CORPORATE GOVERNANCE MODEL OF STATE-HELD LISTED COMPANIES IN CHINA

Ph.DDOCTOR OF PHILOSOPH

The Reverse Hölder Inequality for the Solution to p-Harmonic Type System

Some inequalities to A-harmonic equation A(x,du)=d∗v have been proved. The A-harmonic equation is a particular form of p-harmonic type system A(x,a+du)=b+d∗v only when a=0 and b=0. In this paper, we will prove the Poincaré inequality and the reverse Hölder inequality for the solution to the p-harmonic type system

Singlino-dominated dark matter in general NMSSM

The general Next-to-Minimal Supersymmetric Standard Model (NMSSM) describes the singlino-dominated dark-matter (DM) property by four independent parameters: singlet-doublet Higgs coupling coefficient $\lambda$, Higgsino mass $\mu_{tot}$, DM mass $m_{\tilde{\chi}_1^0}$, and singlet Higgs self-coupling coefficient $\kappa$. The first three parameters strongly influence the DM-nucleon scattering rate, while $\kappa$ usually affects the scattering only slightly. This characteristic implies that singlet-dominated particles may form a secluded DM sector. Under such a theoretical structure, the DM achieves the correct abundance by annihilating into a pair of singlet-dominated Higgs bosons by adjusting $\kappa$'s value. Its scattering with nucleons is suppressed when $\lambda v/\mu_{tot}$ is small. This speculation is verified by sophisticated scanning of the theory's parameter space with various experiment constraints considered. In addition, the Bayesian evidence of the general NMSSM and that of $Z_3$-NMSSM is computed. It is found that, at the cost of introducing one additional parameter, the former is approximately $3.3 \times 10^3$ times the latter. This result corresponds to Jeffrey's scale of 8.05 and implies that the considered experiments strongly prefer the general NMSSM to the $Z_3$-NMSSM.Comment: 29 pages, 9 figure

The Obstacle Problem for the -Harmonic Equation

Firstly, we define an order for differential forms. Secondly, we also define the supersolution and subsolution of the A-harmonic equation and the obstacle problems for differential forms which satisfy the A-harmonic equation, and we obtain the relations between the solutions to A-harmonic equation and the solution to the obstacle problem of the A-harmonic equation. Finally, as an application of the obstacle problem, we prove the existence and uniqueness of the solution to the A-harmonic equation on a bounded domain Ω with a smooth boundary ∂Ω, where the A-harmonic equation satisfies d⋆A(x,du)=0,x∈Ω; u=ρ,x∈∂Ω, where ρ is any given differential form which belongs to W1,p(Ω,Λl-1)