The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define geometric mean aid which we investigate geometry equipped with show that geodesic segment joining arbitrary $\mu_1$ and $\mu_2$ is expressed using normalized its endpoints. As an application, any two ...

The purpose of this paper is to investigate the properties spectral and tiling subsets cyclic groups, with an eye towards set conjecture in one dimension, which states that a bounded measurable subset $\mathbb{R}$ accepts orthogonal basis exponentials if only it tiles by translations. This strongly connected its discrete counterpart, namely every finite group, tile. tools presented herein are r...

A Morley–Wang–Xu (MWX) element method with a simply modified right hand side is proposed for fourth order elliptic singular perturbation problem, in which the discrete bilinear form standard as usual nonconforming finite methods. The sharp error analysis given this MWX method. And Nitsche’s technique applied to MXW achieve optimal convergence rate case of boundary layers. An important feature s...

<p style='text-indent:20px;'>A minimal system <inline-formula><tex-math id="M1">\begin{document}$ (X,T) $\end{document}</tex-math></inline-formula> is topologically mildly mixing if for all non-empty open subsets id="M2">\begin{document}$ U,V $\end{document}</tex-math></inline-formula>, id="M3">\begin{document}$ \{n\in {\mathbb Z}: U\cap T^{-n}V\n...

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\alpha$ is presented for ground and $n = 2$ excited states helium-like ions. After subtracting first terms expansion from all-order results, we identify higher-order order $m\alpha^7$ higher. Combining remainder with results complete through $m\alpha^6$ [V. A. Yerokhin K. Pachucki, Phys. Rev. 81,...

Motivated by an optimal visiting problem, we study a switching mean-field game on network, where both decisional and time-variable is at disposal of the agents for what concerns, respectively, instant to decide perform switch. Every switch between nodes network represents from $0$ $1$ one component string $p = (p_1,\ldots, p_n)$ which, in interpretation, gives information visited targets, being...

In recent paper Fakkousy et al. show that the 3D Hénon-Heiles system with Hamiltonian $$ H = \frac{1}{2} (p_1 ^2 + p_2 p_3 ^2) +\frac{1}{2} (A q_1 C q_2 B q_3 (\alpha \gamma ^2)q_3 \frac{\beta }{3}q_3 ^3 is integrable in sense of Liouville when $$\alpha , \frac{\alpha }{\beta } 1, A C$$ ; or \frac{1}{6}, B-arbitrary; \frac{1}{16}, C, \frac{A}{B} \frac{1}{16}$$ (and course, =\gamma =0$$ which ca...

The remarkable recent progress in the precision of Lattice QCD computations for a number physical quantities relevant flavour physics has motivated introduction isospin-breaking effects, including particular electromagnetic corrections, to computations. isospin breaking corrections are necessary fully exploit this improved determination fundamental parameters Standard Model, CKM matrix elements...