The application of the extended negative factor counting method to deal with the electronic energy levels of pig insulin

The quantum-chemical calculation for pig insulin was done by the ENFC method in which the matrix elements were calculated in the ab initio level with the help of a minimal basis. The aqueous solution surrounding insulin was simulated by putting point charges around the residues that have electric charges. The electronic density of states (DOS) of insulin confirmed the conclusions obtained from aperiodic model peptide chains. It is shown that the frontier orbitals of the insulin were mainly localized on those residues which are involved in the expression of biological activity of insulin.     

A method of calculating eigenvectors of real symmetric tridiagonal matrices in a hyperspherical space

A novel direct method of calculating eigenvectors for real symmetric tridiagonal matrices has been proposed. An eigenvector is represented as a unit vector in a hyperspherical space set by hyperpolar angle coordinates. An algorithm has been examined for a series of tridiagonal matrices. Numerical calculations as compared with a conventional Householder algorithm have shown a good agreement within 8-byte double precision for most eigenvectors computed.     

Concerning the negative thermal expansion for extended chain polyethylene

Thermal expansion coefficients have been measured on ultraoriented polyethylene fibers. Samples were prepared by a solid-state (crystalline) extrusion in an Instron Capillary Rheometer at 136°, 2100 atm. and at a draw ratio of 50. The expansion coefficients between –150 and +50°, perpendicular to the fiber axis, were positive and of the order of 10^–4 °C^–1. Conversely, parallel to that direction, the observed values were both negative and small, of the order –10^–6 °C^–1. Length changes were reversible and reproducible between –150 and < +50°. Negative coefficients were attributed to the presence of highly-extended and fully-aligned chains along the fiber. Valuable information about chain conformation, dynamics and lattice perfection can be obtained for the ultraoriented morphologies simply by measuring the linear thermal expansion.

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Zusammenfassung Thermische Expansionkoeffizienten wurden an ultraorientierten Polyäthylenfasern gemessen. Die Proben wurden durch Festphasen -(kristalliner) Extrusion in einem Instron Kapillar-Rheometer bei 136°, 2100 Atm. und einem Ziehverhältnis von 50 hergestellt. Die zur Achse der Phase perpendikulären Expansionskoeffizienten zwischen –150 und +50° waren positiv und in der Größenordnung von 10^–4°C^–1. Umgekehrt waren die parallel zu dieser Richtung beobachteten Werte sowohl negativ wie auch kleiner, in der Größenordnung von 10^–6 °C^–1. Die Längenveränderungen zwischen –150 und > +50° waren reversibel und reproduzierbar. Negative Koeffizienten wurden der Anwesenheit stark gedehnter und voll geordneter Ketten längs der Fasern zugeschrieben. Wertvolle Informationen betreffs Kettenkonformation, Dynamik und Gitterstruktur ultraorientierter Morphologien können durch einfaches Messen der linearen thermischen Expansion erhalten werden.

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Résumé On a mesuré les coefficients d'expansion thermique de fibres de polyéthylène ultra-orientées. Les échantillons ont été préparés par extrusion à l'état solide (état cristallisé) dans un rhéomètre capillaire Instron, à 136°, 2100 atm., avec un rapport d'étirement de 50. Entre –150 et +50° les coefficients d'expansion perpendiculaires à l'axe des fibres sont positifs et de l'ordre des 10^–4 °C^–1. Les valeurs observées parallèlement à cette direction sont, par contre, négatives et faibles, de l'ordre de –10^–6 °C^–1. Entre –150 et > 50° les changements de longueur sont réversibles et reproductibles. On a attribué les coefficients négatifs à la présence de chaînes fortement allongées et complètement alignées le long des fibres. On peut obtenir des renseignements précieux sur la conformation des chaînes, la dynamique et la perfection des réseaux dans le cas de morphologies ultra-orientées en mesurant simplement l'expansion thermique linéaire.

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. () 136°, 2100 50. –150 +50° 10^–4 °^{– 1}. , , — –10^–6 °^{– 1}. –150 > +50°. - . , .

