Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

Energy isosbestic points in third-row transition metal alloys

The total electronic energies of the six electrons per atom (e per atom) alloys W, TaRe, HfOs, and YIr and the seven electrons per atom alloys Re, WOs, TaIr, HfPt, and YAu have been calculated in the local density approximation of density functional theory. When one considers common alloy structures such as atomically ordered variants of the body-centered cubic, face-centered cubic, or hexagonally closest packed structures and plots the total electronic energy as a function of the unit cell parameter, one finds for both the six and seven electrons per atom series energetic isosbestic points. An energetic isosbestic point corresponds to a critical value of the size parameter for which all members of the 6 or 7 e per atom series of compounds have nearly identical total electronic energy. Just as in spectroscopy, where the existence of such isosbestic points is the hallmark of two compounds present in the mixture, an energy isosbestic point implies there are just two separate energy curves. For both series it is found that the total electronic energy can be viewed as the weighted sum of a purely covalent term and a purely ionic term. Two semi-quantitative models are proposed to account for these two separate energies. In the first model the total energy is viewed as the sum of the elemental structural energy plus an ionic energy based on the Born-Mayer ionic model. In the second model one considers within the confines of mu2-Hückel theory the evolution of the total electronic energy as the Coulombic Hii integrals change in value.     

Ligand-protein docking using a quantum stochastic tunneling optimization method

A novel hybrid optimization method called quantum stochastic tunneling has been recently introduced. Here, we report its implementation within a new docking program called EasyDock and a validation with the CCDC/Astex data set of ligand-protein complexes using the PLP score to represent the ligand-protein potential energy surface and ScreenScore to score the ligand-protein binding energies. When taking the top energy-ranked ligand binding mode pose, we were able to predict the correct crystallographic ligand binding mode in up to 75% of the cases. By using this novel optimization method run times for typical docking simulations are significantly shortened.     

Uranium analysis in urine by inductively coupled plasma dynamic reaction cell mass spectrometry

Urine uranium concentrations are the best biological indicator for identifying exposure to depleted uranium (DU). Internal exposure to DU causes an increased amount of urine uranium and a decreased ratio of ²³⁵U/²³⁸U in urine samples, resulting in measurements that vary between 0.00725 and 0.002 (i.e., natural and depleted uraniums ²³⁵U/²³⁸U ratios, respectively). A method based on inductively coupled plasma dynamic reaction cell mass spectrometry (ICP-DRC-MS) was utilized to identify DU in urine by measuring the quantity of total U and the ²³⁵U/²³⁸U ratio. The quantitative analysis was achieved using ²³³U as an internal standard. The analysis was performed both with and without the reaction gas oxygen. The reaction gas converted ionized ²³⁵U⁺ and ²³⁸U⁺ into ²³⁵UO₂⁺ (m/z=267) and ²³⁸UO₂⁺ (m/z=270). This conversion was determined to be over 90% efficient. A polyatomic interference at m/z 234.8 was successfully removed from the ²³⁵U signal under either DRC operating conditions (with or without oxygen as a reaction gas). The method was validated with 15 urine samples of known uranium compositions. The method detection limit for quantification was determined to be 0.1 pg U mL^–1 urine and an average coefficient of variation (CV) of 1–2% within the sample measurements. The method detection limit for determining ²³⁵U/²³⁸U ratio was 3.0 pg U mL^–1 urine. An additional 21 patient samples were analyzed with no information about medical history. The measured ²³⁵U/²³⁸U ratio within the urine samples correctly identified the presence or absence of internal DU exposure in all 21 patients.The opinions and assertions expressed herein are those of the authors and are not to be construed as official or as representing the views of the Armed Forces Institute of Pathology, the Department of the Army, or the Department of Defense     

An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

Extremal problems for certain analytic (Nevanlinna) functions

We obtain sharp bounds on some basic functionals defined on the sets of all analytic functions having the representations \(f\left( z \right) \equiv \int\limits_{ - 1}^1 {\frac{{d\mu \left( t \right)}}{{z - t}}} \) and \(\varphi \left( z \right) \equiv \int\limits_{ - 1}^1 {\frac{{z\mu \left( t \right)}}{{1 - tz}}} \) ; respectively. Here μ is a probability measure.     

Arsenic Speciation in Urine and Blood Reference Materials

Acute and chronic exposure to arsenic is a growing problem in the industrialized world. Arsenic is a potent carcinogen and toxin in humans. In the body, arsenic is metabolized to produce several species, including inorganic forms, such as trivalent (As^III) and pentavalent (As^V), and the methylated metabolites such as monomethylarsonic acid, (MMA^V), and dimethylarsinic acid (DMA^V), in addition to arsenobetaine (AsB) which is ingested and excreted from the body in the same form. Each of these species has been reported to possess a specific but different degree of toxicity. Thus, not only is the measurement of total As required, but also quantification of the individual metabolites is necessary to evaluate the toxicity and risk assessment of this element. There are a large number of reference materials that are used to validate methodology for the analysis of As in blood and urine, but they are limited to total As concentrations. In this study, the speciation of five arsenic metabolites is reported in blood and urine from commercial available control materials certified for total arsenic levels. The separation was performed with an anion exchange column using inductively coupled plasma mass spectrometry as a detector. Baseline separation was achieved for As^III, As^V, MMA^V, DMA^V, and AsB, allowing us to quantify all five species. Excellent agreement between the total arsenic levels and the sum of the speciated As levels was obtained.     

Electric light scattering from single-stranded DNA in linear polyacrylamide solutions

The electric light scattering (ELS) of ssDNA (calf thymus, 10 kbp, 55 micrograms/mL) in denaturing polyacrylamide (PAA) solutions was studied as a function of applied sinusoidal electric field and polymer concentration. Electric fields of strengths up to 300 V/cm and of frequencies between 100 and 5000 Hz were applied. It was found that the ELS effect increases with the field strength and decreases at high frequencies. The dependence of the ELS effect of ssDNA on polymer concentration passes through a maximum at 1% PAA. The relaxation times of decay of the ELS effect increase with increasing polymer concentrations. It was demonstrated that ELS is a useful method for investigation of ssDNA behavior in the course of pulse-field electrophoresis in polymer solutions.