On the simplicial cohomology of Banach operator algebras

We investigate the simplicial cohomology of certain Banach operator algebras. The two main examples considered are the Banach algebra of all bounded operators on a Banach space and its ideal of approximable operators. Sufficient conditions will be given forcing Banach algebras of this kind to be simplicially trivial.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

1-amenability of A(X) for Banach spaces with 1-unconditional bases

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property A has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property A are discussed.

An upper mass limit for the progenitor of the Type II-P supernova SN 1999gi

Masses and progenitor evolutionary states of Type II supernovae remain almost unconstrained by direct observations. Only one robust observation of a progenitor (SN 1987A) and one plausible observation (SN 1993J) are available. Neither matched theoretical predictions, and in this Letter we report limits on a third progenitor (SN 1999gi). The Hubble Space Telescope (HST) has imaged the site of the Type II-P supernova SN 1999gi with the Wide Field Planetary Camera 2 (WFPC2) in two filters (F606W and F300W) prior to explosion. The distance to the host galaxy (NGC 3184) of 7.9 Mpc means that the most luminous, massive stars are resolved as single objects in the archive images. The supernova occurred in a resolved, young OB association 2.3 kpc from the center of NGC 3184 with an association age of about 4 Myr. Follow-up images of SN 1999gi with WFPC2 taken 14 months after discovery determine the precise position of the supernova on the preexplosion frames. An upper limit of the absolute magnitude of the progenitor is estimated (M-v greater than or equal to -5.1). By comparison with stellar evolutionary tracks, this can be interpreted as a stellar mass, and we determine an upper mass limit of 9(-2)(+3) M.. We discuss the possibility of determining the masses or mass limits for numerous nearby core-collapse supernovae using the HST archive enhanced by our current SNAP program.

Free and projective Banach lattices

We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties. We give much more detailed results about their structure in the case when there are only a finite number of generators, and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice P to be projective if, whenever X is a Banach lattice, J is a closed ideal in X, Q : X → X/J is the quotient map, T: P → X/J is a linear lattice homomorphism and ε > 0, there exists a linear lattice homomorphism : P → X such thatT = Q º and ∥∥ ≤ (1 + ε)∥T∥. We establish the connection between projective Banach lattices and free Banach lattices, describe several families of Banach lattices that are projective and prove that some are not.

Chaotic Banach algebras

We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization $A^{\#}=A\oplus \spann\{{\bf 1}\}$ of $A$. As a byproduct, we get a hypercyclic operator $T$ on a Banach space such that $T\oplus T$ is non-cyclic and $\sigma(T)=\{1\}$.

Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

The Influence of Structural Modeshape Variability on Limit Cycle Oscillation Behaviour

Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is compo
sed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing’s structure and the store centre of gravity location is investigated in two cases:- supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

Microbial community of the deep-sea brine Lake Kryos seawater-brine interface is active below the chaotropicity limit of life as revealed by recovery of mRNA

Within the complex of deep, hypersaline anoxic lakes (DHALs) of the Mediterranean Ridge, we identified a new, unexplored DHAL and named it ‘Lake Kryos’ after a nearby depression. This lake is filled with magnesium chloride (MgCl2)-rich, athalassohaline brine (salinity > 470 practical salinity units), presumably formed by the dissolution of Messinian bischofite. Compared with the DHAL Discovery, it contains elevated concentrations of kosmotropic sodium and sulfate ions, which are capable of reducing the net chaotropicily of MgCl2-rich solutions. The brine of Lake Kryos may therefore be biologically permissive at MgCl2 concentrations previously considered incompatible with life. We characterized the microbiology of the seawater–Kryos brine interface and managed to recover mRNA from the 2.27–3.03 MMgCl2 layer (equivalent to 0.747–0.631 water activity), thereby expanding the established chaotropicity window-for-life. The primary bacterial taxa present there were Kebrit Deep Bacteria 1 candidate division and DHAL-specific group of organisms, distantly related toDesulfohalobium. Two euryarchaeal candidate divisions, Mediterranean Sea Brine Lakes group 1 and halophilic cluster 1, accounted for > 85% of the rRNA-containing archaeal clones derived from the 2.27–3.03 M MgCl2 layer, but were minority community-members in the overlying interface-layers. These findings shed light on the plausibility of life in highly chaotropic environments, geochemical windows for microbial extremophiles, and have implications for habitability elsewhere in the Solar System.