$${f(\mathcal R)}$$ quantum cosmology

We have quantized a flat cosmological model in the context of the metric 22g4/10714_2008_617_Article_IEq2.gif" alt="$${f(\mathcal R)}$$" align="middle" border="0"> models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.     

Investigation of neutron induced reactions on ^23Na by using Talys1.4

The neutron induced reactions on ^23Na are investigated by using the Talys1.4 program. The calculated results for the ^23Na（n, 2n）22Na reaction are found to agree with the experimental results. The cross sections of the residues of the（n, n）,（n, γ）,（n, p）, and（n, np） channels in the reactions are presented, and at the same time, the neutron induced reactions on22 Ne are also investigated.     

用XRD法研究MCM-22分子筛的逐级放大合成

在100,250和1 000 mL高压釜静态成功合成MCM-22分子筛的基础上,在2,5和200 L高压釜中进行了MCM-22分子筛的动态合成试验,对合成的样品用XRD等技术进行了表征。结果表明,在静态和动态条件下合成的样品,全部为纯相MCM-22分子筛,且结晶度较高,从100 mL到200 L的放大试验是成功的。     

On the nilpotent * - Fourier transform

LetG be a nilpotent Lie group. The adapted nilpotent Fourier transform was introduced by D. Arnal and J. C. Cortet,:L(G) C (V,L(^2d )), whereL(G) is the Schwartz space ofG andV × ^2k is aG-invariant Zariski open set ing ^* the dual of the Lie algebra ofG. We prove the surjectivity of this transformation, which allows us to extend it to distribution spaces.     

Isogroups of differential ideals of vector-valued differential forms: Application to partial differential equations

An older geometric technique for the study of invariance groups of partial differential equations, originally proposed by one of the authors and F. B. Estabrook, is generalized and extended to problems involving exterior equations for vector-valued or Lie algebra-valued exterior differential forms. Use of the method is demonstrated in the study of the symmetry groups of the two-dimensional Dirac equation and the full Yang-Mills free-field equations in Minkowski spacetime.     

Hypergeometric systems of Gelfand-type equations and series in orthogonal polynomials

We describe multivariable hypergeometric series in orthogonal polynomials. These series are solutions of special systems of Gelfand-type equations. The difference andq-analogs are also given.     

Loop group decompositions in almost split real forms and applications to soliton theory and geometry

We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action–by the whole subgroup of loops which extend holomorphically to the exterior disc–on the U$U$-hierarchy of the ZS-AKNS systems, on curved flats and on various other integrable systems, is global for compact cases. It also implies a global infinite dimensional Weierstrass-type representation for Lorentzian harmonic maps (1+1$1+1$ wave maps) from surfaces into compact symmetric spaces. An “Iwasawa-type” decomposition of the same type of real form, with respect to a fixed point subgroup of an involution of the second kind, is also proved, and an application given.     

Lee–Yang Problems and the Geometry of Multivariate Polynomials

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.