Optimal Actuator Location of the Minimum Norm Controls for Stochastic Heat Equations

In this paper, we study the approximate controllability for the stochastic heat equation over measurable sets, and the optimal actuator location of the minimum norm controls. We formulate a relaxed optimization problem for both actuator location and its corresponding minimum norm control into a two-person zero sum game problem and develop a sufficient and necessary condition for the optimal solution via Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem

Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications

This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed optimal actuator location problem is formulated, and the existence of its solution is proved. Finally, the solution is characterized by a Nash equilibrium of the associated game problem

The longlived charged massive scalar field in the higher-dimensional Reissner--Nordstr\"{o}m spacetime

The quasinormal resonance frequency of the higher-dimensional Reissner--Nordstr\"{o}m (RN) black hole due to charged massive scalar field perturbation is deduced analytically in the eikonal regime. The characteristic decay timescale of the charged massive scalar perturbation in the background of the higher-dimensional RN spacetime is then obtained. The result reveals that longlived charged massive scalar field can exist in higher-dimensional RN spacetime under a certain condition.Comment: 6 pages, 1 figur

Scalar Invariants of surfaces in conformal 3-sphere via Minkowski spacetime

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for a surface in conformal round 3-sphere from that of the associate 4-surface in Minkowski 5-spacetime. More importantly, following the idea of Fefferman and Graham, we construct local scalar invariants for a surface in conformal round 3-sphere. One distinct feature of our construction is to link the classic work of Blaschke to the works of Bryan and Fefferman-Graham.Comment: 37 page

Corporate Governance Assessment on the Top 100 Chinese Listed Companies.

Corporate governance of listed companies has become a focus in China capital market. Corporate governance being the most important organization structure and control mechanism of modern enterprises is directly affected by its external environment and internal mechanism. In view of the external environment, legal system, market system, monitoring capability, socio-economic system, cultural environmental etc. will all affect the effectiveness of corporate governance from different aspects. The effectiveness of corporate governance is very much related to government governance or the even broader public governance. In view of a companys internal environment, corporate governance involves the balance amongst the board of directors, the management, shareholders and other stakeholders. The core objective is to solve the agency issues of the companys internal and external parties by appropriately arranged policies, so that management can endeavor for the maximization of profits for shareholders and stakeholders. Well corporate governance not only can provide effective monitoring, but can also encourage enterprises to create wealth for the society to the uttermost, and become a pattern for enterprise citizen.Corporate governance, China, firm behaviour