An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

On formation, growth and concentrations of air ions

Aerosol particles have effect on climate, visibility, air quality and human health. However, the strength of which aerosol particles affect our everyday life is not well described or entirely understood. Therefore, investigations of different processes and phenomena including e.g. primary particle sources, initial steps of secondary particle formation and growth, significance of charged particles in particle formation, as well as redistribution mechanisms in the atmosphere are required. In this work sources, sinks and concentrations of air ions (charged molecules, cluster and particles) were investigated directly by measuring air molecule ionising components (i.e. radon activity concentrations and external radiation dose rates) and charged particle size distributions, as well as based on literature review. The obtained results gave comprehensive and valuable picture of the spatial and temporal variation of the air ion sources, sinks and concentrations to use as input parameters in local and global scale climate models. Newly developed air ion spectrometers (Airel Ltd.) offered a possibility to investigate atmospheric (charged) particle formation and growth at sub-3 nm sizes. Therefore, new visual classification schemes for charged particle formation events were developed, and a newly developed particle growth rate method was tested with over one year dataset. These data analysis methods have been widely utilised by other researchers since introducing them. This thesis resulted interesting characteristics of atmospheric particle formation and growth: e.g. particle growth may sometimes be suppressed before detection limit (~ 3 nm) of traditional aerosol instruments, particle formation may take place during daytime as well as in the evening, growth rates of sub-3 nm particles were quite constant throughout the year while growth rates of larger particles (3-20 nm in diameter) were higher during summer compared to winter. These observations were thought to be a consequence of availability of condensing vapours. The observations of this thesis offered new understanding of the particle formation in the atmosphere. However, the role of ions in particle formation, which is not well understood with current knowledge, requires further research in future.

Crystallization characteristics of vitrovac 4040 (Fe39Ni39Mo4Si6B12)

The metallic glass Vitrovac 4040 with the composition Fe39Ni39Mo4Si6B12 crystallizes in the order alpha-Fe, hexagonal Ni5Si2 and gamma-(Fe,Ni,Mo) by primary, secondary and polymorphic modes, respectively. The activation energies determined from the non-isothermal kinetics using Kissinger method turn out to be 490, 550 and 449 kJ.mol-1 for the above crystallization reactions. It has been observed that alpha transforms to gamma during annealing. Further, the bct (Fe1-xNix)3B phase has been identified when the glass is annealed above 1023 K.

Synthesis Of (+/-)-Beta-Cuparenone Via 3-Oxa-Beta-Cuparenone

Grignard reaction followed by ozonolysis, or ozonolysis followed by Grignard reaction on the pentenoate 8, generates the diol 9. Cyclodehydration of 9 leads to the 3-oxacuparene (6), whereas PCC oxidation furnishes the 3-oxa-beta-cuparenone (7). Methanesulfonic acid-P2O5 transforms 7 into cyclopentenones 4, 5, known precursors to beta-cuparenone (3), and the naphthalenone 14.

The identification of 14 alpha,17 beta-dihydroxyandrost-4-en-3-one monohydrate and 14 alpha,17 beta-dihydroxyandrosta-1,4-dien-3-one monohydrate, metabolites of androstenedione in Mucor piriformis

The microorganism Mucor piriformis transforms androst-4-ene-3,17-dione into a major and several minor metabolites. X-ray crystallographic analysis of two of these metabolites was undertaken to determine unambiguously their composition and chirality. Crystals belong to the orthorhombic space-group P2(1)2(1)2(1), with a = 7.199(4) angstrom and a = 6.023(3) angstrom, b = 11.719(3) angstrom and b = 13.455(4) angstrom, c = 20.409(3) angstrom and c = 20.702(4) angstrom for the two title compounds, respectively. The structures have been refined to final R values of 0.060 and 0.040, respectively.

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

The general time dependent source problem has been solved by the method of transforms (Laplace, Lebedev–Kontorovich in succession) and the solution is obtained in the form of an infinite series involving Legendre functions. The solutions in the case of harmonic time dependence and the incident plane wave have been derived from the above solution and are presented in the form of an infinite series. In the case of an incident plane wave, the series has been summed and the final solution involves an improper integral which behaves like a complementary error function for large values of the argument. Finally, the far field evaluation has been shown. The results are compared with those of Sommerfeld's half-plane diffraction problem with unmixed boundary conditions.

