Equivariant semiprojectivity

We define equivariant semiprojectivity for C* -algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: A. Arbitrary finite dimensional C*-algebras with arbitrary actions of compact groups. - B. The Cuntz algebras Od and extended Cuntz algebras Ed, for finite d, with quasifree actions of compact groups. - C. The Cuntz algebra O∞ with any quasifree action of a finite group. For actions of finite groups, we prove that equivariant semiprojectivity is equiv- alent to a form of equivariant stability of generators and relations. We also prove that if G is finite, then C*(G) is graded semiprojective.

Graded algebra automorphisms

We consider the Clifford algebra C(q) of a regular quadratic space (V, q) over a field K with its structure of Z/2Z-graded K-algebra. We give a characterization of the group of graded automorphisms of C(q). In the last section we introduce the Z/nZ-graded algebras and we study as well as the group of graded automorphisms for some of them.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

General Interaction Picture from Action Principle for Mechanics

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

A radiochemical method for carbamoyl-phosphate synthetase I: application to rats fed a hyperproteic diet

A method for the measurement of carbamoyl-phosphate synthetase I activity in animal tissues has been developed using the livers of rats under normal and hyperproteic diets. The method is based on the incorporation of 14C-ammonium bicarbonate to carbamoyl-phosphate in the presence of ATP-Mg and N-acetyl-glutamate. The reaction is stopped by chilling, lowering the pH and adding ethanol. Excess bicarbonate is flushed out under a gentle stream of cold CO2. The only label remaining in the medium was that incorporated into carbamoyl-phosphate, since all 14C-CO2 from bicarbonate was eliminated. The method is rapid and requires only a low pressure supply of CO2 to remove the excess substrate. The reaction is linear up to 10 min using homogenate dilutions of 1:20 to 1:200 (w/v). Rat liver activity was in the range of 89±8 nkat/g. Hyperproteic diet resulted in a significant 1.4-fold increase. The design of the method allows for the processing of multiple samples at the same time, and incubation medium manipulation is unnecessary, since the plastic incubation vial and its contents are finally counted together.

Intrinsic subspace convergence in TDD MIMO communication

In numerical linear algebra, students encounter earlythe iterative power method, which finds eigenvectors of a matrixfrom an arbitrary starting point through repeated normalizationand multiplications by the matrix itself. In practice, more sophisticatedmethods are used nowadays, threatening to make the powermethod a historical and pedagogic footnote. However, in the contextof communication over a time-division duplex (TDD) multipleinputmultiple-output (MIMO) channel, the power method takes aspecial position. It can be viewed as an intrinsic part of the uplinkand downlink communication switching, enabling estimationof the eigenmodes of the channel without extra overhead. Generalizingthe method to vector subspaces, communication in thesubspaces with the best receive and transmit signal-to-noise ratio(SNR) is made possible. In exploring this intrinsic subspace convergence(ISC), we show that several published and new schemes canbe cast into a common framework where all members benefit fromthe ISC.

A radiochemical method for carbamoyl-phosphate synthetase I: application to rats fed a hyperproteic diet

A method for the measurement of carbamoyl-phosphate synthetase I activity in animal tissues has been developed using the livers of rats under normal and hyperproteic diets. The method is based on the incorporation of 14C-ammonium bicarbonate to carbamoyl-phosphate in the presence of ATP-Mg and N-acetyl-glutamate. The reaction is stopped by chilling, lowering the pH and adding ethanol. Excess bicarbonate is flushed out under a gentle stream of cold CO2. The only label remaining in the medium was that incorporated into carbamoyl-phosphate, since all 14C-CO2 from bicarbonate was eliminated. The method is rapid and requires only a low pressure supply of CO2 to remove the excess substrate. The reaction is linear up to 10 min using homogenate dilutions of 1:20 to 1:200 (w/v). Rat liver activity was in the range of 89±8 nkat/g. Hyperproteic diet resulted in a significant 1.4-fold increase. The design of the method allows for the processing of multiple samples at the same time, and incubation medium manipulation is unnecessary, since the plastic incubation vial and its contents are finally counted together.

Monoidal functors, acyclic models and chain operads

We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.

Structural control on present-day topography of a basement massif: the Central and Eastern Anti-Atlas (Morocco)

The Anti-Atlas basement massif extends South of the High Atlas, and, despite a very mild Cenozoic deformation, its altitude exceeds 1500m in large areas, reaching 3305m in Jbel Sirwa. Structural contours of the present elevation of a polygenic planation surface (the High Erosional surface) and of the base of Cretaceous and Neogene inliers have been performed to characterize the major tectonic structures. Gentle Cenozoic WSW-ENE- and N-Strending folds, of 60 to100km wavelength, reactivate Variscan structures, being the major contributors to the local topography of the Anti-Atlas. Reactivated thrusts of decakilometric to kilometric-scale and E-W trend involving the Neogene rocks exhibit a steep attitude and a small displacement, but they also produce a marked topographic expression. The resulting Cenozoic horizontal shortening along N-S sections across the Anti-Atlas is about 1%. The position of the major anticlinal hinges determines the location of the fluvial divides of the Warzazat basin and the Anti-Atlas, and a structural depression on one of these hinges (Jbel Saghro anticline) allowed the formerly endorheic Warzazat basin to drain southwards. The first Cenozoic structures generating local topography are of pre-mid Miocene age (postdated by 6.7Ma volcanic rocks at the Jbel Saghro), whereas the youngest thrust movements postdate the Pliocene sedimentary and volcanic rocks (involving 2.1Ma volcanic rocks at Jbel Sirwa). In addition to these features, the mean elevation of the Anti-Atlas at the regional scale is also the result of a mantle thermal anomaly reported in previous works for the entire Atlas system.