The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Chromatographic Detection of Trimetoquinol (Inolin®) and its Major Urinary Metabolites in the Horse: A Preliminary Report

Trimetoquinol (TMQ) (1-(3,4,5-trimethoxybenzyl)-6,7-dihydroxy-1,2,3,4-tetrahydroisoquinoline, m.w. 345) is the prototype tetrahydroisoquinoline pharmaceutical. TMQ is marketed as a bronchodilator in human medicine; in horse racing, TMQ is listed as an Association of Racing Commissioners International (ARCI) class 3 foreign substance. As such, TMQ is considered to have the potential to affect racing performance in horses, and a validated qualitative confirmatory method is required to regulate its use in racing. We selected 8 g kg^–1 of TMQ IV as a safe and effective dose for studies on its metabolism and analytical detection in horses. We developed a solid phase extraction method for recovery of TMQ and its metabolites from equine urine, identified suitable high performance liquid chromatographic conditions for these substances and our internal standard, papaverine, and developed a highly sensitive ESI(+)-LC-MS-MS method (estimated LOD, 100 pg mL^–1) for TMQ and its major metabolites in equine urine. Multiple Reaction Monitoring (MRM) analysis of unhydrolyzed post-administration urine showed small amounts of unchanged TMQ, along with glucuronide, methylated, and sulfated metabolites, with glucuronide metabolites predominating. Following glucuronidase hydrolysis, recovered parent TMQ peaked at relatively high concentrations (>300 ng mL^–1) within 1 h of administration and thereafter declined. The methylated metabolites of TMQ peaked later and at comparable total concentrations, and thereafter declined more slowly. These data suggest that glucuronide hydrolysis of post-administration urine samples will allow recovery of readily identifiable quantities of parent TMQ. These findings, combined with the highly sensitive LC-MS-MS detection of parent TMQ described herein suggest that glucuronide hydrolysis of post-administration urine, followed by LC-MS-MS or other analysis, will allow effective regulatory control of this agent in racing horses.Published as # 351 from the Equine Pharmacology, Therapeutics and Toxicology Program at the Maxwell H. Gluck Equine Research Center and Department of Veterinary Science, University of Kentucky. Published as Kentucky Agricultural Experiment Station Article # 04-14-048 with the approval of the Dean and Director, College of Agriculture and the Kentucky Agricultural Experimental Station.Revised: 8 June and 12 July 2004     

Solid-state Al NMR investigation of thermal decomposition of LiAlH4

Solid-state nuclear magnetic resonance is used to study the thermal decomposition of lithium tetrahydroaluminate into metallic aluminum, hydrogen and trilithium hexahydroaluminate. Aluminum sites in LiAlH₄ and Li₃AlH₆ were characterized using static, magic angle spinning (MAS) and multiple-quantum MAS NMR. By applying the in situ NMR method, it has been demonstrated that melting is not a prerequisite for the decomposition of LiAlH₄. Based on the observed data, a decomposition path has been established that is consistent with the concentrations of observed Al species at various stages of the thermally induced reaction.     

Changes in the Seam-Filtration Mode with Stress Redistribution in Country Rock

A mathematical model for the mechanism of increasing oil output of productive seams is developed. The model involves a deliberate conversion of segments of the fault zone of the country rock to a supercritical state, which leads to a local redistribution of stresses in the block massif of rocks and an increase in contour and seam pressures. Based on solving the problem of restricted filtration, it is shown that the use of the proposed mechanism can ensure a relative increase in well production of 5–8%.     

Arithmetic Progressions,Prime Numbers,and Squarefree Integers

In this paper we establish the distribution of prime numbers in a given arithmetic progression p l for which ap + b is squarefree.     

Positive solutions for three-point boundary value problems with dependence on the first order derivative

A new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three-point boundary value problem

     

Computational Modeling of Organizations Comes of Age

As they are maturing—i.e., as they are becoming validated, calibrated and refined—computational emulation models of organizations are evolving into: powerful new kinds of organizational design tools for predicting and mitigating organizational risks; and flexible new kinds of organizational theorem-provers for validating extant organization theory and developing new theory. Over the past 50 years, computational modeling and simulation have had enormous impacts on the rate of advancement of knowledge in fields like physics, chemistry and, more recently, biology; and their subsequent application has enabled whole new areas of engineering practice. In the same way, as our young discipline comes of age, computational organizational models are beginning to impact behavioral, organizational and economic science, and management consulting practice. This paper attempts to draw parallels between computational modeling in natural sciences and computational modeling of organizations as a contributor to both social science and management practice.To illustrate the lifecycle of a computational organizational model that is now relatively mature, this paper traces the evolution of the Virtual Design Team (VDT) computational modeling and simulation research project at Stanford University from its origins in 1988 to the present. It lays out the steps in the process of validating VDT as a computational emulation model of organizations to the point that VDT began to influence management practice and, subsequently, to advance organizational science. We discuss alternate research trajectories that can be taken by computational and mathematical modelers who prefer the typical natural science validation trajectory—i.e., who attempt to impact organizational science first and, perhaps subsequently, to impact management practice.The paper concludes with a discussion of the current state-of-the-art of computational modeling of organizations and some thoughts about where, and how rapidly, the field is headed.     

Fast topological analysis of 2D and 3D grids of data: application to the atoms in molecule (AIM) and the electron localization function (ELF)

The topological analysis of grids of data is used for determination of surfaces or volumes around maxima. The volumes are then related to chemical information such as atoms or bonds, and can be used for integration of local properties such as electronic population. The problem of global connectivity is reversed into the question of local connectivity yielding a linear scaling partition algorithm. Two packages are developed for a very fast analysis and partition of 2D or 3D grids of data, applications being made to C2H2, C2H4, C6H6, H2CO, and H2CS molecules using the Atoms in Molecule (AIM) or Electron Localization Function (ELF).     

Determination of lead and nickel in Apple-Leaves and sea-water by electrothermal atomic absorption spectrometry after solid-phase extraction using Chromosorb-107 filled in a syringe

Lead and nickel were concentrated and separated after sorbing on Chromosorb-107 filled in a syringe prior to their determination by electrothermal atomic absorption spectrometry. To retain the analytes, the sample solution treated with or without ammonium pyrolidine dithiocarbamate (APDC) was drawn into the syringe filled with Chromosorb-107 and discharged back manually. Then the analyte elements were eluted by drawing and discharging the suitable eluent. The optimum experimental conditions for quantitative recoveries of analytes (amount of sorbent, pH of sample, concentration and kind of eluent, flow rates of sample and eluent and adding of the effect of complexing agent) were investigated. Nickel was quantitatively retained at pH6 irrespective of whether it was complexed with APDC while the quantitative sorption of lead was achieved at pH8 only if it was treated with APDC prior to passing through the sorbent. The lead and nickel retained on the sorbent were eluted drawing and discharging 4.5 M HNO(3), respectively. If the concentration of analyte elements in the sample were too low to be detected, then they were concentrated by increasing the ratio of sample value to eluent volume as needed. The lead and nickel in spiked sea-water samples and in certified reference Apple-Leaves (NIST SRM 1515) standards were quantitatively (95%) recovered with R.S.D. of around +/-2%.