Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio

Accidental Degeneracy and Berry Phase of Resonant States

We study the complex geometric phase acquired by the resonant states of an open quantum system which evolves irreversibly in a slowly time dependent environment. In analogy with the case of bound states, the Berry phase factors of resonant states are holonomy group elements of a complex line bundle with structure group C*. In sharp contrast with bound states, accidental degeneracies of resonances produce a continuous closed line of singularities formally equivalent to a continuous distribution of "magnetic" charge on a "diabolical" circle, in consequence, we find different classes of topologically inequivalent non-trivial closed paths in parameter space.Comment: 23 pages, 2 Postscript figures, LaTex, to be published in: Group 21: Symposium on Semigroups and Quantum Irreversibility (Proc. of the XXI Int. Colloquium on Group Theoretical Methods in Physics

Variational separable expansion scheme for two-body Coulomb-scattering problems

We present a separable expansion approximation method for Coulomb-like potentials which is based on Schwinger variational principle and uses Coulomb-Sturmian functions as basis states. The new scheme provides faster convergence with respect to our formerly used non-variational approach.Comment: some typos correcte

A superadditivity and submultiplicativity property for cardinalities of sumsets

For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold sumset A1 + · · · + An compared to those of (n − 1)-fold sumsets A1 + · · · + Ai−1 + Ai+1 + · · · + An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets

Altered mitochondrial response to activation of T-cells in neonate

Mitochondrial functions have a major impact on T-cell functionality. In this study we characterized whether mitochondrial function in the neonatal T-cells differs from that in the adult T-cells during short T-cell activation. Methods: We used fow cytometry methods to test mitochondrial mass and to monitor mitochondrial Ca2+ levels, mitochondrial potential and superoxide generation in parallel with cytoplasmic Ca2+ levels during phythohaemagglutinine-induced activation of CD4+ and CD8+ T-cells of 12 term neonates and 11 healthy adults. Results: Baseline mitochondrial mass of CD4+ and CD8+ cells was lower in the neonate than in the adult. In comparison with the adult, neonatal resting CD4+ T-cells had lower cytoplasmic Ca2+ levels and this was associated with normal activation induced Ca2+-response. During short-term activation cytoplasmic Ca2+-response was lower in neonatal than in adult CD8+ T-cells. Mitochondrial Ca2+ uptake was increased in CD4+ neonatal T cells while it decreased in CD8+ T-cells. Mitochondrial depolarization was increased in CD4+ and decreased in CD8+ neonatal T-cells compared to adults. Superoxide generation was higher and equal in neonatal CD4+ and CD8+ cells, respectively, compared to the adult ones. Conclusion: Our data suggest that neonatal T-cells exhibit marked differences in mitochondrial function and superoxide generation compared to adult T-cells

Altered mitochondrial response to activation of T-cells in neonate

Mitochondrial functions have a major impact on T-cell functionality. In this study we characterized whether mitochondrial function in the neonatal T-cells differs from that in the adult T-cells during short T-cell activation. METHODS: We used fow cytometry methods to test mitochondrial mass and to monitor mitochondrial Ca(2+) levels, mitochondrial potential and superoxide generation in parallel with cytoplasmic Ca(2+) levels during phythohaemagglutinine-induced activation of CD4+ and CD8+ T-cells of 12 term neonates and 11 healthy adults. RESULTS: Baseline mitochondrial mass of CD4+ and CD8+ cells was lower in the neonate than in the adult. In comparison with the adult, neonatal resting CD4+ T-cells had lower cytoplasmic Ca(2+) levels and this was associated with normal activation induced Ca(2+)-response. During short-term activation cytoplasmic Ca(2+)-response was lower in neonatal than in adult CD8+ T-cells. Mitochondrial Ca(2+) uptake was increased in CD4+ neonatal T cells while it decreased in CD8+ T-cells. Mitochondrial depolarization was increased in CD4+ and decreased in CD8+ neonatal T-cells compared to adults. Superoxide generation was higher and equal in neonatal CD4+ and CD8+ cells, respectively, compared to the adult ones. CONCLUSION: Our data suggest that neonatal T-cells exhibit marked differences in mitochondrial function and superoxide generation compared to adult T-cells

