The groups mentioned in the title are certain matrix of infinite size over a finite field $\mathbb F_q$. They built from classical and at same time they similar to reductive $p$-adic Lie groups. In present paper, we initiate study invariant measures for coadjoint action these infinite-dimensional We examine first group $\mathbb{GLB}$, topological completion inductive limit $\varinjlim GL(n, \ma...

Let $SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices and set $SM(\mathbb{R})^g = \cup_n SM_n(\mathbb{R})^g$. A free quadrilateral is the collection tuples $X \in SM(\mathbb{R})^2$ which have positive semidefinite evaluation on linear equations defining a classical quadrilateral. Such closed under rich class convex combinations called matrix combination. That is, gi...

Abstract We study radiative charm decays $$D \rightarrow P_1 P_2 \gamma $$ D → P 1 2 γ , $$P_{1,2}=\pi ,K$$ , = π K</mml...

We study the interstellar medium (ISM) properties as a function of molecular gas size for 77 infrared-selected galaxies at $z \sim 1.3$. Molecular sizes are measured on ALMA images that combine CO(2-1), CO(5-4) and underlying continuum observations, include CO(4-3), CO(7-6)+[CI]($^3 P_2-^3P_1$), [CI]($^3 P_1-^3P_0$) observations subset sample. The $\gtrsim 46 \%$ our have compact reservoir, lie...

Abstract We study the integrability of 2D Hamiltonian systems $$H_\mu =\frac{1}{2}(p_1^2+p_2^2) + \omega (p_1q_2-p_2q_1) -\tfrac{\mu }{r}+ V(q_1,q_2)$$ H μ = 1 2 ( ...

A bstract The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle O p 1 2 3 4 </mm...

Let $P=(p_1, p_2, \dots, p_n)$ be a polygonal chain in $\mathbb{R}^d$. The stretch factor of $P$ is the ratio between total length and distance its endpoints, $\sum_{i = 1}^{n-1} |p_i p_{i+1}|/|p_1 p_n|$. For parameter $c \geq 1$, we call $c$-chain if $|p_ip_j|+|p_jp_k| \leq c|p_ip_k|$, for every triple $(i,j,k)$, $1 i<j<k n$. global property: it measures how close to straight line, involves al...

To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution multiple moons, orbiting extremely irregular body and including their mutual interactions. Such orbits are generally non-Keplerian orbital elements not constants. Consequently, use a modified $N$-body integrator, which was significantly extended include the multipole expansion gravitational field up o...