Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Thermogravimetric determination of the carbon dioxide reactivity of char from some New Zealand coals and its association with the inorganic geochemistry of the parent coal

Thermogravimetrically-determined carbon dioxide reactivities of chars formed from New Zealand coals, ranging in rank from lignite to high volatile bituminous, vary from 0.12 to 10.63 mg/h/mg on a dry, ash-free basis. The lowest rank subbituminous coal chars have similar reactivities to the lignite coal chars. Calcium content of the char shows the strongest correlation with reactivity, which increases as the calcium content increases. High calcium per se does not directly imply a high char reactivity. Organically-bound calcium catalyses the conversion of carbon to carbon monoxide in the presence of carbon dioxide, whereas calcium present as discrete minerals in the coal matrix, e.g., calcite, fails to significantly affect reactivity. Catalytic effects of magnesium, iron, sodium and phosphorous are not as obvious, but can be recognised for individual chars. The thermogravimetric technique provides a fast, reliable analysis that is able to distinguish char reactivity differences between coals, which may be due to any of the above effects. Published by Elsevier Science B.V.

Bioimpedance spectrometry in the determination of body water compartments: Accuracy and clinical significance

Bioelectrical impedance analysis (BIA) offers the potential for a simple, portable and relatively inexpensive technique for the in vivo measurement of total body water (TBW). The potential of BIA as a technique of body composition analysis is even greater when one considers that body water can be used as a surrogate measure of lean body mass. However, BIA has not found universal acceptance even with the introduction of multi-frequency BIA (MFBIA) which, potentially, may improve the predictive accuracy of the measurement. There are a number of reasons for this lack of acceptance, although perhaps the major reason is that no single algorithm has been developed which can be applied to all subject groups. This may be due, in part, to the commonly used wrist-to-ankle protocol which is not indicated by the basic theory of bioimpedance, where the body is considered as five interconnecting cylinders. Several workers have suggested the use of segmental BIA measurements to provide a protocol more in keeping with basic theory. However, there are other difficulties associated with the application of BIA, such as effects of hydration and ion status, posture and fluid distribution. A further putative advantage of MFBIA is the independent assessment not only of TBW but also of the extracellular fluid volume (ECW), hence heralding the possibility of,being able to assess the fluid distribution between these compartments. Results of studies in this area have been, to date, mixed. Whereas strong relationships of impedance values at low frequencies with ECW, and at high frequencies with TBW, have been reported, changes in impedance are not always well correlated with changes in the size of the fluid compartments (assessed by alternative and more direct means) in pathological conditions. Furthermore, the theoretical advantages of Cole-Cole modelling over selected frequency prediction have not always been apparent. This review will consider the principles, methodology and applications of BIA. The principles and methodology will,be considered in relation to the basic theory of BIA and difficulties experienced in its application. The relative merits of single and multiple frequency BIA will be addressed, with particular attention to the latter's role in the assessment of compartmental fluid volumes. (C) 1998 Elsevier Science Ltd. All rights reserved.

Structure determination of the three disulfide bond isomers of alpha-conotoxin GI: A model for the role of disulfide bonds in structural stability

The three possible disulfide bonded isomers of alpha-conotoxin GI have been selectively synthesised and their structures determined by H-1 NMR spectroscopy. alpha-Conotoxin GI derives from the venom of Conus geographus and is a useful neuropharmacological tool as it selectively binds to the nicotinic acetylcholine receptor (nAChR), a ligand-gated ion channel involved in nerve signal transmission. The peptide has the sequence ECCNPACGRHYSC-NH2, and the three disulfide bonded isomers are referred to as GI(2-7;3-13), GI(2-13;3-7) and GI(2-3;7-13). The NMR structure for the native isomer GI(2-7;3-13) is of excellent quality, with a backbone pairwise RMSD of 0.16 Angstrom for a family of 35 structures, and comprises primarily a distorted 3(10),, helix between residues 5 to 11. The two non-native isomers exhibit multiple conformers in solution, with the major populated forms being different in structure both from each other and from the native form. Structure-activity relationships for the native GI(2-7;3-13) as well as the role of the disulfide bonds on folding and stability of the three isomers are examined. It is concluded that the disulfide bonds in alpha-conotoxin GI play a crucial part in determining both the structure and stability of the peptide. A trend for increased conformational heterogeneity was observed in the order of GI(2-7;3-13) < GI(2-13;3-7) < GI(2-3;7-13). It was found that the peptide bond joining Cys2 to Cys3 in GI(2-3;7-13) is predominantly trans, rather than cis as theoretically predicted. These structural data are used to interpret the varying nAChR binding of the non-native forms. A model for the binding of native GI(2-7;3-13) to the mammalian nAChR is proposed, with an alpha-subunit binding face made up of Cys2, Asn4, Pro5, Ala6 and Cys7 and a selectivity face, comprised of Arg9 and His10. These two faces orient the molecule between the alpha and delta subunits of the receptor. The structure of the CCNPAC sequence of the native GI(2-7;3-13) is compared to the structure of the identical sequence from the toxic domain of heat-stable enterotoxins, which forms part of the receptor binding region of the enterotoxins, but which has a different disulfide connectivity. (C) 1998 Academic Press Limited.

