Radial pulsations of neutron stars and strange quark stars with nuclear crust are studied. The avoided crossing phenomenon occurring for the radial modes is found and discussed. Neutron star models are constructed using a realistic equation of state of dense matter and strange star models using a phenomenological bag model of quark matter. The eigenfrequencies of the three lowest modes of linea...

This paper concerns the equation ∆mu = |u|p, where m ∈ N, p ∈ (1,∞), and ∆ denotes the Laplace operator in RN, for some N ∈ N. Specifically, we are interested in the structure of the set L of all large radial solutions on the open unit ball B in RN . In the well-understood second-order case, the set L consists of exactly two solutions if the equation is subcritical, of exactly one solution if i...

where 1 < p < N+2 N−2 , N ≥ 3. It is well-known that this equation has a unique positive radial solution. The existence of sign-changing radial solutions with exactly k nodes is also known. However the uniqueness of such solutions is open. In this paper, we show that such sign-changing radial solution is unique when p is close to N+2 N−2 . Moreover, those solutions are non-degenerate, i.e., the...

Abstract The radial basis function (RBF) method is widely used for the numerical solution of Poisson problem in high dimension, where approximate can be found by solving a large system linear equations. We demonstrate that RBF accelerated on quantum computer using an efficient algorithm compare theoretical performance our with standard classical algorithm, and find achieve polynomial speedup.

A recent publication [F. I. Parra et al., Plasma Phys. Control. Fusion 50, 065014 (2008)] warned against the use of the lower order gyrokinetic Poisson equation at long wavelengths because the long wavelength, radial electric must remain undetermined to the order the equation is obtained. Another reference [W. W. Lee et al., Phys. Plasmas 16, 044506 (2009)] criticizes these results by arguing t...

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for solving the equation. For the earth media with curved boundaries, the pseudospectral methods could be less attractive to handle the irregular computational doma...