Soft almost disjoint families

An almost disjoint family is said to be soft if there is an infinite set that meets each in a nonempty but finite set. We consider the associated cardinal invariant defined to be the minimal cardinality of an almost disjoint family that is not soft. We show that this cardinal coincides with J. Brendle's cardinal .

     

Small-Mass Behavior of Quantum Gibbs States for Lattice Models with Unbounded Spins

We construct the distribution of the infinite-dimensional Markov process associated with a finite-temperature Gibbs state for a quantum mechanical anharmonic crystal. The corresponding state is constructed via a cluster expansion technique for an arbitrary fixed temperature and, correspondingly, small enough masses of particles.     

Perturbed steepest-descent technique in multiextremal problems

The steepest-descent technique dealing with the perturbed values of the objective function and its gradients and with nonexact line searches is considered. Attention is given to the case where the perturbations do not decrease on the algorithm trajectories; the aim is to investigate how perturbations at every iteration of the algorithm perturb its original attractor set.Based on the Liapunov direct method for attraction analysis of discrete-time processes, a sharp estimation of the attractor set generated by a perturbed steepest-descent technique with respect to the perturbation magnitudes is obtained. Some global optimization properties of finite-difference analogues of the gradient method are discovered. These properties are not inherent in methods which use exact gradients.The author is grateful to the referees for many useful suggestions.     

Analytical perfect fluid perturbation for the matter dominated epoch

We present the analytical solution to the linear evolution equation of a one component Friedmann perturbation using an equation of state of the form p = (1/3)μσ²(t), where μ is the mass density and σ(t) is the root mean square (rms) velocity in the matter dominated epoch. It is assumed that this rms velocity depends only on the time coordinate and decreases as 1/a, a being the expansion factor of the Friedmann background. The evolution equations are written for scales below the horizon using the longitudinal gauge. The general solution, in the coordinate space, of the evolution equation for the scalar mode is obtained. In the case of spherical symmetry, this solution is expressed in terms of unidimensional integrals of the initial conditions: the initial values of the Newtonian potential and its first time derivative. This perfect fluid solution is a good approximation to the evolution of warm dark matter perturbations obtained by solving the Vlasov’s equation for collisionless particles.     

The ν1 and ν4 fundamental bands of H3SiCl investigated with high resolution

The gas phase infrared spectrum of monoisotopic H₃Si³⁷Cl has been reinvestigated in the ν₁/ν₄ region near 2200 cm⁻¹, using a Fourier transform spectrometer, with a nominal resolution of 0.0027 cm⁻¹. The rovibrational analysis confirms, besides the weak Coriolis x, y resonance between the (v₁ = 1) and (v₄ = 1) levels, the existence of two strong local perturbations in the ν₄ band. These are caused by rotational (Δk = Δl = ±1) type resonances with and , respectively. Another local perturbation of the 12 ? KΔK ? 14 subbands of the ν₄ band, probably due to a (Δk = Δl = ±1) interaction with , was detected and analyzed. All these local perturbations have been studied individually using a simple model of two interacting sublevels. Without the transitions involved in the local perturbations, more than 2000 lines of the ν₁/ν₄ band system were used to obtain a complete set of vibration-rotation parameters set for the v₁ = 1 and v₄ = 1 states. By means of a band contour simulation, both the transition moment ratio ∣M₄:M₁∣ = 1.25 and a positive sign of the Coriolis intensity perturbation were determined.The present results, together with the accurate existing data for ν₂, ν₃, ν₅, and ν₆ bands, allowed us to derive the experimental values, A_e = 2.8722945(37) cm⁻¹ and B_e = 0.2182248(22) cm⁻¹, which are compared with those of ab initio calculations.     

Turbulence investigations during ergodic divertor operation with induced 2/1 tearing mode

Within the last year of TEXTOR operation a major part of the experiments were dedicated to the interaction of the ergodized plasma edge, induced by the dynamic ergodic divertor (DED), with the core plasma. Systematic experiments are performed in the 3/1 configuration of the DED. Depending on , the DED generates a locked 2/1 mode in the plasma at a critical current in the DED coils. Different diagnostics were used to measure the plasma response in the core and edge. The investigations in this paper are focused on the measurement of density fluctuation and the analysis of the coherent-mode structure outside the q = 2 surface using O-mode poloidal correlation reflectometry. A reduction of the quasi-coherent mode amplitude and frequency is observed, caused by the 2/1 mode together with a decrease of the density scale length. Moreover, the deduced poloidal rotation velocity at the q = 3 surface changes from the electron to the ion diamagnetic drift direction with the onset of the 2/1 island. Also a reduction of the density fluctuations is observed as well as a decrease in the poloidal correlation length. From Ar-injection a delayed inward propagation of the emission maximum is observed for different Ar ionization stages when the 2/1 mode is generated.Similar experiments with a slowly rotating DED show that the steepened density gradients are spatially localized and confirm the hypothesis that the 2/1 mode is responsible for the observations.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

A characterization of the Hamiltonian

The classical Hamiltonian ) of the very classical quantum harmonic oscillator, which is regarded as a germ of the most of what comes about in quantum mechanics, can be sublimed to an abstract operator in a separable Hilbert space. Having this done one may ask for a condition which would allow it to be identified among operators of a suitable class. This class is that corresponding to three diagonal matrices and the property which makes the action successful is a kind of diagonal invariance (up to change of basis) within the class in question.     

Continuous-Time Controlled Markov Chains with Discounted Rewards

This paper studies denumerable state continuous-time controlled Markov chains with the discounted reward criterion and a Borel action space. The reward and transition rates are unbounded, and the reward rates are allowed to take positive or negative values. First, we present new conditions for a nonhomogeneous Q(t)-process to be regular. Then, using these conditions, we give a new set of mild hypotheses that ensure the existence of -optimal (0) stationary policies. We also present a martingale characterization of an optimal stationary policy. Our results are illustrated with controlled birth and death processes.