

Bis ( η¹, η²-allyl) palladium phosphine complexes react with carbon dioxide and sulphur dioxide by insertion into the palladium-carbon σ-bond to give η³-allylpalladium-carboxylate and -S-sulphinate complexes.     

Thermodynamics of the decomposition processes of donor-acceptor complexes MX3 x en x MX3 and MX3 x en.

The structural and thermodynamic properties of the donor-acceptor (DA) complexes of Group 13 metal halides (MX3) with ethylenediamine and their decomposition products have been studied theoretically at the B3LYP/LANL2DZ(d,p) level of theory. Gas-phase dissociation into various components and HX elimination reactions are considered. Both processes are endothermic but favored by entropy. Complexes of 2:1 composition are predicted to be stable in the gas phase up to 640-1000 K. It is found that complexation with the second acceptor molecule lowers the HX elimination enthalpy; in turn, HX elimination increases DA bonding with a second MX3 molecule. Exceptionally high values of the dissociation enthalpies (310-390 kJ mol(-1)) and HX elimination reactions (360-420 kJ mol(-1)) of the amido compounds MX2NHC2H4NH2 and MX2NHC2H4NHMX2 make them important intermediates in the decomposition processes. Dissociation reactions of the complexes are more favorable than HX elimination reactions; however, the subsequent oligomerization and cyclization processes of coordinationally unsaturated amido and imido compounds may facilitate HX elimination. Since HI elimination reactions are predicted to be the least endothermic, and aluminum-containing compounds have the strongest M-N dissociation enthalpies, it is expected that compounds based on aluminum iodide are promising objects for experimental studies.     

Thermodynamics of binding of 2-methoxy-3-isopropylpyrazine and 2-methoxy-3-isobutylpyrazine to the major urinary protein

In the present study we examine the thermodynamics of binding of two related pyrazine-derived ligands to the major urinary protein, MUP-I, using a combination of isothermal titration calorimetry (ITC), X-ray crystallography, and NMR backbone (15)N and methyl side-chain (2)H relaxation measurements. Global thermodynamics data derived from ITC indicate that binding is driven by favorable enthalpic contributions, rather than the classical entropy-driven hydrophobic effect. Unfavorable entropic contributions from the protein backbone and side-chain residues in the vicinity of the binding pocket are partially offset by favorable entropic contributions at adjacent positions, suggesting a "conformational relay" mechanism whereby increased rigidity of residues on ligand binding are accompanied by increased conformational freedom of side chains in adjacent positions. The principal driving force governing ligand affinity and specificity can be attributed to solvent-driven enthalpic effects from desolvation of the protein binding pocket.     

The co-production approach to service: a theoretical background

The paper develops a theoretical background on the co-production approach as an extension of operations management principles, in which co-production function assumes well-defined functional form with the input presence of both firm and customers. The co-production approach not only views a customer as a co-producer, but also conducts strategic trade-offs between a firm and customers in service systems. Moreover, the value and the process of value co-creation are also explored under the co-production approach. The experimental study with a hypothetical service system indicates that the co-production function is feasible under economic and institutional considerations, and the co-production approach generalizes both the firm approach and the customer approach. Furthermore, the co-production approach creates many rich opportunities for future research on service operations management.     

A splitting algorithm for equilibrium problem given by the difference of two bifunctions

In this paper, we introduce a splitting algorithm for solving equilibrium problems given by the difference of two bifunctions in a real Hilbert space. Under suitable assumptions on component bifunctions, we prove strong convergence of the proposed algorithm. In contrast to most existing projection-type methods for equilibrium problems, our algorithm does not require any convexity or monotonicity conditions on the resulting bifunction. Some numerical experiments and comparisons are given to illustrate the efficiency of the proposed algorithm.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.