A General Theory of Ultra-short Wave Circuits I

Ultra-Short-Wave Therapy in Medical Practice

are the basis of visible and still shorter wave radiations. The electric waves in the narrow sense of the Hertzian waves occur as the result of oscillations of fairly large electric charges in oscillatory circuits. With a frequency of 10s cycles per second the wave-length is 3 metres and with 107 cycles per second it is 30 metres. The wave-lengths we are now concerned with are generally between...

A general theory of self-similarity I

Consider a self-similar space X . A typical situation is that X looks like several copies of itself glued to several copies of another space Y , and Y looks like several copies of itself glued to several copies of X , or the same kind of thing with more than two spaces. Thus, the self-similarity of X is described by a system of simultaneous equations. Here I formalize this idea and the notion o...

General Theory of Elastic Wave Scattering

A q-Queens Problem. I. General Theory

By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways to place q identical nonattacking pieces on a board of variable size n but fixed shape is (up to a normalization) given by a quasipolynomial function of n, ...

The Theory of Ultra-Coarse-Graining. 1. General Principles.

Coarse-grained (CG) models provide a computationally efficient means to study biomolecular and other soft matter processes involving large numbers of atoms correlated over distance scales of many covalent bond lengths and long time scales. Variational methods based on information from simulations of finer-grained (e.g., all-atom) models, for example the multiscale coarse-graining (MS-CG) and re...