Recurrence conditions for Markov decision processes with Borel state space: A survey

This paper describes virtually all the recurrence conditions used heretofore for Markov decision processes with Borel state and action spaces, which include some forms of mixing and contraction properties, Doeblin's condition, Harris recurrence, strong ergodicity, and the existence of bounded solutions to the optimality equation for average reward processes. The aim is to establish (when possible) implications and equivalences between these conditions.This research was partially supported by the Third World Academy of Sciences under grant RG MP 898-152.     

On heat conductors with a stationary hot spot

We consider a heat conductor having initial constant temperature and zero boundary temperature at every time.The hot spot is the point at which temperature attains its maximum at each given time. For convex conductors, if the hot spot does not move in time, we prove symmetry results for planar triangular and quadrangular conductors.Then, we examine the case of a general conductor and, by an asymptotic formula, we prove that, if there is a stationary critical point, not necessarily the hot spot, then the conductor must satisfy a geometric condition. In particular, we show that there is no stationary critical point inside planar non-convex quadrangular conductors. Mathematics Subject Classification (2000) Primary 35K05, 35K20, 35J05; Secondary 35J25, 35B38, 35B40     

A subsystem-independent generalization of entanglement

We present a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to this observable-based setting, suggesting new ways of measuring and classifying multipartite entanglement. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in interacting many-body systems.     

Two-dimensional microfabricated sources for nanoelectrospray

The idea of a novel two-dimensional (2D) nanoelectrospray ionization emitter tip with the shape of a nib is explored here. This novel planar design is studied as an alternative to the needle-like standard emitter tips that suffer from a lack of reproducibility and robustness and from an inherent incompatibility with high-throughput analysis. The composition of the micro-nib sources is analogous to the working of a simple fountain pen, with a liquid reservoir linked to a micro-nib tip from which the sample is electrosprayed via a capillary slot. The micro-nib prototypes described here were fabricated using microtechnology techniques and using the epoxy-based negative photoresist SU-8. The resulting free-standing micro-nib structure was supported by a silicon wafer. We present here two series of such micro-nib sources, the latter series exhibiting improved characteristics such as a 8 micro m source width of the nib tip. They were tested in mass spectrometry experiments on an ion trap mass spectrometer (LCQ Deca XP+, Thermo Finnigan) using standard peptide samples having concentrations down to 1 micro M and with a high voltage (HV) supply around 1 kV for the second series of micro-nib sources. In addition to the stability of the spray, the obtained mass spectra showed the reliability of these sources for peptide analysis; the signal of the spectra was as intense and the signal-to-noise ratio (S/N) as high as that obtained with the use of standard emitter tips.     

1H NMR study of the reaction of ornithine and lysine with pyridoxal-5′-phosphate

The composition of the mixture from the reaction of the basic amino acids ornithine or lysine with pyridoxal-5′-phosphate was investigated in D₂O by ¹H NMR and was found to be dependent on pH, α attack being favoured at acid pH and ω attack in basic solutions.     

Dimerisation oxydante d'anions de sulfones (XXI)

Cupric salts, particularly triflates, convert α-sulphonyl carbanions into α-disulphones. Allylphenylsulphones couple preferentially in the 3-3′ mode.     

Note on exterior lines to two disjoint reguli

LetR ₁ andR ₂ be two disjoint reguli in the projective 3-space over the field GF(q) whereq=p ^e ,p an odd prime. Ifp is not a point in neither of the two doubly-ruled quadrics associated to the given reguli, then there is at least one line through P which does not meet neither of the two reguli. Supported in part by FONDECYT Project N. 0343 and DIB E-2586/8712.     

The spatial critical points not moving along the heat flow

We consider solutions of the heat equation, in domains inR ^N, and their spatial critical points. In particular, we show that a solutionu has a spatial critical point not moving along the heat flow if and only ifu satisfies some balance law. Furthermore, in the case of Dirichlet, Neumann, and Robin homogeneous initial-boundary value problems on bounded domains, we prove that if the origin is a spatial critical point never moving for sufficiently many compactly supported initial data satisfying the balance law with respect to the origin, then the domain must be a ball centered at the origin.     

Weak convergence of semimartingales and discretisation methods

Given a semimartingale one can construct a system (λ, A, B, C) where λ is the distribution of the initial value and (A, B, C) is the triple of global characteristics. Thus, given a process X and a system (λ, A, B, C) one can look for all probability measures P such that X is a P-semimartingale with initial distribution λ and global characteristics (A, B, C). We say that such a measure P is a solution to the semimartingale problem (λ, A, B, C).The paper is devoted to the study of a special type of semimartingale problem. We look for sufficient conditions to insure the existence of solutions and we develop a method to construct them by means of time-discretised schemes, using weak topology for probability measures.