Order Embeddings with Irrational Codomain: Debreu Properties of Real Subsets

The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-valued strictly isotone function (semicontinuous or not) also admits a representation by means of a lower (respectively, upper) semicontinuous strictly isotone function that takes values in the set of irrational numbers. These results are obtained by means of a direct construction. Moreover, they can be related to Cantor’s characterization of the real line to obtain much more general results on the semicontinuous Debreu properties of a wide family of subsets of the real line.      

The Polyakov path integral over bordered surfaces

Following the general scheme of the convariant path integral quantization of gauge systems, two alternative formulations of the first quantized closed bosonic string in a position representation are presented. In both approaches the covariant path integral representations of the propagator and of the higher order off-shell amplitudes are constructed. For a wide class of gauges the explicit formulae for off-shell amplitudes are obtained. This paper is the continuation of our previous work where the corresponding problems in the open string case were considered [20].     

On bulk-service MAP/PH L,N /1/N G-Queues with repeated attempts

We consider a retrial queue with a finite buffer of size N, with arrivals of ordinary units and of negative units (which cancel one ordinary unit), both assumed to be Markovian arrival processes. The service requirements are of phase type. In addition, a PH^L,N bulk service discipline is assumed. This means that the units are served in groups of size at least L, where 1≤ L≤ N. If at the completion of a service fewer than L units are present at the buffer, the server switches off and waits until the buffer length reaches the threshold L. Then it switches on and initiates service for such a group of units. On the contrary, if at the completion of a service L or more units are present at the buffer, all units enter service as a group. Units arriving when the buffer is full are not lost, but they join a group of unsatisfied units called “orbit”. Our interest is in the continuous-time Markov chain describing the state of the queue at arbitrary times, which constitutes a level dependent quasi-birth-and-death process. We start by analyzing a simplified version of our queueing model, which is amenable to numerical calculation and is based on spatially homogeneous quasi-birth-and-death processes. This leads to modified matrix-geometric formulas that reveal the basic qualitative properties of our algorithmic approach for computing performance measures. AMS Subject Classification: Primary 60K25 Secondary 68M20 90B22.     

Enhancing molecular formation in a Rb-MOT

In this paper, we report observation of an enhancement of the ground state molecule Rb₂ formation in a Rb magneto-optical trap due to a photoassociation laser. Such an enhancement effect is due to flux enhancement of atomic pairs at short internuclear distances. Our experimental observations consist in the measurement of the molecular formation rate constant due to a probe laser as a function of the trap laser intensity. The results are compared with a simple semi-classical model, showing good agreement. We conclude that the production of cold Rb₂ may be enhanced using appropriate laser parameters; this may be useful for future experiments involving production and trapping of ultracold ground state molecules.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

More compact invariant manifolds appearing in the non-linear coupling of oscillators

Near partially elliptic rest points of generic families of vector fields or transformations, many types of normally hyperbolic invariant compact manifolds can appear, diffeomorphic to intersections of quadrics. To cite this article: M. Chaperon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Direction of magnetization and domain wall mobility in (Dy,Y)Fe2

Magnetization measurements in the (Dy _x Y_1−x )Fe₂ intermetallic compounds show evidence of blocking of domain wall motion. This effect is a function of concentrationx. The direction of magnetization is also dependent on the Dy concentration. We have used the Mossbauer spectroscopy of⁵⁷Fe to verify the direction of magnetization in the series as a function ofx and temperature. The results show that this change in easy direction occurs at higher temperatures than those where the blocking is detected through DC magnetization measurements. supported by RHAE/SCT.     

Alloy formation in mechanically activated mixtures

The physical mixtures of hydroxocarbonates of Cu and Ni with aluminium were activated using a laboratory planetary mill. The chemical reactions and alloy formations as the effects of grinding were followed by the phase analysis of solid products based on the thermogravimetry and X-ray diffractometry. Experimental evidence indicates that the nature of reactions and products of mechanical activation was dependent on the amount of aluminium and time of grinding. This revised version was published online in July 2006 with corrections to the Cover Date.