Wang Bi\u27s Annotation on Laozi\u27s Place in China and Japan: Focusing on Ogyu Sorai

Wang Bi\u27s Annotation on Laozi 『老子』王弼注 is considered one of the representative notes on Laozi. In Chinahowever, it was not until 1781 when this book was included in Sikuquanshu 『四庫全書』 that the study of Wang Bi\u27s note became popular. In Japan, while Wang Bi\u27s note was introduced before the 5th century, it received rare recognition until Okada Touin\u27s Laozi Daodejing Annotated by Wang Bi 岡田東贇 『老子道徳経王弼注』 published in 1734. However, further research reveals that Ogyu Sorai 荻生徂徠 had pointed out in Keishishiyohran 『経子史要覧』 that, in reading Laozi from the view of classical rhetoric 古文辞学 Wang Bi\u27s annotation should be referred to. Keishishiyohran was based on Sorai\u27s dictation before 1728, and it was earlier than both Okada Touin\u27s Laozi Annotated by Wang Bi (1734) and Sikuquanshu (1781). Therefore< judging from evidences currently available, it seems fair to conclude that Sorai was the pioneer who introduced Wang Bi\u27s annotation into the field of Laozi studies

Decoherence time in self-induced decoherence

A general method for obtaining the decoherence time in self-induced decoherence is presented. In particular, it is shown that such a time can be computed from the poles of the resolvent or of the initial conditions in the complex extension of the Hamiltonian's spectrum. Several decoherence times are estimated: $10^{-13}-$ $10^{-15}s$ for microscopic systems, and $10^{-37}-10^{-39}s$ for macroscopic bodies. For the particular case of a thermal bath, our results agree with those obtained by the einselection (environment-induced decoherence) approach.Comment: 11 page

From bound states to resonances: analytic continuation of the wave function

Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the Schroedinger equation with respect to the coupling strength is exploited to analytically continue the bound-state solutions into the positive-energy region by means of Pade' approximants of the second kind. The method is here applied to single-particle wave functions of the $^{154}Sm$ and $^{131}Eu$ nuclei. A comparison of the results with the direct solution of the Schroedinger equation shows that the method can be confidently applied also in coupled-channel situations requiring high numerical accuracy.Comment: 13 pages, 3 figure

Poly(aspartic acid) with adjustable pH-dependent solubility

© 2016 Acta Materialia Inc.Poly(aspartic acid) (PASP) derivatives with adjustable pH-dependent solubility were synthesized and characterized to establish the relationship between their structure and solubility in order to predict their applicability as a basic material for enteric coatings. Polysuccinimide, the precursor of PASP, was modified with short chain alkylamines, and the residual succinimide rings were subsequently opened to prepare the corresponding PASP derivatives. Study of the effect of the type and concentration of the side groups on the pH-dependent solubility of PASP showed that solubility can be adjusted by proper selection of the chemical structure. The Henderson–Hasselbalch (HH) and the extended HH equations were used to describe the pH-dependent solubility of the polymers quantitatively. The estimate provided by the HH equation is poor, but an accurate description of the pH-dependent solubility can be found with the extended HH equation. The dissolution rate of a polymer film prepared from a selected PASP derivative was determined by fluorescence marking. The film dissolved rapidly when the pH was increased above its pKa. Cellular viability tests show that PASP derivatives are non-toxic to a human cell line. These polymers are thus of great interest as starting materials for enteric coatings. Statement of Significance Poly(amino acid) type biocompatible polymers were synthesized for future use as pharmaceutical film coatings. To this end, we tailored the pH-dependent solubility of poly(aspartic acid) (PASP). It was found that both the solubility and the pKa values of the modified PASP depended strongly on composition. Fluorescent marking was used to characterize the dissolution of a chosen PASP derivative. In acidic media only a negligible amount of the polymer dissolved, but dissolution was very fast and complete at the pH values that prevail in the small intestine. As a consequence, enteric coatings based on such PASP derivatives may be used for drug delivery in the gastrointestinal tract