We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the perturbation reaches some critical value) or continuously. In the latter case we have a smooth transition from the classical form of the set to some forms, cons...

The aim of this note is to show how various facts in classical topology connected with semicontinuous functions and the semicontinuous quasi-uniformity have their counterparts in pointfree topology. In particular, we introduce the localic semicontinuous quasi-uniformity, which generalizes the semicontinuous quasiuniformity of a topological space (known to be one of the most important examples o...

Quasi-Monte Carlo integration is said to be better than Monte-Carlo integration since its error bound can be in the order of O(N (1 )) instead of the O(N 0:5) probabilistic bound of classical Monte-Carlo integration if the integrand has finite variation. However, since in computer graphics the integrand of the rendering equation is usually discontinuous and thus has infinite variation, the supe...

In this paper we prove strong completeness of axiomatic extensions of First Order SMTL logic adding the so-called quasi-witnessed axioms with respect to quasi-witnessed Models. In order to achieve this result, we make use of methods that are typical of Classical Predicate Logic, and have been later generalized by P. Hájek to cope with Predicate Fuzzy Logic. At the end of the paper, we obtain, a...

New concepts are defined, in particular the quasi-question or vertex with an outgoing arc of zero probability. A quasi-questionnaire is a probabilistic homogeneous (rooted) tree with quasiquestions. It is shown that every instantaneous code is a quasi-questionnaire with precise restrictive conditions; it may also be a questionnaire, without an arc of zero probability. Also, an approximation is ...

We rigorously justify the so-called one and one-half layer quasi-geostrophic model from the two layer model as the ratio of the depth of the bottom layer over that of the top layer approaches infinity. The effective dynamics is given by the classical barotropic quasi-geostrophic dynamics for the bottom layer without topography, and the one layer quasi-geostrophic dynamics with the stream functi...

Let Σ be a closed, orientable surface of genus g. It is known that the SU(2, 1) representation variety of π1(Σ) has 2g− 3 components of (real) dimension 16g− 16 and two components of dimension 8g−6. Of special interest are the totally loxodromic, faithful (that is quasi-Fuchsian) representations. In this paper we give global real analytic coordinates on a subset of the representation variety th...

The classical Michaelis-Menten approximation for scheme (la) is the archetypal example for the use of the quasi-steady state (QSS) approximation. This approximation is a major simplifying step throughout biology, with its enormous range of time scales, and indeed in many other branches of science. The quasi-steady state assumption (QSSA) often yields revealing analytic formulas and it frequentl...

In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by ScharfetterGummel fluxes. We establish that all the a priori estimates needed to prove the convergence of the scheme does not...