Related papers: Unavoidable golden ratio
The connection between some features of the metallicity gradient in the Galactic disk, best revealed by Open Clusters and Cepheids, and the spiral structure, is explored. The step-like abrupt decrease in metallicity at 8.5 kpc (with R_0=…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first…
A semiring can be ``completed'' (i.e., embedded into a semiring in which all infinite sums are defined and satisfy some reasonable properties) iff this semiring can be naturally partially ordered. This construction is ``natural'' (a left…
We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalence - it almost surely contains infinitely many copies of…
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…
Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Lexicographic or first choice constructions of geometric objects sometimes lead to amazingly good results. Usually it is difficult to determine the precise identity of these geometries. Here we find infinitely many cases where the…
Although the prime numbers are deterministic, they can be viewed, by some measures, as pseudo-random numbers. In this article, we numerically study the pair statistics of the primes using statistical-mechanical methods, especially the…
The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth-Glibreath…
We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a \emph{topologically non-trivial} way, which, roughly, means that the action for the Goldstone modes contains a quantized…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the range, the random subgraph induced by the set of vertices…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this…
Irreversible transport is generally attributed to vorticity, nonlinear forcing, or explicit symmetry breaking. We show that it can arise even in strictly time-periodic and locally irrotational flows through a purely geometric mechanism. By…
In condensed matter systems, the atoms, electrons or spins can sometimes arrange themselves in ways that result in unexpected properties but that cannot be detected by conventional experimental probes. Several historical and contemporary…
In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of…