We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minimal structures admit definable parameterizations by mild maps. We then use this parameterization to prove a result on the density of rational points on curves defined by restricted Pfaffian functions.

This article focuses mainly on (1) the policy of Delft University of Technology since 1992 as regards the university-wide introduction of a compulsory course on ethics and engineering, and (2) the ideal structure of such a course, including the educational goals of the course.

It is shown that an approach to quantum phenomena in which charged particles are treated as macroscopically extended periodic disturbances in a nonlinear c-number field, interacting with each other via massless excitations of that field, leads almost uniquely to the five basic equations of classical electrodynamics: the Lorentz force law and Maxwell's equations. The fundamental electromagnetic quantity in this approach is the 4-vector potential Aα—interpreted absolutely as a measure of the local shift of each particle off its mass shell—rather than (...) theE andB fields, and it thus provides a new viewpoint on the questions of Aharonov-Bohm phase shifts, the existence of magnetic monopoles, and the role of gauge invariance. (shrink)

It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure, then \ is the logic of any dense-in-itself metrizable space. The McKinsey–Tarski Theorem relies heavily on a metric that gives rise to the topology. We give a new and more topological proof of the theorem, utilizing Bing’s Metrization Theorem.

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of membership logics is obtained when the variable is the only (...) element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

In the seventeenth chapter, the discussion of the relationship between the organic whole of the historical work and its individual storylines (previously mentioned as parts of history), which began in the sixteenth chapter, continues. It turns out which of them are essential to the general course of events, and which do not affect it, and therefore may be ignored. Obviously, the continuation of such consideration is in the following chapters.

In this paper an attempt is made to interpret inertial mass as a consequence of the invariant periodicity associated with physical de Broglie waves. In the case of a free particle, such waves, observed from an arbitrary reference frame, would exhibit the velocity-dependent wavelength given by de Broglie's relation; and it is conjectured that the inertial and additive properties of mass (or, more precisely, the conservation of momentum and energy) can be related to nonlinear interference effects occurring between the de (...) Broglie waves for different particles. This picture could throw light on the physical meaning of quantization and suggests the possibility of reformulating classical and quantum mechanics in terms of a “quasi-classical” nonlinear field theory in which both inertial and quantization effects result essentially from the periodicity of de Broglie waves. (shrink)