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The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate…
A general expression for the spectrum of photons emitted by atom at sudden perturbation is obtained. Some concrete examples of application of the obtained result are considered. The conclusion about the coherence of radiation of the atomic…
The evolution of the spectrum of cosmological fluctuations from one cycle to the next is studied. It is pointed out that each cycle leads to a reddening of the spectrum. This opens up new ways to generate a scale-invariant spectrum of…
We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then…
In this paper, we compute the spectral norms of the matrices related with integer squences and we give some example related with Fibonacci, Lucas, Pell and Perrin numbers.
We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…
The purpose of this note is to present a possible explanation of the spectral distorsions that could be observed in the CMBR spectrum.We propose that distor- sions of the order of $y \sim 10^{- 6}$ can be interpreted as a consequence of…
Some basic features of confinement are reviewed, in particular the symmetry patterns of the dual dynamics. Open problems and possible directions of progress are discussed.
Instead of the infinitesimal extrinsic and intrinsic perturbations on strings, considered so far, we discuss the evolution and propagation of finite-amplitude perturbations. Those intrinsic perturbations may result in appearance of stable…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
For each element of certain families of integer sequences, we study the term-wise ratios of the Hankel transforms of three sequences related to that element by series reversion. In each case, the ratios define well-known sequences, and in…
The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…
We study some aspects of the Quantum Brachistochrone Problem. Physical realizability of the faster pseudo Hermitian version of the problem is also discussed. This analysis, applied to simple quantum gates, supports an informational…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
We study several aspects of the regular deformations of completely integrable systems. Namely, we prove the existence of a Hamiltonian normal form for these deformations and we show the necessary and sufficient conditions a perturbation has…
In many practical situations, the useful signal is contained in a low-dimensional subspace, drown in noise and interference. Many questions related to the estimation and detection of the useful signal arise. Because of their particular…
A brief presentation of basic definitions and notation used in permutation patterns research.
This is a pedagogical introduction to the main concepts of the sterile neutrino - a hypothetical particle, coined to resolve some anomalies in neutrino data and retain consistency with observed widths of the $W$ and $Z$ bosons. We briefly…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…