Numerical implementation of the QMR algorithm by using discrete stochastic arithmetic

In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced byA, it is necessary to decide whether to construct the Lanczos vectorsv _n +1 andw _n +1 as regular or inner vectors. For a regular step it is necessary thatD _k =W _k ^T V _k is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix D_k,σ _min (D _k ), is computed and an inner step is performed ifσ _min (D _k )<∈, where ∈ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance ∈. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.     

Three-dimensional image fusion by use of multiwavelength digital holography

We present three-dimensional (3D) image fusion by use of digital holography. We demonstrate experimentally that, through the image fusion technique with multiresolution wavelet decomposition, it is possible to increase the details and contrast of 3D reconstructed images obtained by multiwavelength digital holography. Although there is substantial activity in the fields of image fusion and holography, to the best of our knowledge, this is the first report of 3D image fusion by use of digital holography.     

Multi-frequency harmonic arrays: initial experience with a novel transducer concept for nonlinear contrast imaging

Nonlinear contrast imaging modes such as second harmonic imaging (HI) and subharmonic imaging (SHI) are increasingly important for clinical applications. However, the performance of currently available transducers for HI and SHI is significantly constrained by their limited bandwidth. To bypass this constraint, a novel transducer concept termed multi-frequency harmonic transducer arrays (MFHA's) has been designed and a preliminary evaluation has been conducted. The MFHA may ultimately be used for broadband contrast enhanced HI and SHI with high dynamic range and consists of three multi-element piezo-composite sub-arrays (A-C) constructed so the center frequencies are 4f(A) = 2f(B) = f(C) (specifically 2.5/5.0/10.0 MHz and 1.75/3.5/7.0 MHz). In principle this enables SHI by transmitting on sub-array C receiving on B and, similarly, from B to A as well as HI by transmitting on A receiving on B and, likewise, from B to C. Initially transmit and receive pressure levels of the arrays were measured with the elements of each sub-array wired in parallel. Following contrast administration, preliminary in vitro HI and SHI signal-to-noise ratios of up to 40 dB were obtained. In conclusion, initial design and in vitro characterization of two MFHA's have been performed. They have an overall broad frequency bandwidth of at least two octaves. Due to the special design of the array assembly, the SNR for HI and SHI was comparable to that of regular B-mode and better than commercially available HI systems. However, further research on multi-element MFHA's is required before their potential for in vivo nonlinear contrast imaging can be assessed.     

Effects of device resolution on three-dimensional integral imaging

We present the effects of a finite number of pixels in elemental images on the resolution and the depth of focus in three-dimensional integral imaging (II). We show that the number of pixels in elemental images determines not only the lateral resolution but also the depth resolution. The minimum number of pixels required in each elemental image is calculated to avoid depth-of-focus degradation. We evaluate how II system performance degrades as the number of pixels in each elemental image changes. The product of the depth of focus and the lateral resolution squared is used as the performance metric.     

Three-dimensional polarimetric integral imaging

A three-dimensional (3D) polarimetric image sensing and display technique based on integral imaging is proposed. Three-dimensional polarization distribution of reflected light from a 3D object can be measured as elemental image arrays by a rotating linear polarizer. After the measurement of the polarization of the 3D object, the 3D polarimetric object can be reconstructed optically by displaying the polarization-selected elemental images in spatial light modulators with two quarter-wave plates. Experimental demonstration of 3D polarimetric imaging of a 3D object attached to two orthogonal linear polarizers is presented. To the best of our knowledge, this is the first report on 3D polarimetric sensing imaging and 3D optical reconstruction by integral imaging.     

Nonlinear signal-processing model for signal generation in multilevel two-dimensional optical storage

A two-dimensional optical storage (TwoDOS) format with binary modulation is being developed in which channel bits are arranged on a two-dimensional hexagonal lattice [W. M. J. Coene, in Optical Data Storage, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), pp. 90-92]. The aim is to increase the capacity by a factor of 2 and the data rate by a factor of 10 over third-generation Blu-ray Disc technology. Following a route similar to that used in one-dimensional conventional optical storage [Jpn. J. Appl. Phys. 42, 1074 (2003)] could lead to a further increase in capacity by the addition of another dimension to writing data, such as the use of multiple levels instead of the two levels (pit and land) used in the binary TwoDOS disk format. We present a nonlinear signal-processing model for signal waveform generation as a function of the M-ary channel symbols, as well as simulated signal readouts for multilevel TwoDOS.     

Three-dimensional integral imaging with large depth of focus by use of real and virtual image fields

We present an integral imaging method to enhance the depth of a three-dimensional image by displaying it throughout real and virtual image fields. When the product of depth and resolution square of the displayed three-dimensional image is used as a figure of merit in integral imaging systems, our method can maximize this merit especially when three-dimensional images with large depth of focus are displayed. The feasibility of our method is experimentally demonstrated by generation of elemental images by a computer.     

Designing different nanomagnets via delocalization of cobalt magnetic moment inside narrow single walled carbon nanotubes

Density functional theory calculations were employed to study the effects of chirality and diameter of single walled carbon nanotubes (SWCNTs) on electronic, structural and magnetic properties of cobalt-doped (9,0), (5,5) and (5,0) nanotube systems. The (9,0) and (5,5) SWCNTs have similar diameters but different chiralities, whereas the (5,0) tube has a very small diameter. The Co-SWCNT systems are considered with four different possible arrangements, three of which are stable and only substitution of the Co with one of the carbon atoms on the surface of the SWCNTs is an exemption. Although the quasi-metallic band gap of the (9,0) SWCNT is eliminated by the cobalt doping process, metallic features of the (5,5) and (5,0) nanotubes remain unchanged. On the other hand, delocalization of the cobalt’s magnetization and inducement of a noticeable magnetization to the tubes provide a vast area of possible total magnetizations for the Co-SWCNT systems. The results are applicable to spintronics and useful for designing other nanomagnetic systems.     

Polystyrene-supported Palladium(II) Ethylenediamine Complex: A Recyclable Catalyst for the Syntheses of 2-Benzyl- imidazo[2,1-b][1,3]benzothiazoles by Sonogashira Reaction

The polymer-supported palladium(II) ethylenediamine complex was used as a catalyst for the heterocyclization during Sonogashira reaction between a substituted phenyl iodide and 2-amino-3-(2-propynyl)-1,3-benzothiazolium bromide, which could readily be recovered from the reaction medium by a simple filtration, and reused without a significant loss in its activity.     

Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called “SANAS” and “SARAF.” In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.