Thermal decomposition of titanyl oxalates-I : Barium titanyl oxalate

Thermal decomposition of barium titanyl oxalate tetrahydrate (BTO) has been investigated employing TGA, DTG and DTA techniques and gas and chemical analysis. The decomposition proceeds through five steps and is not affected much by the surrounding gas atmosphere. The first step which is the dehydration of the tetrahydrate is followed by a low-temperature decomposition of the oxalate groups. In the temperature range 190–250°C half a mole of carbon monoxide is evolved with the formation of a transient intermediate containing both oxalate and carbonate groups. The oxalate groups are completely destroyed in the range 250–450°C, resulting in the formation of a carbonate which retains free carbon dioxide in the matrix. The trapped carbon dioxide is released in the temperature range of 460–600°C. The final decomposition of the carbonate takes place between 600–750°C and yields barium titanate. The i.r. spectra, surface area measurements and X-ray, powder diffraction data support entrapment of carbon dioxide in the matrix.

Rank-Augmented LU-Algorithm for Computing Generalized Matrix Inverses

A rank-augmnented LU-algorithm is suggested for computing a generalized inverse of a matrix. Initially suitable diagonal corrections are introduced in (the symmetrized form of) the given matrix to facilitate decomposition; a backward-correction scheme then yields a desired generalized inverse.

The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

On the explicit determination of the polar decomposition in n-dimensional vector spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

Efficient QR Decomposition Using Low Complexity Column-wise Givens Rotation (CGR)

QR decomposition (QRD) is a widely used Numerical Linear Algebra (NLA) kernel with applications ranging from SONAR beamforming to wireless MIMO receivers. In this paper, we propose a novel Givens Rotation (GR) based QRD (GR QRD) where we reduce the computational complexity of GR and exploit higher degree of parallelism. This low complexity Column-wise GR (CGR) can annihilate multiple elements of a column of a matrix simultaneously. The algorithm is first realized on a Two-Dimensional (2 D) systolic array and then implemented on REDEFINE which is a Coarse Grained run-time Reconfigurable Architecture (CGRA). We benchmark the proposed implementation against state-of-the-art implementations to report better throughput, convergence and scalability.

Significant Residue Features Revealed By Eigenvalue Decomposition Analysis Of Blosum Matrices

Here we attempt to characterize protein evolution by residue features which dominate residue substitution in homologous proteins. Evolutionary information contained in residue substitution matrix is abstracted with the method of eigenvalue decomposition. Top eigenvectors in the eigenvalue spectrums are analyzed as function of the level of similarity, i.e. sequence identity (SI) between homologous proteins. It is found that hydrophobicity and volume are two significant residue features conserved in protein evolution. There is a transition point at SI approximate to 45%. Residue hydrophobicity is a feature governing residue substitution as SI >= 45%. Whereas below this SI level, residue volume is a dominant feature. (C) 2007 Elsevier B.V. All rights reserved.

Detection of specific noncovalent protein-fullerenols complexes by matrix-assisted laser desorption ionization mass spectrometry

Matrix-assisted laser desorption ionization (MALDI) mass spectrometry is difficult for the characterization of noncovalent complexes hitherto because of the limitations in acidic matrix, sample preparation, laser-induced polymerization and adduct formation with matrix. Under our experimental conditions, sinapinic acid is used as a matrix, the specific noncovalent interactions of protein with fullerenols were observed by MALDI mass spectrometry. Some mass spectrometric features, such as mass shifts, broad adduct peaks and stoichiometries, showed that the specific non-covalent complexes between protein and fullerenols have been formed at a ratio of 1 : 4 for hemoglobin-fullerenols or 1 : 1 for myoglobin-fullerenols. The results implied that fullereneols could be used to protect partly hemoglobin from decomposition in acidic media, and therefore, it is possible to realize the molecular weight determination of a quaternary protein by MALDI mass spectrometry via the addition of specific organic compound in the matrix.

