Strong sums of projections in von Neumann factors

This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum converging in the strong operator topology if the collection is infinite. A similar necessary condition is given when the operator and the projections are taken in a type II von Neumann factor, and the condition is proven to be also sufficient if the operator is “diagonalizable”. A simpler necessary and sufficient condition is given in the type III factor case.     

Optimal Estimator for Distributed Anonymous Observers

In this paper, we consider a distributed estimation problem in which multiple observations of a signal process are combined via the maximum function for the decision making. A key result established is that, under suitable technical conditions, the optimal decision function can be implemented by means of thresholds. A natural question is how to determine the optimal threshold value. We propose here an algorithm for threshold adjustment by means of training sequences. The algorithm is a variation of the Kiefer-Wolfowitz algorithm with expanding truncations and randomized differences. A result of the paper is to establish the convergence of the algorithm if the variance of observation noises is small enough.     

A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.     

ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH

In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.     

Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory

The theoretical formulation for bending analysis of functionally graded (FG) rotating disks based on first order shear deformation theory (FSDT) is presented. The material properties of the disk are assumed to be graded in the radial direction by a power law distribution of volume fractions of the constituents. New set of equilibrium equations with small deflections are developed. A semi-analytical solution for displacement field is given under three types of boundary conditions applied for solid and annular disks. Results are verified with known results reported in the literature. Also, mechanical responses are compared between homogeneous and FG disks. It is found that the stress couple resultants in a FG solid disk are less than the stress resultants in full-ceramic and full-metal disk. It is observed that the vertical displacements for FG mounted disk with free condition at the outer surface do not occur between the vertical displacements of the full-metal and full-ceramic disk. More specifically, the vertical displacement in a FG mounted disk with free condition at the outer surface can even be greater than vertical displacement in a full-metal disk. It can be concluded from this work that the gradation of the constitutive components is a significant parameter that can influence the mechanical responses of FG disks.     

A block cipher with dynamic S-boxes based on tent map

In this paper, a block encryption scheme based on dynamic substitution boxes (S-boxes) is proposed. Firstly, the difference trait of the tent map is analyzed. Then, a method for generating S-boxes based on iterating the tent map is presented. The plaintexts are divided into blocks and encrypted with different S-boxes. The cipher blocks are obtained by 32 rounds of substitution and left cyclic shift. To improve the security of the cryptosystem, a cipher feedback is used to change the state value of the tent map, which makes the S-boxes relate to the plaintext and enhances the confusion and diffusion properties of the cryptosystem. Since dynamic S-boxes are used in the encryption, the cryptosystem does not suffer from the problem of fixed structure block ciphers. Theoretical and experimental results indicate that the cryptosystem has high security and is suitable for secure communications.     

Nanostructure PtRu/MWNTs as anode catalysts prepared in a vacuum for direct methanol oxidation

Platinum and ruthenium nanoparticles that are uniformly dispersed on multiwalled carbon nanotubes (MWNTs) were synthesized by vacuum pyrolysis using Pt(acac)2 and Ru(acac)3 as the metal precursors. The resulting nanocomposites were characterized by transmission electron microscopy and X-ray diffraction. The Pt, Pt45Ru55, and Ru nanoparticles had mean diameters of 3.0 +/- 0.6, 2.7 +/- 0.6, and 2.5 +/- 0.4 nm and the same mole number as their metal precursors at 500 degrees C. The electrocatalytic activity of the Pt/MWNTs and PtRu/MWNTs was investigated at room temperature by cyclic voltammetry and chronoamperometry. All of the electrochemical results showed that the PtRu/MWNTs exhibited a high level of catalytic activity for methanol oxidation as a result of the large surface area of the supporting carbon nanotubes and the wide dispersion of the Pt and Ru nanoparticles. Compared with the Pt/MWNTs, the onset potential for methanol oxidation of the PtRu/MWNTs was significantly lower, and the ratio of the forward anodic peak current to the reverse anodic peak current during methanol oxidation was somewhat higher. The Pt45Ru55/MWNTs displayed the best electrocatalytic activity of all of the carbon-nanotube-supported Pt and PtRu catalysts.     

