Composite Legendre-Laguerre pseudospectral approximation in unbounded domains

A composite Legendre–Laguerre pseudospectral approximationin unbounded domains is developed. Some approximation resultsare obtained. As an application, a composite pseudospectralscheme is proposed for the Burgers equation on the half-line.The stability and convergence of the scheme are proved. By choosingappropriate base functions, the resulting system of this methodhas a sparse structure and can be solved in parallel. Numericalresults are given to show the efficiency of this new method.     

-actions whose fixed data has a section

Given a collection of real vector bundles over a closed manifold , suppose that, for some is of the form , where is the trivial one-dimensional bundle. In this paper we prove that if is the fixed data of a -action, then the same is true for the Whitney sum obtained from by replacing by . This stability property is well-known for involutions. Together with techniques previously developed, this result is used to describe, up to bordism, all possible -actions fixing the disjoint union of an even projective space and a point.     

Changes in the Solubility of β-Cyclodextrin on Complex Formation: Guest Enforced Solubility of β-Cyclodextrin Inclusion Complexes

The most common native host molecule, -cyclodextrin (cycloheptaamylose) is able toform inclusion complexes with a large variety of guestmolecules (or ions) of different size and shape. Theproperties of the included guest molecule are highlyinfluenced by the host-guest interaction, and thepractical usefulness of -cyclodextrin isdependent on these effects. These changes are mainlyinvestigated from the point of view of the guest andto a lesser extent from that of the host. In spite ofthis, the kind of guests and that of the host-guestinteractions during the formation of the inclusioncomplex seem to influence the properties of thehydrophilic domain of -cyclodextrin (i.e. thatof the supramolecule itself), too, and this effect canbe well demonstrated by the change of solubility ofdifferent -cyclodextrin inclusion complexes.This change can be best correlated with the solubilityof the guest as if the guest enforced its solubilityon the supramolecule.     

Quasi-P*-Maps,P(τ, α, β)-Maps,Exceptional Family of Elements,and Complementarity Problems

Quasi-P_*-maps and P(, , )-maps defined in this paper are two large classes of nonlinear mappings which are broad enough to include P_*-maps as special cases. It is of interest that the class of quasi-P_*-maps also encompasses quasimonotone maps (in particular, pseudomonotone maps) as special cases. Under a strict feasibility condition, it is shown that the nonlinear complementarity problem has a solution if the function is a nonlinear quasi-P_*-map or P(, , )-map. This result generalizes a classical Karamardian existence theorem and a recent result concerning quasimonotone maps established by Hadjisawas and Schaible, but restricted to complementarity problems. A new existence result under an exceptional regularity condition is also established. Our method is based on the concept of exceptional family of elements for a continuous function, which is a powerful tool for investigating the solvability of complementarity problems.     

Crystal structures of 4,7-phenanthrolino-5,6:5′,6′-pyrazine tetrahydrate and 1,4,5,8,9,12-hexaazatriphenylene dihydrate

The crystal structures of 4,7-phenanthrolino-5,6:5,6-pyrazine tetrahydrate (I) and 1,4,5,8,9,12-hexaazatriphenylene dihydrate (II) have been determined from low temperature (173 K) x-ray single crystal diffraction data. I crystallizes in the triclinic system, space group P with a = 11.2687(6), b = 12.4766(6), c = 12.7068(7) Å, = 113.4740(10), = 91.605(2), = 114.587(2)°, V = 1449.33(13) ų, and Z = 4. II crystallizes in the orthorhombic system, space group Pca2₁ with a = 18.187(2), b = 9.2576(11), c = 6.9672(8) Å, V = 1173.0(2) ų, and Z = 4. In both structures the planar heterocyclic molecules stack with interplanar distances down to 3.3 Å, which is consistent with self--complexation. The crystal water molecules provide links between the columns of stacked molecules through hydrogen bonds. In each compound the N-C bond lengths fall into two distinct groups (mean values 1.330(3) vs 1.361(1) Å in I and 1.320(3) vs 1.357(5) Å in II), as do the C-C bonds of the central phenyl rings (1.411(4) vs 1.467(1) Å in I and 1.405(5) vs 1.458(4) Å in II).     

Strongly Regular Graphs and Designs with Three Intersection Numbers

We investigate BIBDs with three intersection numbers,x, y, and z, such that the relation on the block set given byA B iff the cardinality of the intersectionof A and B is not equal to x is an equivalence relation. Withsuch a design, we associate a family of strongly regular graphswith the same parameters. Two constructions producing infinitefamilies of such designs are given.     

On the étale Descent Problem for Topological Cyclic Homology and Algebraic K-Theory

We investigate étale descent properties of topological Hochschild and cyclic homology. Using these properties we deduce a general injectivity result for the descent map in algebraic K-theory, and show that algebraic K-theory has étale descent for rings of integers in unramified and tamely ramified p-adic fields.     

New investigation of the decay of the high-spin isomer in 151Er

The decay of the T _1/2 = 420 ns isomer in ¹⁵¹Er has been reinvestigated. The multipolarities of the decaying transitions have been established by measuring the electron conversion coefficients. An I ^π = 67/2⁻ assignment is proposed for this isomer with a π[h ₁₁^2/4 d ₃^2/1 d ₅^2/−1]⊗ν[f _7/2 h _9/2 h ₁₁^2/−1] configuration.     

Production of heavy neutron-rich nuclei “south" of lead

The production of heavy neutron-rich nuclei is investigated using cold-fragmentation reactions. More than 25 new heavy neutron-rich nuclei were produced in the fragmentation of ²⁰⁸Pb projectiles at 1 A GeV impinging a beryllium target. The precise measurement of their production cross sections enables to benchmark the predictive power of different model calculations and make reliable predictions of the production rates expected in future radioactive beam facilities.     

Magnetohydrodynamic properties of incompressible Meissner fluids

We consider a superconducting material that exists in the liquid state, more precisely, in which the Meissner-Ochsenfeld effect persists in the liquid state. First, we investigate how the shape of such a hypothetical Meissner liquid will adapt to accomodate for an applied external field. In particular, we analyse the case of a droplet of Meissner fluid, and compute the elongation of the droplet and its quadrupole frequency as a function of the applied field. Next, the influence of an applied field on the flow of the liquid is studied for the case of a surface wave. We derive the dispersion relation for surface waves on an incompressible Meissner fluid. We discuss some candidate realizations of the Meissner fluids and for the case of a superconducting colloid discuss which regime of wave lengths would be most affected by the Meissner effect.