Equivalent Constructions of Cartan Pairs

Feldman and Moore [4] introduce Cartan subalgebra of the von Neumann algebra M on a separable Hilbert space H from the natural subalgebra of M(R, sigma), the twisted algebra of matrices over the relation R on a Borel space (X, B, muy). They show that if M has a Cartan subalgebra A, then M is isomorphic to M(R, sigma) where A is the twisted algebra onto the diagonal subalgebra L^inf (X, muy). The relation R is unique to isomorphism and the orbit of the two-cohomology class on R in the torus T, which is the automorphism group of R, is also unique. Three decades later, based on Feldman-Moore work and utilizing etale groupoids from C*(G, Sigma), Renault [9] constructs equivalent Cartan pairs. Nearly another decade later, using extensions of inverse semigroups from extensions of Cartan inverse monoids and Feldman-Moore work, Donsig, Fuller, and Pitts [2] construct other equivalent Cartan pairs. In this paper, we study all Cartan pairs of Feldman and Moore, Renault, and Donsig et al. Our objective is to show that these Cartan pairs are equivalent

Stokesian Dynamics simulation of Brownian suspensions

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownian-motion-dominated regime (Pe ≤ 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe ≈ 10), the dispersion forms a new ‘phase’ with the particles aligned in ‘strings’ along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of Pe and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Péclet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment

The Influence of Pulsed Voltage Shape and Period on Active Species Production by Pulsed Discharge

国立大学法人長岡技術科学大学博士（工学）Articledoctoral thesi

DETERMINANTS OF THE INTENTION TO USE LOAN SHARKS OF STUDENTS: EMPIRICAL EVIDENCES FROM VIETNAMESE UNIVERSITIES

Based on the development of the Unified Theory of Acceptance and Use of Technology model (UTAUT), the authors measured the intention to use loan sharks for students in Vietnamese universities. The research utilizes both quantitative and qualitative methods with the primary data collected from students in Vietnamese universities. The results demonstrate that three main variables significantly impact on intention to use loan sharks, namely "Social Influence," "Financial Literacy," and "Expectancy Effort." In particular, the authors added the "Financial Literacy" element through the results of in-depth interviews. Besides, "Gender" and "Academic Year" also affect the relationship between three main variables and the intention to use loan sharks. Based on the research results, the authors propose several specific policy implications for authorities to eliminate loan sharks through social media and promote financial literacy in universities

Recommendations on developing leadership style for the contingent of leaders and managers of military schools following Ho Chi Minh leadership style

Nowadays, the contingent of leaders and managers in military schools has an especially important position, directly contributing to the successful implementation of the task of educating and training high-quality human resources for the sake of building Vietnam People’s Army to become revolutionary, regular, elite, and gradually modernized. Building a proper leadership style for leaders and managers in military schools is the foundational, long-term task and an urgent issue. The article summarizes the history of research and presents the fundamental contents of Ho Chi Minh’s leadership style as well as the application in building leadership styles for leaders and managers at military schools