we show that in {bf zf} set theory without choice, the ultrafilter mbox{principle} ({bf up}) is equivalent to several compactness theorems for alexandroff discrete spaces and to rudin's lemma, a basic tool in topology and the theory of quasi-continuous domains. important consequences of rudin's lemma are various lift lemmas, saying that certain properties of posets are inherited by th...

This paper departs from traditional calibration in the sense that the pixels forming the camera have a completely unknown topology. Previous works have shown that the statistical properties of natural scenes, and a uniform motion of a camera both in translation and rotation, allow determining the topology of a central camera [10, 6]. Here we show that there is a quasi-linear relationship betwee...

An improved topology of a voltage-fed quasi-resonant soft switching LCrCdc series-parallel half bridge inverter with a constant-frequency for electronic ballast applications is proposed in this paper. This new topology introduces a low-cost solution to reduce switching losses and circuit rating to achieve high-efficiency ballast. Switching losses effect on ballast efficiency is discussed throug...

In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion valuation maps from F-quasi-valuation map based hoops and related properties them are investigated. By using these notions, quasi-metric space. The continuity operations is studied with topology induced by quasi-valuation. Also, homomorphism investigated that under which condition an map...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

This paper presents dual-switch Quasi-Resonant (QR) flyback topology as a cost effective and reliable alternative to the LLC resonant converter for energy efficiency regulation. The proposed topology shows excellent efficiency performance, while maintaining simple design of the conventional flyback converters. It offers higher efficiency than LLC resonant converter at medium and light load, res...

We begin this paper with a discussion of n-dimensional algebraic Vector bundles. Vector bundles of rank n may be identified with locally free Ox-modules of rank n. Several sections are dedicated to reviewing the basic notions of scheme-theory. We show how to construct the projectization of arbitrary rings. This construction corresponds to the construction of the tautological line bundle over an...

An improved topology of a voltage-fed quasi-resonant soft switching LCrCdc series-parallel half bridge inverter with a constant-frequency for electronic ballast applications is proposed in this paper. This new topology introduces a low-cost solution to reduce switching losses and circuit rating to achieve high-efficiency ballast. Switching losses effect on ballast efficiency is discussed throug...

The notion of completeness in metric spaces and that of completing a metric space are traditionally discussed in terms of Cauchy sequences. The main reason being that this concept deals precisely with the issue of convergence of sequences in the sense that every convergent sequence is a Cauchy sequence. The paper deals with completion in a setting that avoids explicit reference to Cauchy sequen...

We periodically modulate the lattice trapping potential of a $^{87}$Sr optical clock to Floquet engineer transition. In context atomic gases in lattices, engineering has been used shape dispersion and topology Bloch quasi-energy bands. Differently from these previous works manipulating external (spatial) quasi-energies, we target internal degrees freedom. spin quasi-energies measure their reson...