The present book consists of 17 select scientific papers from ten years of work around 2003-2013. The topic covered here is quantization in Astrophysics. We also discuss other topics for instance Pioneer spacecraft anomaly.
We discuss a number of sub-topics, for instance the use of Schrödinger equation to describe celestial quantization. Our basic proposition here is that the quantization of planetary systems corresponds to quantization of circulation as observed in superfluidity. And then we extend it
further to the use of (complex) Ginzburg-Landau equation to describe possible nonlinearity of planetary quantization.
The present book is suitable for young astronomers and astrophysicists as well as for professional astronomers who wish to update their knowledge in the vast topic of quantization in astrophysics. This book is also suitable for college students who want to know more about this subject.
If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and then we check all possible situations, and of course we retain among them only those solutions that verify our equation.
In other words, we say that the equation does not have solutions in the search domain, or the equation has n solutions in this domain. This mode of solving is called partial resolution. Partially solving a Diophantine equation may be a good start for a complete solving of the problem.
The authors have identified 62 Diophantine equations that impose such approach and they partially solved them. For an efficient resolution it was necessarily that they have constructed many useful ”tools” for partially solving the Diophantine equations into a reasonable time.
The computer programs as tools were written in Mathcad, because this is a good mathematical software where many mathematical functions are implemented. Transposing the programs into another computer language is facile, and such algorithms can be turned to account on other calculation systems with various processors.
This book contains 21 papers of plane geometry.
It deals with various topics, such as: quasi-isogonal cevians,
nedians, polar of a point with respect to a circle, anti-bisector,
aalsonti-symmedian, anti-height and their isogonal.
A nedian is a line segment that has its origin in a triangle’s vertex
and divides the opposite side in n equal segments.
The papers also study distances between remarkable points in the
2D-geometry, the circumscribed octagon and the inscribable octagon,
the circles adjointly ex-inscribed associated to a triangle, and several
classical results such as: Carnot circles, Euler’s line, Desargues
theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s
theorem, Pantazi’s theorem, and Newton’s theorem.
Special attention is given in this book to orthological triangles, biorthological
triangles, ortho-homological triangles, and trihomological
Each paper is independent of the others. Yet, papers on the same or similar
topics are listed together one after the other.
The book is intended for College and University students and instructors that
prepare for mathematical competitions such as National and International
Mathematical Olympiads, or for the AMATYC (American Mathematical
Association for Two Year Colleges) student competition, Putnam competition,
Gheorghe Ţiţeica Romanian competition, and so on.
The book is also useful for geometrical researchers.