We find upper bounds for the spherical cap discrepancy of set minimizers Riesz s-energy on sphere $$\mathbb S^d.$$ Our results are based a Sobolev introduced by Thomas Wolff in an unpublished manuscript where estimates logarithmic energy S^2$$ were obtained. result improves previously known $$0\le s<2$$ and $$s\ne 1$$ S^2,$$ $$s=0$$ is Wolff’s result, $$d-t_0<s<d$$ with $$t_0\approx 2.5$$ when ...

In this paper we explore a finite volume renormalization scheme that combines three main ingredients: coupling based on the gradient flow, use of twisted boundary conditions and particular asymmetric geometry, for $SU(N)$ gauge theories consists hypercubic box size $l^2 \times (Nl)^2$, choice motivated by study independence in large $N$ theories. We argue has several advantages make it particul...

In recent years, much attention has been paid to the study of forward and inverse problems for Rayleigh-Stokes equation in connection with importance this applications. This plays an important role, particular, behavior certain non-Newtonian fluids. The includes a fractional derivative order $$\alpha $$ , which is used describe viscoelastic flow. paper, we solution such equations depending on p...

The optical properties of monocrystalline, intrinsic silicon are interest for technological applications as well fundamental studies atom-surface interactions. For an enhanced understanding, it is great to explore analytic models which able fit the experimentally determined dielectric function $\epsilon(T_\Delta, \omega)$, over a wide range frequencies and temperature parameter $T_\Delta = (T-T...

This article analyzes the global stability of synchronous reference frame phase-locked loops (SRF-PLLs) from a large signal viewpoint. First, large-signal model SRF-PLL is accurately established, without applying any linearization method. Then, according to phase portrait and Lyapunov argument, performance discussed in nonlinear frame. Compared with small-signal analysis methods, proposed analy...

The Hawking--Page phase transitions of the $d$-dimensional Schwarzschild and charged black holes are explored in a cavity. transition temperature $T_{\rm HP}$, minimum hole $T_0$, Gibbs free energy $G$ systematically calculated. A dual relation for anti-de Sitter space, HP}(d)=T_0(d+1)$, is found to be also approximately valid cavity case high precision, this can further generalized suitable fo...

In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...

We put constraints on the degenerate higher-order scalar-tensor (DHOST) theories using Planck 2018 likelihoods. In our previous paper, we developed a Boltzmann solver incorporating effective field theory parameterised by six time-dependent functions, $\alpha_i$ $(i={\rm B},{\rm K},{\rm T},{\rm M},{\rm H})$ and $\beta_1$, which can describe DHOST theories. Using Markov-Chain Monte-Carlo method w...