On the Conservativeness of Some Markov Processes

We give a unified method to obtain the conservativeness of a class of Markov processes associated with lower bounded semi-Dirichlet forms on L ²(X;m), including symmetric diffusion processes, some non-symmetric diffusion processes and jump type Markov processes on X, where X is a locally compact separable metric space and m is a positive Radon measure on X with full topological support. Using the method, we give an example in each section, providing the conservativeness of the processes, that are given by the “increasingness of the volume of some sets(balls)” and “that of the coefficients on the sets” of the Markov processes.     

On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities

Journal of Theoretical Probability - We consider symmetric stable-type processes with degenerate/singular Lévy densities via Dirichlet form theory. We give conditions of some global path...     

Tanaka Formula for Multidimensional Brownian Motions

We study the Tanaka formula for multidimensional Brownian motions in the framework of generalized Wiener functionals. More precisely, we show that the submartingale U(B _t –x) is decomposed in the sence of generalized Wiener functionals into the sum of a martingale and the Brownian local time, U being twice of the kernel of Newtonian potential and B _t the multidimensional Brownian motion. We also discuss on an aspect of the Tanaka formula for multidimensional Brownian motions as the Doob–Meyer decomposition.     

Structure,transport and field-emission properties of compound nanotubes: CN<Subscript>x</Subscript> vs. BNC<Subscript>x</Subscript> (<Emphasis Type="Italic">x</Emphasis><0.1)

Transport and field-emission properties of as-synthesized CN_x and BNC_x (x<0.1) multi-walled nanotubes were compared in detail. Individual ropes made of these nanotubes and macrofilms of those were tested. Before measurements, the nanotubes were thoroughly characterized using high-resolution and energy-filtered electron microscopy, electron diffraction and electron-energy-loss spectroscopy. Individual ropes composed of dozens of CN_x nanotubes displayed well-defined metallic behavior and low resistivities of ∼10–100 kΩ or less at room temperature, whereas those made of BNC_x nanotubes exhibited semiconducting properties and high resistivities of ∼50–300 MΩ. Both types of ropes revealed good field-emission properties with emitting currents per rope reaching ∼4 μA(CN_x) and ∼2 μA (BNC_x), albeit the latter ropes se- verely deteriorated during the field emission. Macrofilms made of randomly oriented CN_x or BNC_x nanotubes displayed low and similar turn-on fields of ∼2–3 V/μm. 3 mA/cm² (BNC_x) and 5.5 mA/cm² (CN_x) current densities were reached at 5.5 V/μm macroscopic fields. At a current density of 0.2–0.4 mA/cm² both types of compound nanotubes exhibited equally good emission stability over tens of minutes; by contrast, on increasing the current density to 0.2–0.4 A/cm², only CN_x films continued to emit steadily, while the field emission from BNC_x nanotube films was prone to fast degradation within several tens of seconds, likely due to arcing and/or resistive heating. Received: 29 October 2002 / Accepted: 1 November 2002 / Published online: 10 March 2003 RID="*" ID="*"Corresponding author. Fax: +81-298/51-6280, E-mail: golberg.dmitri@nims.go.jp     

Generation of 12-fs pulses from a diode-pumped Kerr-lens mode-locked Cr:LiSAF laser

We demonstrate 12-fs-pulse generation from a diode-pumped Kerr-lens mode-locked Cr:LiSAF laser. This is to our knowledge the shortest pulse ever produced from a mode-locked Cr:LiSAF laser. Based on an improved estimation of the intracavity dispersions, we utilized BK7 glass for the Brewster-prism-pair material.