Use of a ruthenium-containing conjugated polymer as a photosensitizer in photovoltaic devices fabricated by a layer-by-layer deposition process

Multilayer polymer films composed of a ruthenium terpyridine complex containing poly(p-phenylenevinylene) (Ru-PPV) and sulfonated polyaniline (SPAN) were prepared by a layer-by-layer electrostatic self-assembly deposition. The deposition process was carried out from SPAN solution in water and Ru-PPV in dimethylformamide (DMF). Optical-quality multilayer thin films were obtained. The film growth process was monitored by quartz crystal microbalance, and the surface morphology of the films was studied by atomic force microscopy. It was found that the properties of the multilayer films were dependent on deposition conditions such as the pH of the SPAN solution, the presence of salt in the polymer solutions, and the post-film-forming thermal annealing process. Cross-section transmission electron microscopic images suggested that there was no stratified structure formed in the multilayer films. Photovoltaic cells were fabricated by sandwiching the multilayer films between indium-tin-oxide and aluminum electrodes. The device performances were examined by illumination with AM 1.5 simulated solar light. The power conversion efficiencies of these devices were on the order of 10(-3)%. The maximum incident photon-to-electron conversion efficiency (IPCE) of the devices was found to be approximately 2% at 510 nm, which is consistent with the absorption maximum of the ruthenium complex. This indicates that the photosensitization process is due to the electronic excitation of the ruthenium complex.     

Sub part-per-million mass accuracy by using stepwise-external calibration in fourier transform ion cyclotron resonance mass spectrometry

A new external calibration procedure for FT-ICR mass spectrometry is presented, stepwise-external calibration. This method is demonstrated for MALDI analysis of peptide mixtures, but is applicable to any ionization method. For this procedure, the masses of analyte peaks are first accurately measured at a low trapping potential (0.63 V) using external calibration. These accurately determined (< 1 ppm accuracy) analyte peaks are used as internal calibrant points for a second mass spectrum that is acquired for the same sample at a higher trapping potential (1.0 V). The second mass spectrum has a approximately 10-fold improvement in detection dynamic range compared with the first spectrum acquired at a low trapping potential. A calibration equation that accounts for local and global space charge is shown to provide mass accuracy with external calibration that is nearly identical to that of internal calibration, without the drawbacks of experimental complexity or reduction of abundance dynamic range. For the 609 mass peaks measured using stepwise-external calibration method, the root-mean-square error is 0.9 ppm. The errors appear to have a Gaussian distribution; 99.3% of the mass errors are shown to lie within three times the sample standard deviation (2.6 ppm) of their true value.     

Combining low and high mass ion accumulation for enhancing shotgun proteome analysis by accurate mass measurement

A simple procedure is described that increases sensitivity and dynamic range for the analysis of a proteome batch digest by FT-ICR mass spectrometry. Ions at the low and high mass ranges are preferentially collected using two different sets of tuning conditions. By combing data collected using tuning conditions that favor low mass (m/z < 2000) and high mass (m/z > 2000) ions, 277 proteins are identified for a whole cell lysate of Methanococcus maripaludis in a single HPLC-MALDI FT-ICR mass spectrometry experiment, a 70% improvement compared with previous analyses using a wide mass range acquisition. This procedure improves the detection of low abundance ions and thereby increases the range of proteins that are observed. Because the observed mass range is effectively narrower for each spectrum, mass calibration is more accurate than for the standard method that provides a wide range of masses. The trap plate potential on the analyzer cell may be set to a higher value than used for wide mass range measurements, increasing the ion capacity of the analyzer cell and extending the dynamic range, while still maintaining mass accuracy.