Traditional Quanta

Acoustic Quanta

This paper presents a novel approach to sound analysis and resynthesis based on Gabor wavelets. These wavelets are mathematically simple and computationally modest, and are well suited to musical applications. This paper outlines the principles and equations behind quanta. It then gives examples of their applications in analysis and synthesis, and presents results from implementation on the PC.

Quanta of Geometry

Ali H. Chamseddine, 2, ∗ Alain Connes, 2, 4, † and Viatcheslav Mukhanov 6, ‡ Physics Department, American University of Beirut, Lebanon I.H.E.S. F-91440 Bures-sur-Yvette, France College de France, 3 rue Ulm, F75005, Paris, France Department of Mathematics, The Ohio State University, Columbus OH 43210 USA Theoretical Physics, Ludwig Maxmillians University,Theresienstr. 37, 80333 Munich, Germany ...

Energy, Quanta, and Vision

1. Direct measurements of the minimum energy required for threshold vision under optimal physiological conditions yield values between 2.1 and 5.7 x 10(-10) ergs at the cornea, which correspond to between 54 and 148 quanta of blue-green light. 2. These values are at the cornea. To yield physiologically significant data they must be corrected for corneal reflection, which is 4 per cent; for ocul...

Taming the Quanta

Roots Appear in Quanta

We start with a special case. Consider an irreducible quintic polynomial f(X) = X + a1X + a2X + a3X + a4X + a5 with rational coefficients and with three real roots and one pair of complex conjugate roots. For example, f(X) could be X − 10X + 5. Question. If α is a root of f , then how many roots of f lie in the field Q(α)? The field Q(α) is obtained by adjoining the root α to Q. Thus Q(α) conta...