On the Beurling dimension of exponential frames

We study Fourier frames of exponentials on fractal measures associated with a class of affine iterated function systems. We prove that, under a mild technical condition, the Beurling dimension of a Fourier frame coincides with the Hausdorff dimension of the fractal.     

Submicrosecond real-time fluorescence sampling: application to protein folding

Time-resolved fluorescence detection has become a central tool in the study of protein folding. This article briefly reviews modern fluorescence techniques and then focuses on recent improvements made possible by array photomultipliers, computer-controlled data gating, and long-memory multi-channel digitizers. It is now possible to detect fluorescence wavelength profiles and/or fluorescence decay transients very cost effectively with sub-microsecond kinetic time resolution out to long times. Folding kinetics can be analyzed by singular value decomposition (SVD) or chi-analysis. The latter provides an objective method for detecting nonexponential kinetics in two-state systems.     

Generalized Walsh Bases and Applications

We investigate convergence properties of generalized Walsh series associated with signals f∈L ¹[0,1]. We also show how the dependence of the generalized Walsh bases on N×N unitary matrices allows for applications in signal encoding and encryption, provided the signals are piece-wise constant on N-adic subintervals of [0,1].     

Electrical conductivity of a metal powder struck by a spark

Equivalent resistance of a polydisperse powder layer struck by an electric spark is evaluated. Particles were computationally created and mixed using discrete element method; the mixing protocol homogenized particle size distribution within the sample. The conductivity was determined from the equivalent resistance network for the simulated powder bed. A plasma streamer attached to a particle on top of the sample. For each particle contact, an electrical breakdown was assumed; each individual contact resistance was calculated considering its geometry and plasma resistivity. Results of calculations compare well with the available experimental data.     

Gas-phase acidities and O-H bond dissociation enthalpies of phenol, 3-methylphenol, 2,4,6-trimethylphenol, and ethanoic acid

Energy-resolved, competitive threshold collision-induced dissociation (TCID) methods are used to measure the gas-phase acidities of phenol, 3-methylphenol, 2,4,6-trimethylphenol, and ethanoic acid relative to hydrogen cyanide, hydrogen sulfide, and the hydroperoxyl radical using guided ion beam tandem mass spectrometry. The gas-phase acidities of Delta(acid)H298(C6H5OH) = 1456 +/- 4 kJ/mol, Delta(acid)H298(3-CH3C6H4OH) = 1457 +/- 5 kJ/mol, Delta(acid)H298(2,4,6-(CH3)3C6H2OH) = 1456 +/- 4 kJ/mol, and Delta(acid)H298(CH3COOH) = 1457 +/- 6 kJ/mol are determined. The O-H bond dissociation enthalpy of D298(C6H5O-H) = 361 +/- 4 kJ/mol is derived using the previously published experimental electron affinity for C6H5O, and thermochemical values for the other species are reported. A comparison of the new TCID values with both experimental and theoretical values from the literature is presented.     

A localized specific interaction alters the unfolding pathways of structural homologues

Reductive unfolding studies of proteins are designed to provide information about intramolecular interactions that govern the formation (and stabilization) of the native state and about folding/unfolding pathways. By mutating Tyr92 to G, A, or L in the model protein, bovine pancreatic ribonuclease A, and through analysis of temperature factors and molecular dynamics simulations of the crystal structures of these mutants, it is demonstrated that the markedly different reductive unfolding rates and pathways of ribonuclease A and its structural homologue onconase can be attributed to a single, localized, ring-stacking interaction between Tyr92 and Pro93 in the bovine variant. The fortuitous location of this specific stabilizing interaction in a disulfide-bond-containing loop region of ribonuclease A results in the localized modulation of protein dynamics that, in turn, enhances the susceptibility of the disulfide bond to reduction leading to an alteration in the reductive unfolding behavior of the homologues. These results have important implications for folding studies involving topological determinants to obtain folding/unfolding rates and pathways, for protein structure-function prediction through fold recognition, and for predicting proteolytic cleavage sites.     

Crosslinked QA‐PEI nanoparticles: synthesis reproducibility,chemical modifications,and stability study

Quaternary ammonium polyethylenimine (QA‐PEI) nanoparticles were synthesized by PEI crosslinking and alkylation with octyliodide followed by quaternization by methyl iodide. The present study focuses on the reproducibility of particles formation with respect to particle size, positive charge, oxidative, thermal stability and antibacterial activity. The QA‐PEI‐based nanoparticles with particle size in the range of 160–190 nm were synthesized in high reproducibility and showed high chemical stability against environmental changes including exposure to different oxidizers and storage conditions. QA‐PEI nanoparticles incorporated in dental restorative resin composites at 2% w/w demonstrated strong antibacterial activity. Copyright © 2013 John Wiley & Sons, Ltd.     

Variational formulation for the stationary fractional advection dispersion equation

In this article a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces H^s. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. Numerical results are included that confirm the theoretical estimates. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005