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On leave from Universidad Nacional del Sur, Bahia Bianca, Argentina.

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Acknowledgement is hereby given to Professor M. Jacovi and Mr. W. Perkins for their help and to the Office of Naval Research for financial support.     

A complementarity for extended Langmuir method

The interaction free energy per unit area between parallel flat plates with high surface potential in the case of constant surface potential is again presented. It is complementarity for extended Langmuir method [G. Luo, H. Wang, J. Jin, Langmuir 17 (2001) 2167 and G. Luo, R. Feng, J. Jin, H. Wang, J. Colloid Interface Sci. 241 (2001) 81]. These approximate expressions work quite well for all values of the surface potentials so as the plates separations are small.     

Rapid method for alpha counting with extractive scintillator and pulse shape analysis

A rapid method for alpha counting with liquid scintillation is presented. The interference of beta and gamma radiation with the determination of alpha emitting nuclides by liquid scintillation counting was examined. In extractive scintillator cocktail, TOPO-PPO-naphthalene-toluene has been developed for transferring actinide elements into organic scintillator and separating the undesirable materials as well as most beta emitters. Pulse Shape Analysis (PSA) was applied for the discrimination of beta radiation. The influence of cocktail composition on PSA has been studied and compared with that of the commercial cocktail. An analytical procedure was suggested for the rapid determination of actinide elements U, Pu, Am and Cm in the nuclear fuel cycle or in environmental samples.     

Lanthanide-transition heterometallic extended structures with novel orthogonal metalloligand as building block

One-dimensional lanthanide-transition heterometallic chains of squares, [LnNi(2)L(3)(HL)(DMF)(4)(ClO(4))(4).S]( infinity ) (Ln = Gd and Tb; HL is the Schiff base obtained by the condensation of 2-pyridylaldehyde with isonicotinic hydrazide N-oxide; S = solvent) and [LnNi(2)L(4)(DMF)(4)(ClO(4))(3).S]( infinity ) (Ln = Dy; S = solvent), were synthesized by self-assembly between well-designed orthogonal metalloligands [Ni(HL)L](+) and the Ln(III) ions, which act as the bridging units and nodes, respectively.     

A software counting loss correction method for neutron activation analysis with short-lived radionuclides

A method has been developed for the correction of counting losses in NAA for the case of a mixture of short-lived radionuclides. It is applicable to systems with Ge detectors and Wilkinson or successive approximation ADC's and will correct losses from pulse pileup and ADC dead time up to 90%. The losses are modeled as a constant plus time-dependent terms expressed as a fourth order polynomial function of the count rates of the short-lived radionuclides. The correction factors are calculated iteratively using the peak areas of the short-lived radionuclides in the spectrum and the average losses as given by the difference between the live time and true time clocks of the MCA. To calibrate the system a measurement is performed for each short-lived nuclide. In a test where the dead time varied from 70% at the start of the measurement to 13% at the end, the measured activities were corrected with an accuracy of 1%.     

The spin-flip extended single excitation configuration interaction method

An extension of the spin-flip single excitation configuration interaction (SF-CIS) method is introduced. The extension, abbreviated as SF-XCIS, includes all configurations in which no more than one virtual level of the high spin triplet reference becomes occupied and no more than one doubly occupied level becomes vacant. The number of such configurations is quadratic with molecule size, and the method is implemented in a direct algorithm whose cost scales in the same way with molecule size as CIS itself, thus permitting applications to large systems. Starting from a spin restricted triplet determinant, SF-XCIS yields spin-pure singlet, triplet, and quintet states, and treats both half-occupied reference orbitals in a fully balanced way to allow application to strongly correlated problems. Tests on bond dissociation in the HF molecule, the torsional potential of ethylene, and excited states of polyenes show encouraging improvements using SF-XCIS compared to SF-CIS and a previously suggested extension, the spin-complete CIS model.     

