Regular subspaces of Dirichlet forms

The regular subspaces of a Dirichlet form are the regular Dirichlet forms that inherit the original form but possess smaller domains. The two problems we are concerned are: (1) the existence of regular subspaces of a fixed Dirichlet form, (2) the characterization of the regular subspaces if exists. In this paper, we will first research the structure of regular subspaces for a fixed Dirichlet form. The main results indicate that the jumping and killing measures of each regular subspace are just equal to that of the original Dirichlet form. By using the independent coupling of Dirichlet forms and some celebrated probabilistic transformations, we will study the existence and characterization of the regular subspaces of local Dirichlet forms.Comment: This paper is collected in Festschrift Masatoshi Fukushima, In Honor of Masatoshi Fukushima's Sanju, pp: 397-420, 201

S-model speed planning of NURBS curve based on uniaxial performance limitation

As more complex curves are used in current productions, curve speed planning has become a key technique to overcome the bottleneck of high-speed and high-precision computerized numerical control (CNC) systems. This paper first establishes the model of particle velocity, acceleration and jerk in Cartesian coordinate system, and then improves the uniaxial performance limit algorithm.We set up a real-time speed planning process of spline curves, design a S-model look-ahead algorithm, simplify the S-model speed planning algorithm, and achieve real-time non-uniform rational B-splines (NUBRS) curve S-model speed planning based on uniaxial performance limitation. Simulation results show that all the actual interpolation velocity, acceleration and jerk under the proposed method meet the preset single-axis limit. Experimental results show that the tracking performance under the proposed method has been significantly improved compared with that under the small line segments method. Compared with the NUBRS curve trapezoidal model speed planning, the vibration spikes during machining can be eliminated

Regional Finance and Regional Disparities in China

China’s growth has been spectacularly high and persistent over the last few decades. However, there have been regular expressions of concern about the uneven distribution of the benefits across regions and, at times, it has been asserted that the regional distribution of available investment funds has played an important role – national financial institutions (mainly state-owned banks) have redirected deposits from the inland to loans to large institutions in the more prosperous coastal regions. At the same time, smaller regionally-focussed institutions are likely to improve the distribution of funds. We use a panel data set disaggregated by province for the years 1986 to 2004 to test these propositions. We employ recent panel unit roots and cointegration tests using data for state-owned bank loans as well as loans by rural credit cooperatives. We find that financial disparities are related to output disparities, that this relationship is positive, that it is stronger for rural credit cooperatives than for state-owned banks and that this relationship is causal in both the long and short runs. A reduction in financial disparities can be expected to lead a narrowing of output disparities in the short run and in the long run with the effect being larger for rural credit cooperatives than for state-owned commercial banks.regional disparities, panel econometrics, regional finance, China

Dramatically reduced lattice thermal conductivity of Mg_2Si thermoelectric material from nanotwinning

Tuning phonon transport to reduce the lattice thermal conductivity (κ_L) is crucial for advancing thermoelectrics (TEs). Traditional strategies on κ_L reduction focus on introducing scattering sources such as point defects, dislocations, and grain boundaries, that may degrade the electrical conductivity and Seebeck coefficient. We suggest here, a novel twin boundary (TB) strategy that can decrease the κ_L of Mg_2Si by ∼90%, but which may not degrade the electrical properties significantly. We validate this suggestion using density functional theory (DFT). We attribute the mechanism of TB induced κ_L reduction to (i) the lower phonon velocities and larger Grüneisen parameter, (ii) “rattling” of the Mg--Mg pair induced soft acoustic and optical modes, (iii) shorter phonon lifetime and higher phonon scattering rate. We predict that the size of nanotwinned structure should be controlled between 3 nm and 100 nm in the Mg2Si matrix for the most effective κ_L reduction. These results should be applicable for other TE or non TE energy materials with desired low thermal conductivity, suggesting rational designs of high-performance Mg_2Si TE materials with low κ_L for the energy conversion applications

Revisiting the parametrization of Equation of State of Dark Energy via SNIa Data

In this paper, we revisit the parameterizations of the equation of state of dark energy and point out that comparing merely the $\chi^2$ of different fittings may not be optimal for choosing the "best" parametrization. Another figure of merit for evaluating different parametrizations based on the area of the $w(z) - z$ band is proposed. In light of the analysis of some two-parameter parameterizations and models based on available SNIa data, the area of $w(z)-z$ band seems to be a good figure of merit, especially in the situation that the value of $\chi^2_{\rm min}$ for different parametrizations are very close. Therefore, we argue that both the area of the $w(z)-z$ band and $\chi^2_{\rm min}$ should be synthetically considered for choosing a better parametrization of dark energy in the future experiments.Comment: 7 pages, contains 5 figures and 2 tables, accepted for publication in MNRA