We introduce the notion of quasi-zero-dimensionality as a substitute for the notion of zero-dimensionality, motivated by the fact that the latter behaves badly in the realm of qcb-spaces. We prove that the category QZ of quasi-zero-dimensional qcb0-spaces is cartesian closed. Prominent examples of spaces in QZ are the spaces of the Kleene-Kreisel continuous functionals equipped with the respect...

Abstract: In pointfree topology, the point-finite covers introduced by Dowker and Strauss do not behave similarly to their classical counterparts with respect to transitive quasi-uniformities, contrarily to what happens with other familiar types of interior-preserving covers. The purpose of this paper is to remedy this by modifying the definition of Dowker and Strauss. We present arguments to j...

Quasi-phase-matched second-harmonic generation of 532 nm radiation in 25 degrees -rotated, x-cut, near-stoichiometric lithium tantalate has been performed. Using a face-normal topology for frequency conversion applications allows scalable surface area to avoid surface and volume damage in high-power interactions. First-order, quasi-phase-matched second-harmonic generation was achieved using nea...

Let A be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space AA]. Then A is called a topological partial *-algebra if it satisses a number of conditions, which all amount to require that the topology ts with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of...

It is well known [Hoc69, Joy71] that profinite T0-spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space. (2) The T0-reflection of (X,τ) is a profinite T0-space. (3) (X,τ) is a quasi spectral space (in the sense of [BMM08]). (4) (X,τ) admits a ...

We study integral vectorial functionals F(u;) ? Z f(x; u(x); Du(x))dx where f satisses quasi-convexity assumption and its growth is controlled in term of N-functions. We obtain semicontinuity results in the weak * topology of Orlicz-Sobolev spaces.

The work of Constantin-Majda-Tabak [1] developed an analogy between the Quasi-geostrophic and 3D Euler equations. Constantin, Majda and Tabak proposed a candidate for a singularity for the Quasi-geostrophic equation. Their numerics showed evidence of a blow-up for a particular initial data, where the level sets of the temperature contain a hyperbolic saddle. The arms of the saddle tend to close...

A characterization of partial metrizability is given which provides a partial solution to an open problem stated by Künzi in the survey paper Nonsymmetric Topology ([Kün93], problem 71). The characterization yields a powerful tool which establishes a correspondence between partial metrics and special types of valuations, referred to as Q-valuations (cf. also [Sch00]). The notion of a Q-valuatio...

We sharpen the notion of a quasi-uniform space to spaces which carry with them functional means of approximating points, opens and compacts. Assuming nothing but sobriety, the requirement of uniform approximation ensures that such spaces are compact ordered (in the sense of Nachbin). We study uniformly approximated spaces with the means of topology, uniform topology, order theory and locale the...

Electronic loads are a family of power converters which can be used as a variable impedance load in different applications. This paper analyzes high efficiency zero-voltage electronic loads based on the quasi Z-source converter topology .The proposed topology operate as an ideal current source which enables the operation of the zero input voltage. It can achieve a high efficiency of more than 9...