Differential cross sections for collisions of negative halogen ions and alkali atoms

In this paper we present the relative differential cross sections for collisions of several negative halogen ions with Na and K. The measurements have been carried out in two separate experiments with energy ranges of 5–150 eV and 500–1000 eV and angular ranges of 0-35° and 0-0.3°, respectively. It is shown that in both of these experiments elastic scattering is the dominant process. No significant inelastic contribution to the differetial cross section, especially no electron detachment, has been observed. The measured differential cross sections are used to obtain information on the anion intermolecular potentials. Comparison of these potentials with the potentials of the neutral molecules shows that all systems investigated have a positive electron affinity over a wide range of internuclear distances. An approximately linear relationship between the dipole moments and the electron affinities is obtained for the halides of the specific alkalis.     

A new analytical method for 32P: Liquid scintillation counting with solvent extraction

⁵⁷Fe Mössbauer spectroscopy has been applied to the ultramafic rocks collected from the Jinchuan nickel deposit in China to elucidate their mineralization process. Their Mössbauer spectra consisted of two sextets ascribable to magnetite, two doublets ascribable to Fe²⁺ and Fe³⁺ in chromite, and one doublet ascribable to olivine. The closest sample to the ore body did not contain chromite and contained a doublet ascribable to pyrite and a sextet ascribable to pyrrhotite. The valence and site distribution of iron species suggested low oxygen fugacity for the formation of the Jinchuan nickel deposit.     

Wavelet based spectrum processing for reduction of counting duration for quantitative estimation of ultra-trace activity in environmental matrices

A simple wavelet transformation based pre-processing method is employed to minimize the duration of counting for gamma spectrometric measurements of samples from environmental matrices. Among the various forms of analyzing wavelets, a suitable one is chosen for this purpose. Measurements with 55 different counting durations were subjected to the wavelet based processing and results were compared with long duration counting time measurements of ⁴⁰K, ¹³⁷Cs, radionuclide from ²³⁸U series (²¹⁴Bi, ²¹⁴Pb) and ²³²Th series (²²⁸Ac, ²¹²Bi, ²¹²Pb, ²⁰⁸Tl). It is observed that with a proper choice of the wavelet function a tenfold reduction in counting duration can be achieved with errors <5 %.     

A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.     

The perturbation theory for non-degenerate states and the extended Hückel method

A formal study of the perturbation theory of the pseudosecular equations and particularly of those within the framework of the EHT method, proposed by Hoffmann, is given. In the case of the first-order perturbation in the hamiltonian matrix, it is shown that the classical and the present formalisms are equivalent. In the other more general cases, the recurrence formulae in the n-th order for the eigenvalues and eigenvectors are also given.

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Zusammenfassung Die Störungsrechnung für Pseudo-Säkulärgleichungen, insbesondere für diejenigen, die in der EHT Methode von Hoffmann auftreten, wird untersucht. Im Falle einer Störung erster Ordnung des Hamiltonoperators sind der klassische und der vorliegende Formalismus gleich. In den allgemeineren Fällen werden die Rekursionsformeln n-ter Ordnung für die Eigenwerte und Eigenvektoren gegeben.

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Résumé Etüde formelle de la théorie perturbative des équations pseudo séculaires, en particulier de celles de la méthode EHT de Hoffmann. Au premier ordre de perturbation de la matrice hamiltonienne, le formalisme classique équivaut à celui proposé ici. Dans les autres cas on donne les formules de récurrence à l'ordre n pour les valeurs et les vecteurs propres.

     

A method for population and bonding analyses in calculations with extended basis sets

Summary A method for population and bonding analyses in the calculations with extended basis sets is proposed. The definition and evaluation method of the atomic orbitals in molecular environments (AOIMs) are described. It is shown that the AOIMs can be divided into two subsets, the strongly occupied minimal compact subset {AOIM}_B and the very weakly occupied “Rydberg” subset {AOIM}_R, according to the orbital population obtained from Mulliken analysis with AOIMs as basis sets. The viewpoint of “molecular orbitals consisting of minimal atomic orbital sets” can be optimally realized in terms of {AOIM}_B. The Mulliken population based on AOIMs is reasonable and fairly stable to changes of basis sets. The Mayer bond orders calculated based on {AOIM}_B are quite stable to the changes of basis sets; therefore they can be used to measure objectively the contribution of individual atomic orbitals to bonding.     

