Robust quaternion matrix completion with applications to image inpainting

In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the ?₁‐norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor‐based completion method, and the quaternion completion method using semidefinite programming.     

Generalized lattice‐BGK concept for thermal and chemically reacting flows at low Mach numbers

The lattice‐BGK method has been extended by introducing additional, free parameters in the original formulation of the lattice‐BGK methods. The relationship between these parameters and the macroscopic moment equations is analysed by Taylor series and Chapman–Enskog expansion. The parameters are determined from the macroscopic moment equations by comparisons with the governing equations to be modelled. Extensions are presented for the Navier–Stokes equations at low Mach numbers in Cartesian or axisymmetric coordinates with constant or variable density, for scalar convection–diffusion equations and for equations of Poisson type. The generalized lattice‐BGK concept is demonstrated by two applications of chemical engineering. These are the computation of chemically reacting flow through an axisymmetric reactor and of the transport and deposition of particles to filters under the action of different forces. Copyright © 2006 John Wiley & Sons, Ltd.     

TWO-DIMENSIONAL NUMERICAL SIMULATION OF LOW FREQUENCY OSCILLATIONS OF SPACE CHARGE AND POTENTIAL IN THE GYROTRON ADIABATIC TRAP

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.     

A Novel Millimeter-Wave Power Combining Circuit

This paper presents the analysis and design of a novel millimeter-wave power combining circuit. This combing circuit is composed of a new style 3-dB combiner, which achieves low-loss, wide-band, and symmetric power division. Different from conventional Wilkinson hybrid, the proposed combiner requires no isolating resistor, and is easier fabricated and more suitable for millimeter integrate circuits. Analytical and experimental work on a two-way combining circuit with wave-guide ports in Ka-band shows the combiner has an insertion loss of 0.2dB, and a power-combining efficiency above 80% in 32–33GHz is obtained.     

Analytical Potential of EDS at low Voltages

 This paper addresses some of the principles underpinning chemical microanalysis of bulk specimens in the scanning electron microscope using low beam voltages ( ≤5 kV) and energy dispersive x-ray spectrometry. The advantages of this relatively new method lie primarily in the strong dependence of the sample penetration range on the electron beam energy (∼10x from 5 kV to 20 kV). This directly yields superior spatial resolution and sensitivity for the analysis of sub-micron particles, surface films and at interfaces. The correspondingly shorter x-ray escape range reduces the importance of the complex matrix absorption and fluorescence terms; the parameters for which may not always be known accurately. A useful x-ray signal can only be generated with a beam energy which is at least 1.3x the excitation energy for the relevant characteristic x-rays. Low voltage fluorescent yields are relatively low and depend strongly on overvoltage (U < 3) and low voltage x-ray signals are relatively weak. These considerations lead to the development of a radical new instrument which produces 9000 counts per second from an Aluminium target with a < 2 nm probe containing 0.2 nA of current at 5 kV, fast submicron resolution x-ray maps ( < 0.1 μm is possible), and close to 1 nm electron image resolution at 1 kV. The greatly improved (15x) EDS sensitivity and superior electron and x-ray imaging are being used to extend, to explore and to exploit more fully the superior performance envelope of the SEM with EDS at low voltages.     

Use of 111In–L–LDL radiotracers to detect human pancreatic and mice melanoma tumors

The present study was designed to evaluate the potential of labeled low‐density lipoprotein with ¹¹¹In using a lipid chelating agent (bis(stearylamide) of diethylenetriaminepentaacetic acid: L) to detect pancreatic tumors and melanoma in mice by gamma‐scintigraphy. We compare the biodistribution of radioactivity and scintigraphic images in nude mice heterotransplanted with human cancerous pancreatic duct cells (Capan‐1) and in mice transplanted with murine tumor cells (B16 melanoma). Biodistribution studies showed that radioactivity was twice as high in the Capan‐1 xenograft after injection of the radiolabel than after injection of radiometal alone, and 34‐fold higher in the B16 tumor. On gamma‐scintigraphic imaging, the Capan‐1 tumor was just visible, whereas the B16 melanoma was clearly imaged. The lack of contrast of the Capan‐1 tumor compared with the B16 melanoma could be due to a poor vascularization. Copyright © 2003 John Wiley & Sons, Ltd.     

Influence of the molecular architecture of low‐density polyethylene on the texture and mechanical properties of blown films

Three types of low‐density polyethylene materials were investigated with respect to the influence of the molecular architecture on the mechanical and use properties of blown films. The materials were a branched polyethylene synthesized by free‐radical polymerization under high‐pressure (HP‐LDPE), a linear ethylene–hexene copolymer (ZN‐LLDPE) produced by low‐pressure Ziegler–Natta catalysis, and an ethylene–hexene copolymer (M‐LLDPE) from metallocene catalysis. The extrusion and blowing conditions were identical for the three materials, with a take‐up ratio of 12 and a blow‐up ratio of 2.5. The blown films displayed a decreasing puncture resistance in the order M‐LLDPE, ZN‐LLDPE, and HP‐LDPE. In parallel, the tear resistance of the films became increasingly unbalanced in the same order of the polymers. The morphological study showed an increased anisotropy of the films in the same polymer order, the crystalline lamellae being increasingly oriented normal to the take‐up direction. This texturing caused a detrimental effect on the mechanical properties of the films, notably increasing the capacity for crack propagation. The phenomenon was ascribed to the kinetics of chain relaxation in the melt that governed the ability of the chains to recover an isotropic state from the flow‐induced stretching before crystallization. The puncture resistance was examined in terms of both texture and strain‐hardening capabilities. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 327–340, 2003     

高能Pb离子辐照注碳SiO2的红外谱研究

室温下，先用120keV的C离子注入二氧化硅薄膜样品至剂量2.0×1017、5.0×1017或8.6×1017ions/cm2，再用950MeV的Pb离子分别辐照至剂量5.0×1011、1.0×1012或3.8×1012 ions/cm2，然后测量样品的傅里叶变换红外(FTIR)光谱. 通过分析测量得到的傅里叶变换红外谱，发现Pb离子辐照在注碳SiO₂样品中可引起大量的Si－C和Si (C)－O－C等化学键的形成，大剂量Pb离子辐照可在大剂量注碳的SiO₂中产生分子CO₂. 大量的Si－C键的存在和分子CO₂的形成，预示着高能Pb离子辐照在注碳SiO₂样品中有可能形成了纳米Si团簇和/或SiC晶粒.