Equivariant and nonequivariant module spectra

AbstractLet G be a compact Lie group, let RG, be a commutative algebra over the sphere G-spectrumSG, and let R be its underlying nonequivariant algebra over the sphere spectrum S. When RG is split as an algebra, as holds, for example, for RG = MUG. we show how to “extend scalars” to construct a split RG-modale MG = RG ΛR M from an R-module M. We also show how to compute the coefficients M∗G in terms of the coefficients R∗G, R∗, and M∗. This allows the wholesale construction of highly structured equivariant module spectra from highly structured nonequivariant module spectra. In particular, it applies to construct MUG-modules from MU-modules and therefore gives conceptual constructions of equivariant Brown-Peterson and Morava K-theory spectra

Algebras over equivariant sphere spectra

AbstractWe study the category of algebras over the sphere G-spectrum of a compact Lie group G. A priori, this category depends on which representations appear in the underlying universe on which G-spectra are indexed, but we prove that different universes give rise to equivalent categories of point-set level algebras. The relevant change of universe functors are defined on categories of modules over sphere spectra and induce the classical change of universe functors (which are not equivalences!) on passage to stable homotopy categories. In particular, we show how to construct equivariant algebras from nonequivariant algebras by change of universe. This gives a reservoir of equivariant examples to which recently developed algebraic techniques in stable homotopy theory can be applied

Influence of plant growth regulator application and nitrogen fertilization on oat yield and stand-ability

Non-Peer Reviewe

On the algebraic K-theory of the complex K-theory spectrum

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.Comment: Revised and expanded version, 42 pages

On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Saturated phase densities of (CO2 + H2O) at temperatures from (293 to 450) K and pressures up to 64 MPa

An apparatus consisting of an equilibrium cell connected to two vibrating tube densimeters and two syringe pumps was used to measure the saturated phase densities of (CO2 + H2O) at temperatures from (293 to 450) K and pressures up to 64 MPa, with estimated average standard uncertainties of 1.5 kg · m−3 for the CO2-rich phase and 1.0 kg · m−3 for the aqueous phase. The densimeters were housed in the same thermostat as the equilibrium cell and were calibrated in situ using pure water, CO2 and helium. Following mixing, samples of each saturated phase were displaced sequentially at constant pressure from the equilibrium cell into the vibrating tube densimeters connected to the top (CO2-rich phase) and bottom (aqueous phase) of the cell. The aqueous phase densities are predicted to within 3 kg · m−3 using empirical models for the phase compositions and partial molar volumes of each component. However, a recently developed multi-parameter equation of state (EOS) for this binary mixture, Gernert and Span [32], was found to under predict the measured aqueous phase density by up to 13 kg · m−3. The density of the CO2-rich phase was always within about 8 kg · m−3 of the density for pure CO2 at the same pressure and temperature; the differences were most positive near the critical density, and became negative at temperatures above about 373 K and pressures below about 10 MPa. For this phase, the multi-parameter EOS of Gernert and Span describes the measured densities to within 5 kg · m−3, whereas the computationally-efficient cubic EOS model of Spycher and Pruess (2010), commonly used in simulations of subsurface CO2 sequestration, deviates from the experimental data by a maximum of about 8 kg · m−3

Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).Comment: 42 page

Inferring loop invariants by mutation, dynamic analysis, and static checking

Verifiers that can prove programs correct against their full functional specification require, for programs with loops, additional annotations in the form of loop invariants - properties that hold for every iteration of a loop. We show that significant loop invariant candidates can be generated by systematically mutating postconditions; then, dynamic checking (based on automatically generated tests) weeds out invalid candidates, and static checking selects provably valid ones. We present a framework that automatically applies these techniques to support a program prover, paving the way for fully automatic verification without manually written loop invariants: Applied to 28 methods (including 39 different loops) from various Java.util classes (occasionally modified to avoid using Java features not fully supported by the static checker), our DYNAMATE prototype automatically discharged 97 percent of all proof obligations, resulting in automatic complete correctness proofs of 25 out of the 28 methods - outperforming several state-of-the-art tools for fully automatic verification

Lambda^0 polarization as a probe for production of deconfined matter in ultra-relativistic heavy-ion collisions

We study the polarization change of Lambda^0's produced in ultra-relativistic heavy-ion collisions with respect to the polarization observed in proton-proton collisions as a signal for the formation of a Quark-Gluon Plasma (QGP). Assuming that, when the density of participants in the collision is larger than the critical density for QGP formation, the Lambda^0 production mechanism changes from recombination type processes to the coalescence of free valence quarks, we find that the Lambda^0 polarization depends on the relative contribution of each process to the total number of Lambda^0's produced in the collision. To describe the polarization of Lambda^0's in nuclear collisions for densities below the critical density for the QGP formation, we use the DeGrand-Miettinen model corrected for the effects introduced by multiple scattering of the produced Lambda^0 within the nuclear environment.Comment: 9 pages, 6 figures, uses ReVTeX and epsfig.st