FRA10B structure reveals common elements in repeat expansion and chromosomal fragile site genesis

A common mechanism for chromosomal fragile site genesis is not yet apparent. Folate-sensitive fragile sites are expanded p(CCG)n repeats that arise from longer normal alleles. Distamycin A or bromodeoxyuridine-inducible fragile site FRA16B is an expanded AT-rich similar to 33 bp repeat; however, the relationship between normal and fragile site alleles is not known. Here, we report that bromodeoxyuridine-inducible, distamycin A-insensitive fragile site FRA10B is composed of expanded similar to 42 bp repeats. Differences in repeat motif length or composition between different FRA10B families indicate multiple independent expansion events. Some FRA10B alleles comprise a mixture of different expanded repeat motifs. FRA10B fragile site and long normal alleles share flanking polymorphisms. Somatic and intergenerational FRA10B repeat instability analogous to that found in expanded trinucleotide repeats supports dynamic mutation as a common mechanism for repeat expansion.

Determination of pore size distributions by regularization and finite element collocation

The problem of extracting pore size distributions from characterization data is solved here with particular reference to adsorption. The technique developed is based on a finite element collocation discretization of the adsorption integral, with fitting of the isotherm data by least squares using regularization. A rapid and simple technique for ensuring non-negativity of the solutions is also developed which modifies the original solution having some negativity. The technique yields stable and converged solutions, and is implemented in a package RIDFEC. The package is demonstrated to be robust, yielding results which are less sensitive to experimental error than conventional methods, with fitting errors matching the known data error. It is shown that the choice of relative or absolute error norm in the least-squares analysis is best based on the kind of error in the data. (C) 1998 Elsevier Science Ltd. All rights reserved.

Determination of pindolol enantiomers in human plasma and urine by simple liquid-liquid extraction and high-performance liquid chromatography

A simple method for the measurement of pindolol enantiomers by HPLC is presented. Alkalinized serum or urine is extracted with ethyl acetate and the residue remaining after evaporation of the organic layer is then derivatised with (S)-(-)-alpha-methylbenzyl isocyanate. The diastereoisomers of derivatised pindolol and metoprolol (internal standard) are separated by high-performance liquid chromatography (HPLC) using a C-18 silica column and detected using fluorescence (excitation lambda: 215 nm, emission lambda: 320 nm). The assay displays reproducible linearity for pindolol enantiomers with a correlation coefficient of r(2) greater than or equal to 0.998 over the concentration range 8-100 ng ml(-1) for plasma and 0.1-2.5 mu g ml(-1) for urine. The coefficient of variation for accuracy and precision of the quality control samples for both plasma and urine are consistently

Improved high-performance liquid chromatography determination of methotrexate and its major metabolite in plasma using a poly(styrene-divinylbenzene) column

