Some applications of logic to feasibility in higher types

In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook result on mashine representation of basic feasible functionals. Our proofs are based on essential applications of logic. We introduce a weak fragment of second order arithmetic with second order variables ranging over functions from N into N which suitably characterizes basic feasible functionals, and show that it is a useful tool for investigating the properties of basic feasible functionals. In particular, we provide an example how one can extract feasible "programs" from mathematical proofs which use non-feasible functionals (like second order polynomials)

Excitation and deexcitation processes in atom-Rydberg atom collisions in helium-rich white dwarf atmospheres

We aim to show the importance of non-elastic excitation and deexcitation processes in $\textrm{He}^{*}(n)+ \textrm{He}(1s^{2})$ collisions with the principal quantum number $n \ge 3$ for helium-rich white dwarf atmospheres. We compare the efficiencies of these processes with those of the known non-elastic electron-$\textrm{He}^{*}(n)$ atom processes in the atmospheres of some DB white dwarfs. We show that in significant parts of the considered atmospheres, which contain weakly ionized layers (the ionization degree $\lesssim 10^{-3}$), the influence of the studied atom-Rydberg atom processes on excited helium atom populations is dominant or at least comparable to the influence of the concurrent electron-$\textrm{He}^{*}(n)$-atom processes.Comment: Astronomy & Astrophysics, Accepted: 14 February 201

An evaluation of the analytic continuation by duality technique

In Nucl. Phys. B391 (1993) 127, the value of the oblique correction parameter S for walking technicolor theories was estimated using a technique called Analytic Continuation by Duality (ACD). We apply the ACD technique to the perturbative vacuum polarization function and find that it fails to reproduce the well known result S=1/6\pi. This brings into question the reliability of the ACD technique and the ACD estimate of S.Comment: 8 pages, LaTeX, 1 postscript figure. Uses cite.sty, sprocl.sty, and epsfig.sty. Talk presented at the 1996 International Workshop on Perspectives of Strong Coupling Gauge Theories (SCGT'96), 13-16 Nov. 1996, Nagoy

Ion-atom radiative processes in the solar atmosphere: quiet Sun and sunspots

In the previous works the significance of the symmetric and non-symmetric ion-atom absorption processes in far UV and EUV regions within a model of the quiet Sun atmosphere, has been studied. The considered processes were the processes of the photo-dissociation of the molecular ions H$_{2}^{+}$ and H$X^{+}$ and absorption processes in H+H$^{+}$ and H$+X^{+}$ collisions, where $X$ denotes the metal atom. As the continuation of the previous investigation, these processes are considered also within the corresponding sunspot model. In this work the non-symmetric ion-atom absorption processes are considered with $X=$ Mg, Si, etc. It was analyzed the significance of such processes in far UV and EUV regions in comparison with the concurrent absorption processes, especially with the processes of the photo-ionization of the metal atoms (Na, Mg, Ca, etc.) which were not included in the consideration in the case of the quiet Sun atmosphere. From our analysis it follows that the non-symmetric ion-atom absorption processes considered here, are significant not only for quiet Sun modeling but also for sunspots and should be included {\it ab initio} in both cases.Comment: accepted in Advances in Space Researc

The ion-atom absorption processes as one of the factors of the influence on the sunspot opacity

As a continuation of the previous investigations of the symmetric and strongly non-symmetric ion-atom absorption processes in the far UV region within the models of the quiet Sun photosphere, these processes are studied here within a model of the sunspot. Here we mean the absorption processes in the H$(1s)$+H$^{+}$ and H$(1s)+X^{+}$ collisions and the processes of the photo-dissociation of the H$_{2}^{+}$ and H$X^{+}$ molecular ions, where $X$ is one of the metal atoms: $X=$Na, Ca, Mg, Si and Al. Obtained results show that the influence of the considered ion-atom absorption processes on the opacity of sunspots in the considered spectral region (110 nm $\lesssim \lambda \lesssim$ 230 nm) is not less and in some parts even larger than the influence of the referent electron-atom processes. In such a way, it is shown that the considered ion-atom absorption processes should be included \emph{ab initio} in the corresponding models of sunspots of solar-type and near solar-type stars. Apart of that, the spectral characteristics of the considered non-symmetric ion-atom absorption processes (including here the case $X$ = Li), which can be used in some further applications, have been determined and presented within this work.Comment: Accepted in Monthly Notices of the Royal Astronomical Societ