Countably compact extensions of topological spaces

We study the question whether a topological space X with a property $\text{P}$ can be embedded in a countably compact space X? with the same property $\text{P}$.     

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.     

Infrared Variables for the SU(3) Yang–Mills Field

We generalize the self-dual parameterization of the SU(2) Yang–Mills field proposed by Niemi and Faddeev for describing the infrared limit of the theory to the case of the gauge group SU(3). We demonstrate that the duality property intrinsic to the SU(2) gauge field cannot be transferred automatically to the higher-rank group case. We interpret the algebraic structures appearing in the Lagrangian for the new compact variables in terms of the group products SU(2)³.     

A proof of W. T. Gowers' theorem

W. T. Gowers' theorem asserts that for every Lipschitz function and 0$">, there exists an infinite-dimensional subspace of such that the oscillation of on is at most . The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.

     

An approximation problem of the finite rank operator in Banach spaces

By the method of geometry of Banach spaces, we have proven that a bounded linear operator in Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rank bounded homogeneous operators, which reveals the essence of the counter example given by Enflo.