A sensitive high-performance liquid chromatographic assay has been developed for measuring plasma concentrations of methotrexate and its major metabolite, 7-hydroxymethotrexate. Methotrexate and metabolite were extracted from plasma using solid-phase extraction. An internal standard, aminopterin was used. Chromatographic separation was achieved using a 15-cm poly(styrene-divinylbenzene) (PRP-1(R)) column. This column is more robust than a silica-based stationary phase. Post column, the eluent was irradiated with UV light, producing fluorescent photolytic degradation products of methotrexate and the metabolite. The excitation and emission wavelengths of fluorescence detection were at 350 and 435 nm, respectively. The mobile phase consisted of 0.1 M phosphate buffer (pH 6.5), with 6% N,N-dimethylformamide and 0.2% of 30% hydrogen peroxide. The absolute recoveries for methotrexate and 7-hydroxymethotrexate were greater than 86%. Precision, expressed as a coefficient of variation (n=6), was

Determination of Ralstonia (Pseudomonas) solanacearum rDNA subgroups by PCR tests

Rapid and sensitive polymerase chain reaction (PCR) methods ape described for determination of the two 16 S rDNA subgroups of Ralstonia solanacearum, the causal agent of bacterial wilt. A third subgroup consisting of Indonesian R. solanacearum isolates belonging to Division II, the blood disease bacterium and Pseudomonas syzygii can also be identified. Primers were designed to sequences within R, solanacearum 16 S rDNA (equivalent to Escherichia coli 16 S rDNA positions 74-97, 455-475, 1454-1474), and the internal transcribed spacer region between the 16 S and 23 S rDNA genes. Different combinations of forward and reverse primers allowed selective PCR amplification of (a) R. solanacearum Division I (biovars 3, 4 and 5), (b) Division TI (biovars 1, N2, and 2) including the blood disease bacterium and P. syzygii, or (c) amplification of Division II only except for five biovar 1, 2 or N2 isolates of R. solanacearum from Indonesia, P. syzygii and the BDB. A total of 104 R. solanacearum, 14 blood disease bacterium and 10 P. syzygii isolates were tested. Simultaneous detection of species and subdivision was achieved by designing a multiplex PCR test in which a 288-base pair (bp) band is produced by all R. solanacearum isolates, and an additional 409-bp band in Division I strains.

Determination of chemical shielding tensor of an indole carbon and application of tryptophan orientation of a membrane peptide

Using tryptophan C-13-enriched at the C-4 (C epsilon(3)) of the indole, the orientation of the C epsilon(3) chemical shift tensor relative to the C epsilon(3)-H dipolar axis was determined from the C-13 chemical shift/C-13-H-1 dipolar 2D NMR powder pattern. The principal values obtained were 208, 137 and 15 ppm with sigma(33) perpendicular to the indole plane, and sigma(11) (least shielded direction) 5 degrees off the C epsilon(3)-H bond toward C xi(3). The side off the C epsilon(3)-H bond was determined by comparing the reduced chemical shift anisotropies obtained by solid-state NMR and from molecular dynamics calculations of [4-C-13] tryptophans in gramicidin A aligned in phospholipid membranes. (C) 1999 Elsevier Science B.V. All rights reserved.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Soil carbon determination by high temperature combustion - A comparison with dichromate oxidation procedures and the influence of charcoal and carbonate carbon on the measured value

The measurement of organic carbon in soils has traditionally used dichromate oxidation procedures including the Wakley and Black and the Heanes methods. The measurement of carbon in soils by high temperature combustion is now widely used providing a rapid automated procedure without the use of toxic chemicals. This procedure however measures total carbon thus requiring some means of correction for soil samples containing carbonate and charcoal forms of carbon. This paper examines the effects of known additions of charcoal to a range of soil types on the results obtained by the Walkley and Black, Heanes and combustion methods. The results show, that while the charcoal carbon does not react under Walkley and Black conditions, some proportion does so with the Heanes method. A comparison of six Australian Soil and Plant Analysis Council reference soil samples by the three methods showed good agreement between the Heanes method, the combustion method and only slightly lower recoveries by the Walkley and Black procedure. Carbonate carbon will cause an overestimation of soil organic carbon by the combustion method thus requiring a separate determination of carbonate carbon to be applied as a correction. This work shows that a suitable acid pre-treatment of alkaline soils in the sample boats followed by a drying step eliminates the carbonate carbon prior to combustion and the need for an additional measurement. The measurement of carbon in soils by high temperature combustion in an oxygen atmosphere has been shown to be a rapid and reliable method capable of producing results in good agreement with one of the established dichromate oxidation procedures.