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The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the…

Superconductivity, superfluidity, condensation, cluster formation, etc. are phenomena that might occur in many-particle systems. These are due to residual interactions between the particles. To explain these phenomena consistently in a…

We propose a simple model for periodic clustering of particles under forced oscillation. Effective viscosity is assumed to increase owing to neighboring particles by analogy with the Einstein viscosity law. The linear stability analysis and…

We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…

In these notes we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum…

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects…

Relativistic charge distributions of targets with arbitrary average momentum are introduced. They provide an interpolation between the usual Breit frame and infinite-momentum frame distributions. We find that Breit frame distributions can…

We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…

We elaborate the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. The entanglement is characterized in terms of generalized Segre maps,…

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…

For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a…

We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…

Gravitational lensing allows to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe in this paper the corresponding theory in Lagrangian space…

It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is possible if one considers a unitary ring or a Boolean algebra…

We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we…

In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved

Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…

We transform superstring scattering amplitudes into the correlation functions of primary conformal fields on two-dimensional celestial sphere. The points on celestial sphere are associated to the asymptotic directions of (light-like)…

We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…

Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If…