Truncation of Unitary Operads

We introduce truncation ideals of a $\Bbbk$-linear unitary symmetric operad and use them to study ideal structure, growth property and to classify operads of low Gelfand-Kirillov dimension

Improved Analytic Solution of Black Hole Superradiance

The approximate solution of the Klein-Gordon equation for a real scalar field of mass $\mu$ in the geometry of a Kerr black hole obtained by Detweiler \cite{Detweiler:1980uk} is widely used in the analysis of the stability of black holes as well as the search of axion-like particles. In this work, we confirm a missing factor $1/2$ in this solution, which was first identified in Ref.~\cite{Pani:2012bp}. The corrected result has strange features that put questions on the power-counting strategy. We solve this problem by adding the next-to-leading order (NLO) contribution. Compared to the numerical results, the NLO solution reduces the percentage error of the LO solution by a factor of 2 for all important values of $r_g \mu$. Especially the percentage error is $\lesssim 10\%$ in the region of $r_g\mu \lesssim 0.35$. The NLO solution also has a compact form and could be used straightforwardly.Comment: 5 pages, 3 figures, Accepted by PR

Next-to-leading-order solution to Kerr-Newman black hole superradiance

The superradiant instabilities of Kerr-Newman black holes with charged or uncharged massive spin-0 fields are calculated analytically to the next-to-leading order in the limit of $\alpha\sim r_g \mu \ll 1$. A missing factor of $1/2$ in the previous leading-order result is identified. The next-to-leading order result has a compact form and is in good agreement with existing numerical calculations. The percentage error increases with $\alpha$, from a few percent for $\alpha\sim 0.1$ to about $50\%$ for $\alpha\sim 0.4$. Massive neutral scalars too heavy to be produced with Kerr black hole superradiance may exist in the superradiant region of Kerr-Newman black holes.Comment: 11 pages, 5 figures, 2 tables. Matches Physical Review D versio

Resolving the spurious-state problem in the Dirac equation with finite difference method

To solve the Dirac equation with the finite difference method, one has to face up to the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order derivative on the equal interval lattices. This problem is resolved by replacing the central difference formula with the asymmetric difference formula, i.e., the backward or forward difference formula. To guarantee the hermitian of the Hamiltonian matrix, the backward and forward difference formula should be used alternatively according to the parity of the wavefunction. This provides a simple and efficient numerical prescription to solve various relativistic problems in the microscopic world.Comment: 11 pages, 2 figures, 1 tables, accepted by Physical Review C as a lette

On a Class of Variational-Hemivariational Inequalities Involving Upper Semicontinuous Set-Valued Mappings

This paper is devoted to the various coercivity conditions in order to guarantee existence of solutions and boundedness of the solution set for the variational-hemivariational inequalities involving upper semicontinuous operators. The results presented in this paper generalize and improve some known results