The origins of the sampling theorem

The publications of Claude E. Shannon brought the sampling theorem to the broad attention of communication engineers. This article demonstrates how practicians, theoreticians, and mathematicians discovered the implications of the sampling theorem almost independent of one another     

A first‐order system least‐squares finite element method for the Poisson‐Boltzmann equation

The Poisson‐Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson‐Boltzmann equation. We expose the flux directly through a first‐order system form of the equation. Using this formulation, we propose a system that yields a tractable least‐squares finite element formulation and establish theory to support this approach. The least‐squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Critical parameters in a supported liquid membrane extraction technique for ionizable organic compounds with a stagnant acceptor phase

The reviews cover important critical parameters that are often optimized in a supported liquid membrane extraction technique in both flat sheet and hollow fibre designs for ionizable organic molecules. Understanding of these parameters can enable one to predict the behavior of the compound before hand and thus reduce the number of optimization experiments. Moreover, less number of experiments can be also generated using statistical techniques which are now becoming more commonly used. Supported liquid membrane extraction optimal parameters such as the conditions of the pH of the acceptor and donor phases should easily be fixed from the pKa values of the compounds. Other parameters, including the polarity of the compound can help to predict the partitioning into the membrane and the behavior of the compound. The influence of parameters such as temperature on the mass transfer in supported liquid membrane depends on the design of the module, experimental design and type of mass transfer controlling the extraction process.     

Tripodal Thiols as Ligands for Molecular Magnets: Very Strong Antiferromagnetic Exchange Interactions in Vanadium(III) Clusters

The synthesis, structural and magnetic characterisation of [V^III₃O(tmme)₂(diimine)₂Cl] [diimine=2,2′‐bipyridine ( 1 ) or 1,10‐phenanthroline ( 2 )] and (HNEt₃)₂[V^III₄O(tmme)₄] ( 3 ) is reported, in which H₃tmme is tris(mercaptomethyl)ethane, MeC(CH₂SH)₃, the thiol analogue of the famous tripodal alcohol ligands typified by H₃thme [tris(hydroxymethyl)ethane, MeC(CH₂OH)₃]. Complexes 1 and 3 have “T‐shaped” and square topologies, respectively, and the latter is centred on a rare example of a square‐planar oxide. The tri‐thiolate ligands bind the periphery of the clusters and provide such strong antiferromagnetic exchange pathways that in both cases only a single total spin state is occupied up to room temperature, in the absence of metal–metal bonding. Magnetic data, electronic structure calculations and electrochemical data are reported.     

Exploring lead exposure in ancient Chilean mummies using a single strand of hair by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS)

Lead exposure has received increased attention over the past few decades since it has been shown to have adverse effects on physical and intellectual development in humans. The use of biological tissues such as blood, teeth, hair, and bone for assessment of lead exposure has been previously demonstrated. While analysis of blood for trace metals provides information concerning recent exposure, hair offers insight into a period of several months, and is preferable since it is non-invasively collected and easily stored. The present study analyzed total of 49 ancient hair samples for lead (Pb_H) using LA-ICP-MS. Samples belonged to an ancient fisher hunter–gatherer culture called the “Chinchorro,” and who occupied regions of the Atacama Desert on the northern coast of Chile from approximately 5000–1500 B.C. and practiced the first-known form of artificial mummification. Several samples from a post-Chinchorro agricultural community (n = 12) ca. 1000–1400 A.D. were also analyzed. A suite of hair standards was developed using contemporary hair from the same region and was subsequently used to make linear calibration functions for lead determination in single strands of hair using LA-ICP-MS. Three linear scans ranged from 500 to 1000 μm were performed for each sample and signal intensities were normalized over ¹³C. The distribution of lead in the central medulla in a 100 μm cross-section scan of hair strand demonstrated minimal exogenous contamination. Hair lead (Pb_H) concentrations ranged between 2.2 μg/g and 12.8 μg/g could be accurately quantified with these standards. Twenty one out of 49 samples (43%) showed Pb_H concentrations higher than the average value of 5 μg/g for unexposed individuals (range 1.1–228.0 μg/g). Median hair lead concentrations by burial sites and are shown in order of decreasing concentration: Morro (13.8 μg/g) > Iquique (6.6 μg/g) > Azapa (4.5 μg/g) > Yungay (4.1 μg/g) > Camarones (2.7 μg/g). Most of the burial sites showed Pb_H concentrations greater than the normal value for unexposed individuals and outliers heavily influenced average concentrations. The results suggest that the Chinchorro and later agro-pastoral populations were not widely exposed to naturally elevated lead.     

Binary Alexis sequences with perfect correlation

Binary Alexis (1986) sequences are useful signals for fast start-up equalization, channel estimation, synchronization, or ranging. The aperiodic autocorrelation functions of Alexis sequences vanish in a broad window region when correlated using additional binary preamble and postamble sequences. Originally, Alexis sequences were found by computer search. Two methods are presented by which such sequences can be constructed for any length N=p^a and N=2(p^a+1), where p, is an odd prime and a=1, 2, 3     

Stress Inhomogeneity in Powder Specimens Tested in the Jenike Shear Cell: Myth or Fact?

In the mechanical characterization of powders using the direct shear testers such as the Jenike shear cell, the existence of a uniform or well‐defined stress field in a powder specimen is assumed. This assumption has not been subjected to any serious scrutiny in the literature. In this study, the normal stress variation in a silica powder was locally determined by locating a pressure‐sensitive TekScan pad at the bottom section of a Jenike shear cell. A computer simulation of the consolidation and pre‐shearing stages of the Jenike test procedure was performed using the Discrete Element Method (DEM). The paper presents both experimental and computational evidence for the existence of a complex stress field in the powder specimen, thus clearly invalidating the long‐standing stress homogeneity assumption in the direct shear testing of powders. The implications of the stress inhomogeneity in terms of the accuracy of the material properties extracted from the Jenike test are also presented.     

Single-Mode Emission From Vertical-Cavity Surface-Emitting Lasers With Low-Index Defects

Mode confinement to low-index "defect" regions of a two-dimensional square photonic lattice has been studied as a means to realize single-spatial-mode vertical-cavity surface-emitting lasers (VCSELs). A selective etching process with two-step metal-organic chemical vapor deposition is used to fabricate the low-index defect VCSELs. A device with a 9-mum-wide aperture demonstrates 2.9-mW continuous-wave (CW) output power. The near diffraction-limited single-lobe far-field and high-resolution spectral analyses confirm single fundamental defect mode emission. Comparison studies between pulsed and CW operation indicate that thermal effects have a significant impact on the modal performance of the devices. Single-mode emission with more than 8 mW of peak pulsed power has been observed with short pulsewidth operation (0.1 mus, 2%). Improvements in thermal management are required to achieve higher CW single-mode emission in these devices     

Depolarization in reentrant spin glasses: a comparison between neutron and muon probes

In the amorphous ( Fe_1-x Mn_x)₇₅ P₁₆ B_6 Al_3 alloys, muon and neutron depolarization data, combined with the results of small angle neutron scattering, magnetization and Mössbauer spectroscopy, probe the existence of three distinct magnetic transitions at T_C, T_K and T_F (T_F < _K < _C).