The combinatorial factor method for investigation of surface adsorption

In this work, we have used the combinatorial factor method to find the thermodynamic properties of the monolayer surface adsorption with a limited number of rows and nearest neighbor interactions so that the maximum coordination number of each adsorbed particle could be varied from zero to four. The results show that the thermodynamic properties of models with different number of rows are close to each other. In addition, for adsorbed particles with the nearest neighbor interactions, when the fractional coverage becomes 1/2, a phase transition takes place.     

The extended Langmuir's method and its application to double-layer interaction

On the basis of Langmuir's suggestion we simplified Poisson-Boltzmann equation and derived the relation of surface potential, potential midway and the plate distance. Thus we used the force equation derived by Langmuir to calculate the interaction energy. This method may apply to the cases of high potential, low potential, constant potential, and constant charge.     

Theory and algorithm of the inversion method for pentadiagonal matrices

A recently developed inversion method for pentadiagonal matrices is reconsidered in this work. The mathematical structure of the previously suggested method is fully developed. In the process of establishing the mathematical structure, certain determinantial relations specific to pentadiagonal matrices were also established. This led to a rather general necessary and sufficient condition for the method to work. All the so called forward and backward leading principal submatrices need to be non-singular. While this condition sounds restrictive it really is not so. These are in fact the conditions for forward and backward Gauss Eliminations without any pivoting requirement. Additionally, the method is more effective computational complexity wise then recently published competitive methods.     

Coincidence counting for PGNAA applications: Is it the optimum method?

Summary One of the main advantages of γ-γ coincidence counting is the reduction of the background spectrum, pulse pile-up, and summing effects (for simple schemes). For prompt gamma-ray neutron activation analysis (PGNAA), the sources of background include the gamma-rays from the natural background, from surrounding materials, from the neutron source, and from detector neutron activation. While this counting approach effectively increases the signal-to-noise (S/N) ratio, it also decreases the signal counting rate. This adds some practical limitations to using this approach. In this work, two examples are presented for the efficient use of the coincidence counting approach.     

The building block approach to extended solids: 3,5-pyrazoledicarboxylate coordination compounds of increasing dimensionality

A series of M(II) complexes with the ligand 3,5-pyrazoledicarboxylic acid (H3dcp) has been synthesised mainly via hydrothermal reactions and their structures have been characterised. Simple mononuclear [Ni(Hdcp)(H2O)4] (1), Na2(mu-H2O)2(H2O)8[Ni(Hdcp)2(H2O)2] (2), [M(H2dcp)2(H2O)2] x 2H2O [M = Co (3), Zn (4) and Cu (5)] and dinuclear (Et3NH)2[Cu2(dcp)2(H2O)2] (9) building blocks have been isolated and subsequently linked into 1-D chains [Mn(Hdcp)(H2O)2]infinity (6), [[Mn(H2O)4][Mn(Hdcp)2(H2O)2] x 4H2O]infinity (7), [Ni2(Hdcp)2(mu-H2O)2(H2O)2]infinity (8), [[Ni(H2O)4][Ni2(dcp)2(H2O)4]]infinity (11), or 3-D arrays [[Na2(mu-H2O)2][Cu2(dcp)2]]infinity (10), [Cu3(dcp)2(H2O)4]infinity (12), utilising novel bridging modes of the H3dcp ligand. In the unprecedented 1-D Ni(II) chain 8, rarely reported double aqua-bridges link the Ni(II) ions to form an inter-linked double stranded chain. The magnetic properties of these compounds have been measured and reveal a variety of antiferromagnetic coupling behaviours induced by the ligand bridging modes.