Ve fyzice i v technických oborech býváme postaveni před úkol řešit problémy, které jsou sice svou podstatou prostorové, avšak funkce popisující řešení úlohy jsou závuislé jen na souřadnicích x a y v rovině. Typickým příkladem je rozložení potenciálu elektrostatického pole velmi dlouhého válcového kondenzátoru nebo rozložení teploty mezi trubkami souosého potrubí. I tak však může být přímé řešení problému v rovině xy složité, nebo dokonce neschůdné. Konformní zobrazení umožňuje převést úlohu z definičního oboru D v rovině xy, kterou si představíme jako Gaussovu rovinu a ze souřadnic x a y sestavíme komplexní proměnnou z = x + iy opět do Gaussovy roviny pomocí zobrazení w = f(z) = u(x, y) + iv(x, y) vhodných vlastností, v níž se řešení může významně zjednodušit. Takové zobrazení popíšeme a ukážeme jeho účinnost na příkladech., Jana Musilová, Pavla Musilová., and Obsahuje bibliografické odkazy
In this article I deal with the general question of logical truth or, rather, with the question of what it means when we say that a sentence or a judgement is true for logical reasons. I tackle this question against the background of the most important milestones in the development of logic understood in the broadest sense that is, the projects (1) of Eleatic and Platonic dialectic; (2) Aristotle’s syllogistic approach; (3) Kant’s transcendental logic; and (4) the modern logic of Frege. In relation to the latter I indicate two kinds of influence which formed it, namely (a) the mathematical influence stemming from the problems surrounding the reformed calculus, and (b) the philosophical influence consisting in the rejection of Kant’s definition of mathematics as sciences depending on constructions in space and time. The overall result of the paper will be a critical view of the very idea of formal logic, i.e. of the canon of judgement which is applied quite generally, regardless of the given field, so influentially articulated by, for example, Descartes and Brouwer.
Over the last decade, extensive observations of carbon monoxide emission in the disk of our Galaxy have shown that molecular (H2) gas rather than atomlc (HI) hydrogen is the major actlve component of the interstellar medium. In the Galaxy, virtually all known regions of star formation activity are associated with molecular clouds. In this artlcle, we review the theoretical and empirical basis for using the 2.6 mm CO emission line as a tracer of H2 and summarize the galactic distribution and properties of the molecular clouds.
Molecular clouds are the dominant component of the interstellar medium in the inner half of the galactic disk at R <0.8 R . Most of the molecular gas is in clouds at the hlgh end of the mass spectrum with mass >10^5 (GMC), with over half the mass in clouds with M >4 x 10^5 M^. The longitude and velocity of 'warm' molecular clouds, whose temperatures imply substantial internal heating, are correlated with giant HII regions and may be associated with armlike spiral structure. Cooler clouds are distributed much more widely throughout the disk. The radial distribution of cloud
nuraber denslty is similar to the distribution of CO emlssivity - that is, a ringlike concentratlon at 0.4 - 0.8 Rq with a relatlvely sharp inner edge and a gradual falloff toward large R. Giant molecular clouds do not fit Into a two- or three-phase pressure-equlllbrlum plcture of interstellar matter. They are gravitationally bound and their Internal pressure, domlnated by chaotic raotions, is 2 orders of magnitude greater than the standard Interstellar medium pressure.
A likely orlgin for these clouds is gravitational Instability.
During thee last decade millimeter vvave observations of ihe CO molecule have proved to be one of the most important probes
of the large scale structure and kinematics of the galactic disk. CO surveys show a strong concentralion of molecular gas in
the galactic center region and at a distance of 0.4 - 0.8 Ro often recorded to as the ‘galactic ring’. The shape of the CO radial
distribution is similar to nearly all other tracers of population I material, but quite different from the flat distribution of HI.
Recent high-resolution surveys allow an unprecedented view of individual molecular clouds throughout the disk on all size scales
between a few parsecs and many kiloparsecs. Massive, giant molecular clouds (CMC) are the dominant reservoir of interstellar
matter in the inner galaxy, and are the main active star forming component of the interstellar medium. This article reviews the
theoretical and empirical basis for using the 2.6 mm CO emission line as a tracer of H2 and summarizes the galactic distribution
and properties of the molecular clouds.