Structure of Relativistic States

QCD factorization in the Bjorken limit allows to separate the long-distance physics from the hard subprocess. At leading twist, only one parton in each hadron is coherent with the hard subprocess. Higher twist effects increase as one of the active partons carries most of the longitudinal momentum of the hadron, x -> 1. In the Drell-Yan process \pi N -> \mu^- mu^+ + X, the polarization of the virtual photon is observed to change to longitudinal when the photon carries x_F > 0.6 of the pion. I define and study the Berger-Brodsky limit of Q^2 -> \infty with Q^2(1-x) fixed. A new kind of factorization holds in the Drell-Yan process in this limit, in which both pion valence quarks are coherent with the hard subprocess, the virtual photon is longitudinal rather than transverse, and the cross section is proportional to a multiparton distribution. Generalized parton distributions contain information on the longitudinal momentum and transverse position densities of partons in a hadron. Transverse charge densities are Fourier transforms of the electromagnetic form factors. I discuss the application of these methods to the QED electron, studying the form factors, charge densities and spin distributions of the leading order |e\gamma> Fock state in impact parameter and longitudinal momentum space. I show how the transverse shape of any virtual photon induced process, \gamma^*(q)+i -> f, may be measured. Qualitative arguments concerning the size of such transitions have been previously made in the literature, but without a precise analysis. Properly defined, the amplitudes and the cross section in impact parameter space provide information on the transverse shape of the transition process.

An in situ electron microscope investigation of the icosahedral-to-decagonal quasicrystalline transformation in Al-20 at.% Mn

The solid-state transformation behaviour of the icosahedral phase in rapidly solidified Al-20 at.% Mn has been investigated by in situ heating experiments in the transmission electron microscope. As-rapidly-solidified Al-20 at.% Mn consists mainly of a dendritic icosahedral phase, with a small amount of interdendritic f.c.c. agr-Al. During subsequent heat treatment at temperatures below about 500°C, the dendritic icosahedral phase grows and consumes the interdendritic agr-Al. At about 500°C the decagonal phase nucleates near icosahedral dendrite and grain boundaries and then grows into the icosahedral matrix by lateral motion of ledges 10-20 nm high across facet planes normal to the twofold symmetry axes. At about 600°C the decagonal phase transforms into a crystalline phase. The present study suggests that solid-state decomposition of the icosahedral phase is the mechanism of decagonal phase formation in as-rapidly-solidified Al-Mn alloys.

Optimal explicit guidance of multistage launch vehicle along three-dimensional trajectory

Details of an efficient optimal closed-loop guidance algorithm for a three-dimensional launch are presented with simulation results. Two types of orbital injections, with either true anomaly or argument of perigee being free at injection, are considered. The resulting steering-angle profile under the assumption of uniform gravity lies in a canted plane which transforms a three-dimensional problem into an equivalent two-dimensional one. Effects of thrust are estimated using a series in a recursive way. Encke's method is used to predict the trajectory during powered flight and then to compute the changes due to actual gravity using two gravity-related vectors. Guidance parameters are evaluated using the linear differential correction method. Optimality of the algorithm is tested against a standard ground-based trajectory optimization package. The performance of the algorithm is tested for accuracy, robustness, and efficiency for a sun-synchronous mission involving guidance for a multistage vehicle that requires large pitch and yaw maneuver. To demonstrate applicability of the algorithm to a range of missions, injection into a geostationary transfer orbit is also considered. The performance of the present algorithm is found to be much better than others.

