The approximate Carathéodory theorem states that given a compact convex set $${\mathcal {C}}\subset {\mathbb {R}}^n$$ and $$p\in [2,+\infty [$$ , each point $$x^*\in {\mathcal {C}}$$ can be approximated to $$\epsilon $$ -accuracy in the $$\ell _p$$ -norm as combination of {O}}(pD_p^2/\epsilon ^2)$$ vertices where $$D_p$$ is diameter -norm. A solution satisfying these properties built using prob...

Abstract We present a methodology that allows to measure the dynamics of polydisperse suspension flows by means Astigmatism Particle Tracking Velocimetry (APTV). Measurements are successfully performed with tridisperse suspensions in square duct up $$\varPhi =9.1\%$$ Φ = 9.1 <...

We present a calculation of the contribution $\Theta$-term to neutron and proton electric dipole moments using seven 2+1+1-flavor HISQ ensembles. also estimate topological susceptibility for 2+1+1 theory be $\chi_Q = (66(9)(4) \rm MeV)^4$ in continuum limit at $M_\pi 135$ MeV. The nucleon three-point function is done Wilson-clover valence quarks. CP-violating form factor $F_3$ calculated by exp...

Consider a sequence of Riemannian manifolds $(M^n_i,g_i)$ with scalar curvatures and entropies bounded below by small constants $R_i,\mu_i \geq-\epsilon_i$. The goal this paper is to understand notions convergence the structure limits for such spaces. Even in seemingly rigid case $\epsilon_i\to 0$, we construct examples showing that may converge wildly Gromov-Hausdorff or Intrinsic Flat sense. ...

This study introduces a new family of volumetric flatness factors which give rigorous parametric description the phenomenon intermittency in fully developed turbulent flows. These quantities gather information about most "active" part velocity field at each scale $\ell$, and allows one to define dimension function $p \to D_p$ that recovers correction structure exponents $\zeta_p$ an explicit wa...

Abstract The generalized Cesàro operators $$C_t$$ C t , for $$t\in [0,1]$$ ∈ [ 0 , 1 ] were first investigated in the 1980s. They act continuousl...

A search for the $P$- and $CP(T)$-violating electric dipole moments (EDM) of atoms, particles nuclei with sensitivity up to $10^{-15}$ in units magnetic moments, allowed by all discrete symmetries, is one topical problems modern physics. According Sakharov, $CP$-violation three key criteria baryogenesis generally accepted paradigm Big Bang cosmology. All are supported Standard Model (SM), but i...

We study experimentally the behaviour of negatively buoyant disks and fibres in a turbulent boundary layer. The regime is relevant to transport natural sediment or plastic particles water, with density ratio $\rho _p/\rho _f \sim O(1)$ , major axis lengths $D_p^+ 50$ friction Stokes numbers $\mbox { {St}}^+ O(10)$ Reynolds number {Re}}_\tau = 620$ . translational rotational motion, as well conc...