In this article, we investigate the connection between scalar curvature and first eigenfunctions via positive mass theorem for Brown-York mass. For compact manifolds with nice boundary, we show that a sharp inequality holds for first eigenfunctions w...

Document(s)

Title

The Besse's conjecture was posted on the well-known book Einstein manifolds by Arthur L. Besse, which describes the critical point of Hilbert-Einstein functional with constraint of unit volume and constant scalar curvature. In this article, we show t...

In this dissertation, we defined a new class of non selfadjoint operator algebras---Kadison-Singer algebras or KS-algebras for simplicity. These algebras combine triangularity, reflexivity and von Neumann algebra property into one consideration. Gene...

Optimal control for a family of systems in novel state derivative space form, abbreviated as SDS systems in this study, is proposed. The first step in deriving optimal control laws for SDS systems is to form an augmented cost functional. It turns out...

Augmented reality technology is applied so that driving tests may be performed in various environments using a virtual reality scenario with the ultimate goal of improving visual and interactive effects of simulated drivers. Environmental conditions ...

Multivariate statistical process control is the continuation and development of unitary statistical process control. Most multivariate statistical quality control charts are usually used (in manufacturing and service industries) to determine whether ...

This paper investigates the novel sliding mode control design with state derivative output feedback in nontraditional reciprocal state space (RSS) form. The concepts and the need of RSS form are comprehensively reviewed and explained. Novel switching...

In this article, we define a symmetric 2-tensor canonically associated to Q-curvature called J-tensor on any Riemannian manifold with dimension at least three. The relation between J-tensor and Q-curvature is precisely like Ricci tensor and scalar cu...

The Wigner's theorem, which is one of the cornerstones of the mathematical formulation of quantum mechanics, asserts that every symmetry of quantum system is unitary or anti-unitary. This classical result was first given by Wigner in 1931. Thereafter...

Starting from a (small) rigid C$^*$-tensor category $\mathscr{C}$ with simple unit, we construct von Neumann algebras associated to each of its objects. These algebras are factors and can be either semifinite (of type II$_1$ or II$_\infty$, depending...