Detection of edges from projections

In a number of applications of computerized tomography, the ultimate goal is to detect and characterize objects within a cross section. Detection of edges of different contrast regions yields the required information. The problem of detecting edges from projection data is addressed. It is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data. This not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image. This is accomplished by a convolution backprojection operation. For example, with the Marr-Hildreth edge detection operator, the filtering function that is to be used on the projection data is the Radon transform of the Laplacian of the 2-D Gaussian function which is combined with the reconstruction filter. Simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented

Effect of substrate temperature on the properties of ZrO2 films prepared by d.c. reactive magnetron sputtering

Studies of ZrO2 films prepared by d.c. reactive magnetron sputtering are described. The effects of substrate temperature on the packing density, refractive index, extinction coefficient and crystallinity phase have been investigated in the temperature range 25–450 °C. The refractive index varied from 1.84 to 1.95 and extinction coefficient from 2 × 10−3 to 9.6 × 10−3. This was explained on the basis of an increase in packing density from 0.686 to 0.813. The change in packing density has been attributed to a decrease in the oxygen condensation at higher temperatures. Annealing results in a decrease in refractive index and increase in extinction coefficient. The films deposited at 150 °C showed a monoclinic phase which transforms to a tetragonal phase at higher substrate temperatures.

Fluorination of La2NiO4 and La2CuO4+?

We have carried out fluorination on La2NiO4 and La2CuO4+?. Only a small fraction of fluorine enters the bulk; the rest resides on the surface. The cuprate after fluorination exhibits greater departures from tetragonal symmetry than the parent material and transforms at not, vert, similar40 K to the superconducting state. By contrast, the nickelate deviates less from tetragonal symmetry upon fluorination; no superconductivity was observed down to 4.2 K.

Effect of Li+-ion on enhancement of photoluminescence in Gd2O3:Eu3+ nanophosphors prepared by combustion technique

Gd2O3:Eu3+ (4 mol%) nanophosphor co-doped with Li+ ions have been synthesized by low-temperature solution combustion technique in a short time. Powder X-ray diffractometer (PXRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR), UV-VIS and photoluminescence (PL) techniques have been employed to characterize the synthesized nanoparticles. It is found that the lattice of Gd2O3:Eu3+ phosphor transforms from monoclinic to cubic as the Li+-ions are doped. Upon 254 nm excitation, the phosphor showed characteristic luminescence D-5(0) -> F-7(J) (J= 0-4) of the Eu3+ ions. The electronic transition located at 626 nm (D-5(0) -> F-7(2)) of Eu3+ ions was stronger than the magnetic dipole transition located at 595 nm (D-5(0) -> F-7(1)). Furthermore, the effects of the Li+ co-doping as well as calcinations temperature on the PL properties have been studied. The results show that incorporation of Li+ ions in Gd2O3:Eu3+ lattice could induce a remarkable improvement of their PL intensity. The emission intensity was observed to be enhanced four times than that of with out Li+-doped Gd2O3:Eu3+. (C) 2010 Elsevier B.V. All rights reserved,

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

Quasicrystals, crystals and multiple twins in rapidly solidified Al-Cr-Si, Al-Mn-Si and Al-Mn-Cr-Si alloys

The coexistence of quasicrystals and rational approximant structures (RAS) has been observed in melt-spun Al80Cr14Si6, Al80Mn14Si6 and Al75Mn10Cr5Si10 alloys. The presence of a b.c.c. alpha-AlMnSi phase in Al-Mn-Si and alpha-AlMnSi(Cr) phase in Al-Mn-Cr-Si has been seen. A multiple twinning around an irrational axis of the RAS has been reported in an aggregate of fine size cubic crystallites in all three alloys. Selected area diffraction patterns show that the crystalline aggregate symmetry is linked to the icosahedral point group symmetry (m35). Various ways of expressing the twin relationship in the cubic crystalline aggregates have been discussed. The thermal stability of the icosahedral phase at high temperatures reveals that the icosahedral phase in Al-Mn-Si and Al-Mn-Cr-Si alloys transforms to alpha-AlMnSi at temperatures of 690 and 670 K, respectively. In Al-Cr-Si alloy, heating to a high temperature (615 K) leads to the transformation of the icosahedral phase into a new metastable phase having an ordered cubic structure equivalent to alpha-AlMnSi. The occurrence of multiple twinning leading to icosahedral symmetry in the as-spun Al-Cr-Si alloy is presumably due to this metastable phase. Copyright (C) 1996 Acta Metallurgica Inc.