Signatures of links in rational homology spheres

A theory of signatures for odd-dimensional links in rational homology spheres is studied via their generalized Seifert surfaces. The jump functions of signatures are shown invariant under appropriately generalized concordance and a special care is given to accommodate 1-dimensional links with mutual linking. Furthermore our concordance theory of links in rational homology spheres remains highly nontrivial after factoring out the contribution from links in integral homology spheres.Comment: 21 pages, 3 figures, to appear in Topology; references and pictures update

Quantum Markov chains associated with open quantum random walks

In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. The quantum Markov chain, like the classical Markov chain, is a fundamental tool for the investigation of the basic properties such as reducibility/irreducibility, recurrence/transience, accessibility, ergodicity, etc, of the underlying dynamics. Here we focus on the discussion of the reducibility and irreducibility of open quantum random walks via the corresponding quantum Markov chains. Particularly we show that the concept of reducibility/irreducibility of open quantum random walks in this approach is equivalent to the one previously done by Carbone and Pautrat. We provide with some examples. We will see also that the classical Markov chains can be reconstructed as quantum Markov chains.Comment: 30 page

Manifestations of CP Violation in the MSSM Higgs Sector

We demonstrate how CP violation manifests itself in the Higgs sector of the minimal supersymmetric extension of the Standard Model (MSSM). Starting with a brief introduction to CP violation in the MSSM and its effects on the Higgs sector, we discuss some phenomenological aspects of the Higgs sector CP violation based on the two scenarios called CPX and TrimixingComment: Submitted for the SUSY08 proceedings, 6 pages, 9 figures, Fig.6 correcte

Group of automorphisms for strongly quasi invariant states

For a $*$-automorphism group $G$ on a $C^*$- or von Neumann algebra, we study the $G$-quasi invariant states and their properties. The $G$-quasi invariance or $G$-strongly quasi invariance are weaker than the $G$-invariance and have wide applications. We develop several properties for $G$-strongly quasi invariant states. Many of them are the extensions of the already developed theories for $G$-invariant states. Among others, we consider the relationship between the group $G$ and modular automorphism group, invariant subalgebras, ergodicity, modular theory, and abelian subalgebras. We provide with some examples to support the results.Comment: 25 page

GAIT ANALYSIS OF THE NORMAL AND ACL DEFICIENT PATIENTS AFTER LIGAMENT RECONSTRUCTION SURGERY

Anterior cruciate ligament (ACL) injury of the knee is common in sports. A serious ACL injury leads to ligament reconstruction surgery. In order to evaluate result of surgery or optimize the rehabilitation process, a knee condition must be objectively identified. The purpose of this study is, therefore, to numerically indicate and classify knee condition of patients via the chaos analysis. Lyapunov exponents (LyEs) were used for the comparison of the normal and the patients