Matrix-bound phosphine: A new form of phosphorus found in sediment of Jiaozhou Bay

Matrix-bound phosphine (PH3), a new form of phosphorus, was found in sediment of Jiaozhou Bay in December 2001. Concentration and distribution of PH3 in different layers of sediment with different stations were analyzed. The results show that PH3 concentrations are various with different layers and different stations. PH3 concentrations in the bottom layer of sediment (20-30 cm) are usually higher than those in the surface layer (0-4 cm). The highest PH3 concentration in our investigation reaches 685 ng/kg (dry), which is much higher than those in terrestrial paddy soil, marsh and landfill that have been reported up to now. The correlation analysis indicates that there is no apparent correlation between the concentrations of PH3 and inorganic phosphorus in sediment. However, the correlation between the concentrations of phosphine and organic phosphorus in the bottom layer of sediment is remarkable (R-2=0.83). It is mainly considered that PH3 in sediment of Jiaozhou Bay is produced from the decomposition of organic phosphorus in the anaerobic condition, and so PH3 concentrations are related to organic phosphorus concentration and anaerobic environment in sediment. The discovery of PH3 in sediment will give people some new ideas on the mechanisms of phosphorus supplement and biogeochemical cycle in Jiaozhou Bay.

Distribution characteristics of matrix-bound phosphine along the coast of China and possible environmental controls

Matrix-bound phosphine (MBP) concentrations in surface sediments collected from 37 stations along the coast of China in 2006 are reported. MBP was found in all samples and the average concentration was 6.30 ng kg(-1) dry weight (dw). The distribution of MBP showed certain spatial variation characteristics with high MBP concentrations at stations near to the coast. The average concentrations of MBP in the northern Yellow Sea (NYS), the southern Yellow Sea (SYS), the northern area of East China Sea (NECS), the southern area of East China Sea (SECS), and South China Sea (SCS) were 5.57 +/- 3.78, 3.78 +/- 2.81, 5.27 +/- 3.07, 5.48 +/- 4.05 and 13.52 +/- 7.86 ng kg(-1) dw. respectively. The correlations between MBP and influencing factors, such as the sedimentary environmental characteristics (sediment type, the grain size, contents of phosphorous, organic matters and redox potential) and the aquatic environmental characteristics (temperature, salinity, depth and hydrodynamics) were studied. The results indicated that MBP was strongly influenced by various factors, such as total phosphorus (TP), organic phosphorus (OP), organic carbon (OC), the grain size and hydrodynamics, all of which not only offered reasonable interpretations for the distribution characteristics of MBP but also provided evidence to support the viewpoint that phosphine originated from OP decomposition. This work is the first comprehensive study of the distribution of MBP along the coast of China and its relationships with environmental factors which will lead to a better understanding of the phosphorus (P) biogeochemical cycle in the sea. (C) 2008 Elsevier Ltd. All rights reserved.

A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

Decomposition of spectral density in individual eigenvalue contributions

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

The competition between metastable and equilibrium S (Al2CuMg) phase during the decomposition of AlCuMg alloys

Abstract The decomposition sequence of the supersaturated solid solution leading to the formation of the equilibrium S (Al2CuMg) phase in AlCuMg alloys has long been the subject of ambiguity and debate. Recent high-resolution synchrotron powder diffraction experiments have shown that the decomposition sequence does involve a metastable variant of the S phase (denoted S1), which has lattice parameters that are distinctly different to those of the equilibrium S phase (denoted S2). In this paper, the difference between these two phases is resolved using high-resolution synchrotron and neutron powder diffraction and atom probe tomography, and the transformation from S1 to S2 is characterised in detail by in situ synchrotron powder diffraction. The results of these experiments confirm that there are no significant differences between the crystal structures of S1 and S2, however, the powder diffraction and atom probe measurements both indicate that the S1 phase forms with a slight deficiency in Cu. The in situ isothermal aging experiments show that S1 forms rapidly, reaching its maximum concentration in only a few minutes at high temperatures, while complete conversion to the S2 phase can take thousands of hours at low temperature. The kinetics of S phase precipitation have been quantitatively analysed for the first time and it is shown that S1 phase forms with an average activation energy of 75 kJ/mol, which is much lower than the activation energy for Cu and Mg diffusion in an Al matrix (136 kJ/mol and 131 kJ/mol, respectively). The mechanism of the replacement of S1 with the equilibrium S2 phase is discussed.