Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

Electronic phase separation in a low-temperature tetragonal phase of lanthanum-strontium cuprates according to 139La NQR data

A nonuniform electron density distribution is observed in La_{1−x− y} Nd_ySr_xCuO₄ and La_1−x−y Eu_ySr_xCuO₄, and long-lived magnetic fluctuations in these compounds are studied. The dynamics of the magnetic fluctuations depends strongly on the magnetic properties of the rare-earth ions, which stabilize the low-temperature tetragonal phase. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 344–349 (10 March 1998)     

Energy transfer between the flavin chromophores of electron-transferring flavoprotein fromMegasphaera elsdenii as inferred from time-resolved red-edge and blue-edge fluorescence spectroscopy

Both a mode-locked argon-ion laser and synchrotron radiation were used as excitation sources to obtain time-resolved polarized fluorescence of the two FAD cofactors in electron transferring flavoprotein fromMegasphaera elsdenii. Red-edge excited and blue-edge detected fluorescence anisotropy decay curves did not contain a fast relaxation process which was observed upon mainband excitation and detection. This relaxation was assigned to homo-energy transfer between the two FAD cofactors. Failure of energy transfer as observed with edge spectroscopy on this protein excludes restricted reorientational motion of the flavins as a possible mechanism of depolarization. From the global analysis of the fluorescence anisotropy decay surface obtained at multiple excitation and detection wavelengths, the distance between and the relative orientation of the flavins could be estimated. The methodology described has general applicability in other multichromophoric biopolymers and has the potential to acquire accurate geometrical parameters in these systems.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

Interface analysis of the system Si/YBa2Cu3O7?x

Summary The influence of different preparation conditions and substrate surface orientations on the superconducting properties of thin YBa₂Cu₃O_7–x (YBCO) films on silicon was studied. Comparative electrical and surface spectroscopic measurements were performed. SAM and SIMS depth profile analysis show an enrichment of barium at the interface between the superconductor and silicon for samples with T_c<76 K. Comparison with XPS data obtained for thin silicon films on YBCO indicates the formation of barium and yttrium silicates at the interface under these conditions.     

Is soft physics entropy driven?

The soft physics, p_T<2 GeV/c, observables at both RHIC and the SPS have now been mapped out in quite specific detail. From these results there is mounting evidence that this regime is primarily driven by the multiplicity per unit rapidity, dN_ch/dη. This suggests that the entropy of the system alone is the underlying driving force for many of the global observables measured in heavy-ion collisions. That this is the case and there is an apparent independence on collision energy is surprising. I present the evidence for this multiplicity scaling and use it to make some extremely naive predictions for the soft sector results at the LHC.     

Two observations about free graded hopf algebras

This paper records two results about graded Hopf algebras that do not appear to be stated explicitly in the literature. Let B be a graded set, graded by the positive integers. Let V be the graded vector space with basis B over a field K of characteristic zero and V^'=K⊕V, where K is in grading zero. Let L ne the free graded Lie algebra on B over K and let T be the free graded tensor algebra on B. The first result is the "graded Witt formula" giving the dimension of the subspace of L in each grading. The second result is the observation that any graded coassociative, co-commutative comultiplication Δ:V^'→V^'⊗V^', with co-unit the projection V¹→K. extends to a graded Hopf algebra structure on T that is in fact isomorphic to the natural graded Hopf algebra structure on T. In the ungraded case the statement analogous to the second result is false.