On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Bioactive films produced from self-assembling peptide amphiphiles as versatile substrates for tuning cell adhesion and tissue architecture in serum-free conditions

The development of versatile bioactive surfaces able to emulate in vivo conditions is of enormous importance to the future of cell and tissue therapy. Tuning cell behaviour on two-dimensional surfaces so that the cells perform as if they were in a natural three-dimensional tissue represents a significant challenge, but one that must be met if the early promise of cell and tissue therapy is to be fully realised. Due to the inherent complexities involved in the manufacture of biomimetic three-dimensional substrates, the scaling up of engineered tissue-based therapies may be simpler if based upon proven two-dimensional culture systems. In this work, we developed new coating materials composed of the self-assembling peptide amphiphiles (PAs) C16G3RGD (RGD) and C16G3RGDS (RGDS) shown to control cell adhesion and tissue architecture while avoiding the use of serum. When mixed with the C16ETTES diluent PA at 13 : 87 (mol mol-1) ratio at 1.25 times 10-3 M, the bioactive {PAs} were shown to support optimal adhesion, maximal proliferation, and prolonged viability of human corneal stromal fibroblasts ({hCSFs)}, while improving the cell phenotype. These {PAs} also provided stable adhesive coatings on highly-hydrophobic surfaces composed of striated polytetrafluoroethylene ({PTFE)}, significantly enhancing proliferation of aligned cells and increasing the complexity of the produced tissue. The thickness and structure of this highly-organised tissue were similar to those observed in vivo, comprising aligned newly-deposited extracellular matrix. As such, the developed coatings can constitute a versatile biomaterial for applications in cell biology, tissue engineering, and regenerative medicine requiring serum-free conditions.

Irreducible morphisms of categories of complexes

We study irreducible morphisms of complexes. In particular, we show that the irreducible morphisms having one (finite) irreducible submorphism fall into three canonical forms and we give necessary and sufficient conditions for a given morphism of that type to be irreducible. Our characterization of the above mentioned type of irreducible morphisms of complexes characterizes also some class of irreducible morphisms of the derived category D(-)(A) for A a finite dimensional k-algebra, where k is a field. (C) 2009 Published by Elsevier Inc.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

On moduli spaces for abelian categories

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.

Tilt-critical algebras of tame type

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory of A is tilted. We describe the tilt-critical algebras which are strongly simply connected and tame.

The bar-radical of a class of almost alternative baric algebras

In this article we prove that, if (U, ) is a finite dimensional baric algebra of (gamma, delta) type over a field F of characteristic not equal 2,3,5 such that gamma(2) - delta(2) + delta = 1 and 0,1, then rad(U) = R(U)boolean AND(bar(U))(2), where R(U) is the nilradical (maximal nil ideal) of U.

Filtered Multiplicative Bases of Restricted Enveloping Algebras

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Noncommutative Jordan superalgebras of degree n > 2

We prove a coordinatization theorem for noncommutative Jordan superalgebras of degree n > 2, describing such algebras. It is shown that the symmetrized Jordan superalgebra for a simple finite-dimensional noncommutative Jordan superalgebra of characteristic 0 and degree n > 1 is simple. Modulo a ""nodal"" case, we classify central simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

Abstract types and distributions in independent private value auctions

In this note, in an independent private values auction framework, I discuss the relationship between the set of types and the distribution of types. I show that any set of types, finite dimensional or not, can be extended to a larger set of types preserving incentive compatibility constraints, expected revenue and bidder’s expected utilities. Thus for example we may convexify a set of types making our model amenable to the large body of theory in economics and mathematics that relies on convexity assumptions. An interesting application of this extension procedure is to show that although revenue equivalence is not valid in general if the set of types is not convex these mechanism have underlying distinct allocation mechanism in the extension. Thus we recover in these situations the revenue equivalence.

Estatística não-extensiva aplicada ao cálculo do calor específico eletrônico em estruturas quasiperiódicas

Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

Energy-dependent point interaction: Self-adjointness

Recently, we constructed an energy-dependent point interaction (EDPI) in its most general form in one-dimensional quantum mechanics. In this paper, we show that stationary solutions of the Schrodinger equation with the EDPI form a complete set. Then any nonstationary solution of the time-dependent Schrodinger equation can be expressed as a linear combination of stationary solutions. This, however, does not necessarily mean that the EDPI is self-adjoint and the time-development of the nonstationary state is unitary. The EDPI is self-adjoint provided that the stationary solutions are all orthogonal to one another. We illustrate situations in which this orthogonality condition is not satisfied.

Infrared dynamics in (2+1) dimensions

In this work we study the asymptotic behavior of (2+1)-dimensional quantum electrodynamics in the infrared region. We show that an appropriate redefinition of the fermion current operator leads to an asymptotic evolution operator that contains a divergent Coulomb phase factor and a contribution from the electromagnetic field at large distances, factored from the evolution operator for free fields, and we conclude that the modified scattering operator maps two spaces of coherent states of the electromagnetic field, as in the Kulish-Faddeev model for QED (quantum electrodynamics) in four space-time dimensions.