相关论文: Minimum Riesz Energy Problem on the Hyperdisk

We calculate the first order variation of the Riesz $\alpha$-energy of a log-concave function $f$ with respect to the Asplund sum. Such a variational formula induces the Riesz $\alpha$-energy measure of log-concave function $f$, which will…

This first part of the series treats the Maxwell equations in the exterior of a slowly rotating Kerr black hole. By performing a first-order differential operator on each extreme Newman-Penrose (N-P) scalar in a Kinnersley tetrad, the…

In this paper we study the existence of minimizers for interaction energies with the presence of external potentials. We consider a class of subharmonic interaction potentials, which include the Riesz potentials $|{\bf…

We revisit the spectral appearance of extended self-gravitating accretion disks surrounding compact central objects such as supermassive black holes. Using dust-poor opacities, we show that all optically thick disk solutions possess a…

In this paper, with considering the nonlinear electromagnetic field coupled to Einstein gravity, we obtain the higher dimensional slowly rotating charged black hole solutions. By use of the fact that the temperature of the extreme black…

We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a…

In Einstein-Maxwell-Chern-Simons theory the extremal Reissner-Nordstr\"om solution is no longer the single extremal solution with vanishing angular momentum, when the Chern-Simons coupling constant reaches a critical value. Instead a whole…

In this paper, we present a quantitative central limit theorem for the d-dimensional stochastic heat equation driven by a Gaussian multiplicative noise, which is white in time and has a spatial covariance given by the Riesz kernel. We show…

The Ultra Luminous X-ray Sources (ULXs) are unique in exhibiting moderately bright X-ray luminosities, $L_{\rm x} \sim 10^{38-40} {\rm erg~s^{-1}}$, and relatively high blackbody temperatures, $\Tin \sim 1.0-2.0 {\rm keV}$. From the…

In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is shown that the intersection of a suitable ball with the…

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to…

The supercritical disk accretion flow with radiatively driven outflows is studied based on two-dimensional radiation-hydrodynamic simulations for a wide range of the mass input rate, $\dot{M}_{\rm input}$, which is the mass supplied from…

We set to weigh the black holes at their event horizons in various spacetimes and obtain masses which are substantially higher than their asymptotic values. In each case, the horizon mass of a Schwarzschild, Reissner-Nordstr{\"o}m, or Kerr…

We study the following nonlinear Schr\"{o}dinger system which is related to Bose-Einstein condensate: {displaymath} {cases}-\Delta u +\la_1 u = \mu_1 u^{2^\ast-1}+\beta u^{\frac{2^\ast}{2}-1}v^{\frac{2^\ast}{2}}, \quad x\in \Omega, -\Delta…

In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions…

The matter-antimatter asymmetry cannot be explained by the Standard Model (SM) of elementary particle physics. According to A. Sakharov, additional sources of $\mathcal{CP}$-Violating phenomena are needed to understand the matter-antimatter…

In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of $n$ electrons and $n-1$ pairs of external protons of charge $+1/2$. It is shown that all the critical points of…

Let $v \ne 0$ be a vector in $\R^n$. Consider the Laplacian on $\R^n$ with drift $\Delta_{v} = \Delta + 2v\cdot \nabla$ and the measure $d\mu(x) = e^{2 \langle v, x \rangle} dx$, with respect to which $\Delta_{v}$ is self-adjoint. This…

We consider the Brans-Dicke Reissner-Nordstrom spacetime in isotropic coordinates and the electrostatic field of an electric point charge placed outside its surface of inversion. We treat the static electric point charge as a linear…

We derive Adams inequalities for potentials on general measure spaces, extending and improving previous results obtained by the authors. The integral operators involved, which we call "Riesz subcritical", have kernels whose decreasing…