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Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…
Complicated hardenings and softenings of the spectra of cosmic ray protons and helium have been revealed by the newest measurements, which indicate the existence of multiple source populations of Galactic cosmic rays. We study the physical…
Ultra-high-energy cosmic rays (UHECRs) are atomic nuclei from space with vastly higher energies than any other particles ever observed. Their origin and chemical composition remain a mystery. As we show here, the large- and…
We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a $2$-dimensional subspace forms a Hadamard matrix. It is shown that such a matrix of order $n$ exists, if…
The reduced density matrices (RDMs) of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical…
A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases. As their key feature these split matroids can be studied via techniques from polyhedral geometry. It turns out that the…
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times…
The hundreds of exoplanets that have been discovered in the past two decades offer a new perspective on planetary structure. Instead of being the archetypal examples of planets, those of our Solar System are merely possible outcomes of…
Ever since the very first photometric studies of Centaurs and Kuiper Belt Objects (KBOs) their visible color distribution has been controversial. That controversy gave rise to a prolific debate on the origin of the surface colors of these…
By means of periodic orbit theory and deformed cavity model, we have investigated semiclassical origin of superdeformed shell structure and also of reflection-asymmetric deformed shapes. Systematic analysis of quantum-classical…
The cerebrum of mammals spans a vast range of sizes and yet has a very regular structure. The amount of folding of the cortical surface and the proportion of white matter gradually increase with size, but the underlying mechanisms remain…
The emergence of Lorentzian geometries in spin-foams and group field theories is investigated. The spectral dimension of periodic Euclidean spin-foam frusta is studied. At large scales, the spectral dimension is generically four. At lower…
Equiangular tight frames provide optimal packings of lines through the origin. We combine Steiner triple systems with Hadamard matrices to produce a new infinite family of equiangular tight frames. This in turn leads to new constructions of…
The recent discovery of hidden non-axysimmetric and disk-like structures in bright Virgo dwarf elliptical and lenticular galaxies (dE/dSph/dS0) indicates that they may have late-type progenitors. Using N-body simulations we follow the…
Dendritic growth patterns exhibiting four-fold anisotropy are observed when polyethylene oxide undergoes phase segregation from a solution phase to a solid phase. When this phase transition occurs on a substrate that has patterns of…
Organisms have increased in complexity through a series of major evolutionary transitions, in which formerly autonomous entities become parts of a novel higher-level entity. One intriguing feature of the higher-level entity after some major…
Binary systems consisting of a white dwarf and a main-sequence companion with orbital periods up to $\approx 100$ d are often thought to be formed through common envelope evolution which is still poorly understood. To provide new…
We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only…
We report a linear ordering of orbits in a sample of multiple extrasolar planetary systems with super-Earth planets. We selected 20 cases, mostly discovered by the Kepler mission, hosting at least four planets within \sim 0.5 au. The…
Motivated by a system consisting of a number of parallel M5-branes, we study possible local deformations of a chiral two-form in six dimensions. Working to first order in the coupling constant, this reduces to the study of the local BRST…