A very rigid Boolean algebra

A Boolean algebra is constructed having only those endomorphisms corresponding to prime ideals, which are present in any BA. The BA constructed is of powerc, has 2 ^c endomorphisms, and is not rigid in Bonnet’s sense.     

A combined LC-MS/MS and LC-MS3 multi-method for the quantification of iodothyronines in human blood serum

We report here a novel approach for the extraction and analysis of thyroid hormones (TH) and their metabolites (THM) from human serum samples. Our method features a compact, 96-well micro-titre plate-based pre-analytic extraction/clean-up workflow combined with an isotope dilution LC-MS/MS-MS³ analytical method. In particular, these features make possible the detection of iodothyronines at their endogenous concentrations in serum differing by a factor of ca. 10⁴, with potential to semi-automate the pre-analytics. The method was validated by the assessment of linearity, lower limits of quantification and detection (LLOQ and LLOD respectively), intra- and inter-day accuracy, precision, process efficiency (PE), matrix effect (ME) and relative recovery (RE). Calibration curves were linear in the concentration range in sample matrix from 0.1–250 nM for T₃, rT₃, T₄ and 3-T₁AM and from 0.005–1 nM for 3,5-T₂ and 3,3′-T₂. Using a 200-μL sample volume, the analyte dependant LLOQ were in the range 0.005 (3,5-T₂) to 0.25 (T₄) nM and LLOD were between 0.002 (3,5-T₂) and 0.052 nM (T₄). We applied the LC-MS/MS-MS³ method to the analysis of a cross section of patients with disorders of the thyroid hormone axis. T₄, T₃ and rT₃ concentrations (± standard deviation) were 120 ± 18, 1.9 ± 0.4 and 0.45 ± 0.09 nM respectively. 3,3′-T₂ concentrations (± standard deviation) were 0.079 ± 0.022 nM; 3,5-T₂ concentrations were below the LLOQ and/or LLOD in all but a single sample (0.013 nM). This method expands the analytical spectrum to endogenous thyroid hormone metabolites such as 3,5-T₂ which exert biological actions and rT₃ which may act as surrogate markers for disturbed thyroid hormone metabolism.

Graphical abstract

     

Pseudo-trees and Boolean algebras

We consider Boolean algebras constructed from pseudo-trees in various ways and make comments about related classes of Boolean algebras.     

The inverse electromagnetic scattering problem for a partially coated dielectric

We use the linear sampling method to determine the shape and surface conductivity of a partially coated dielectric infinite cylinder from knowledge of the far field pattern of the scattered TM polarized electromagnetic wave at fixed frequency. A mathematical justification of the method is provided based on the use of a complete family of solutions. Numerical examples are given showing the efficiency of our method.     

Linear grain growth kinetics and rotation in nanocrystalline Ni

We report three-dimensional atomistic molecular dynamics studies of grain growth kinetics in nanocrystalline Ni. The results show the grain size increasing linearly with time, contrary to the square root of the time kinetics observed in coarse-grained structures. The average grain boundary energy per unit area decreases simultaneously with the decrease in total grain boundary area associated with grain growth. The average mobility of the boundaries increases as the grain size increases. The results can be explained by a model that considers a size effect in the boundary mobility.     

A finite element method for approximating the time-harmonic Maxwell equations

Summary In this paper we study the use of Nédélec's curl conforming finite elements to approximate the time-harmonic Maxwell equations on a bounded domain. The analysis is complicated by the fact that the bilinear form is not coercive, and the principle part has a very large null-space. This difficulty is circumvented by using a discrete Helmholtz decomposition of the error vector. Numerical results are presented that compare two different linear elements.Research supported in part by grants from AFOSR and NSF     

An atomless interval Boolean algebra A such that $ \mathfrak{a} (A) $ < $ \mathfrak{t} (A) $

For any Boolean algebra A, is the smallest cardinality of an infinite partition of unity in A. A tower in a Boolean algebra A is a subset X of A well-ordered by the Boolean ordering, with but with is the smallest cardinality of a tower of A. Given a linearly ordered set L with first element, the interval algebra of L is the algebra of subsets of L generated by the half-open intervals [a, b). We prove that there is an atomless interval algebra A such that . Received January 21, 2002; accepted in final form March 13, 2002.