We study the matrix completion problem: an underlying $$m \times n$$ P is low rank, with incoherent singular vectors, and a random A equal to on (uniformly) subset of entries size dn. All other are zero. The goal retrieve information from observation A. Let $$A_1$$ be where each entry multiplied by independent $$\{0,1\}$$ -Bernoulli variable parameter 1/2. This paper about when, how why non-Her...

K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...

The non-linear realisation based on $A_1^{+++}$ is known to describe gravity in terms of both the graviton and dual graviton. We extend this analysis at linearised level find equations motion for first higher description that it contains. also give a systematic method finding additional fields beyond those are required construct actions all possible descriptions realisation. show these closely ...

The lowest critical point of one unitary matrix model with cosine plus logarithmic potential is known to correspond the $(A_1, A_3)$ Argyres-Douglas (AD) theory and its double scaling limit derives Painlev\'{e} II equation parameter. Here, we consider points associated all potentials determine operators, their vevs dimensions from perturbed string equations at planar level. These agree those $(...

In the article we deepen metric component of theory infinite $A_2$-continued fractions $[0;a_1,a_2,...,a_n,...]$ with a two-element alphabet $A_2=\{\frac12,1\}$, $a_n\in A_2$ and establish normal property numbers segment $I=[\frac12;1]$ in terms their $A_2$-representations: $x=[0;a_1,a_2,...,a_n,...]$. It is proved that almost all (in sense Lebesgue measure) $I$ $A_2$-representations use each t...

Abel's quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety $A$. If $A$ is isogenous direct product varieties $A\cong A_1\times\cdots\times A_k$, can be used construct various Lax matrices on factors $A_1,\ldots,A_k$. As an example, we discuss 2-dimensional reducible $A=E_+\times E_-$, which 1-dimensional $E_\pm$ obtained by Euler in ...

The COMPASS experiment recently discovered a new isovector resonance-like signal with axial-vector quantum numbers, the $a_1(1420)$, decaying to $f_0(980)\pi$. With mass too close and width smaller than ground state $a_1(1260)$, it was immediately interpreted as light exotic meson, similar $X$, $Y$, $Z$ states in hidden-charm sector. We show that fully matching experimental data is produced by ...