On the strength of the finite intersection principle

We study the logical content of several maximality principles related to the finite intersection principle (F\IP) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their strengths vary: some are equivalent to \ACA over \RCA, while others are strictly weaker, and incomparable with \WKL. We show that there is a computable instance of F\IP all of whose solutions have hyperimmune degree, and that every computable instance has a solution in every nonzero c.e.\ degree. In terms of other weak principles previously studied in the literature, the former result translates to F\IP implying the omitting partial types principle ($\mathsf{OPT}$). We also show that, modulo $\Sigma^0_2$ induction, F\IP lies strictly below the atomic model theorem ($\mathsf{AMT}$).Comment: This paper corresponds to section 3 of arXiv:1009.3242, "Reverse mathematics and equivalents of the axiom of choice", which has been abbreviated and divided into two pieces for publicatio

An Algorithm for Segment Stability

In this note an algorithm for testing on stability-unstability of polynomial segments with stable end-points is given. The algorithm is based on well-known segment lemma and on approximate positive real roots of suitable polynomial equation. In this paper an upper bound for absolute error of approximate root that guarantees the segment stability or unstability is established. In the case of unstability the algorithm, differs from the existing algorithms, explains the segment behavior in the parameter space. Some illustrative examples also are given

Isomerization of 14-hydroxy-17-ketosteroids: New examples of two-centered inversion of the C/D ring fusion and X-ray diffraction structural analysis of d,ℓ-3-methoxy-14β-hydroxy-8β, 9α-estra-1,3,5(10)-trien-17-one

d,ℓ-3-Methoxy-14β-hydroxy-8α,9β-estra-1,3,5(10)-trien-17-one (I) undergoes two-centered isomerization in alkaline medium to d,ℓ-3-methoxy-14β-hydroxy-8β,9α-estra-1, 3,5(10)-trien-17-one (II) in 70% yield. Under analogous conditions, natural isomer (II) is converted into synthetic isomer (I) in 20% yield. The crystalline and molecular structure of isomer (II) was established

Performance improvement of silicon solar cells by nanoporous silicon coating

In the present paper the method is shown to improve the photovoltaic parameters of screen-printed silicon solar cells by nanoporous silicon film formation on the frontal surface of the cell using the electrochemical etching. The possible mechanisms responsible for observed improvement of silicon solar cell performance are discussed