Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle

We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.     

Five Novel Taccalonolides from the Roots of the Vietnamese Plant Tacca paxiana

Chemical investigation of the roots of the Vietnamese plant Tacca paxiana resulted in the isolation of five new steroidal compounds, taccalonolide R ( 6 ), S ( 7 ), T ( 8 ), U ( 9 ), and V ( 10 ). Their structures were established on the basis of NMR and mass‐spectral data. In addition, the five known taccalonolides A ( 1 ), B ( 2 ), E ( 3 ), K ( 4 ), and N ( 5 ) were also isolated and identified.     

Expressive equivalence of least and inflationary fixed-point logic

We study the relationship between least and inflationary fixed-point logic. In 1986, Gurevich and Shelah proved that in the restriction to finite structures, the two logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivalent to any LFP-formula was left open.

In this paper, we answer the question negatively, i.e. we show that the two logics are equally expressive on arbitrary structures. We give a syntactic translation of IFP-formulae to LFP-formulae such that the two formulae are equivalent on all structures.

As a consequence of the proof we establish a close correspondence between the LFP-alternation hierarchy and the IFP-nesting depth hierarchy. We also show that the alternation hierarchy for IFP collapses to the first level, i.e. the complement of any inflationary fixed point is itself an inflationary fixed point.     

Correlated polarization propagator calculations of static polarizabilities

We present a systematic comparison of the correlation contribution at the level of the second-order polarization propagator approximation (SOPPA ) and MP 2 to the static dipole polarizability of (1) Be, BeH^?, BH, CH⁺, MgH^?, AIH, SiH⁺, and GeH⁺; (2) BH₃, CH₄, NH₃, H₂O, HF, BF, and F₂; and (3) N₂, CO, CN^?, HCN, C₂H₂, and HCHO . Fairly extended basis sets were used in the calculations. We find that the agreement with experimental values is improved in SOPPA and MP .2 over the results at the SCF level. The signs and magnitudes of the correlation contribution in SOPPA are similar to those obtained in analytical derivative MP 2 calculations. However, it is not possible to say, in general, which method gives the largest correlation contribution or the best agreement with experiment, nor is it possible to make a priori prediction of the sign of the correlation contribution. For the first group of molecules, which have a quasi-degenerate ground state, additional CCDPPA and CCSDPPA calculations were performed and compared with polarizabilities obtained as analytical/numerical derivatives of the CCD and CCSD energies. The CCSDPPA results were found to be in better agreement with other calculations than were the SOPPA results, demonstrating the necessity of using methods based on infinite-order perturbation theory for these systems. © 1994 John Wiley & Sons, Inc.     

Current correlators to all orders in the quark masses

The contributions to the coefficient functions of the quark and the mixed quark-gluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short- and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms ofnon-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.Supported by the German Bundesministerium für Forschung und Technologie, under the contract 06 TM 761     

Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002