Non-symmetric perturbations of symmetric Dirichlet forms

We provide a path-space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local Dirichlet form. The representation is a combination of Feynman-Kac and Girsanov formulas, and extends previously known results in the framework of symmetric diffusion processes through the use of the Hardy class of smooth measures, which contains the Kato class of smooth measures.     

Heterochain model for simultaneous long‐chain branching and crosslinking. II. Application to free‐radical polymerization

The matrix formula developed in the context of hetrochain theory, M?_w = M?_wp + WF ( I ? M )^?1 S , was applied to describe the molecular weight development during free‐radical homopolymerization. All of the required probabilistic parameters are expressed in terms of the kinetic‐rate constants and various concentrations. In free‐radical polymerization, the primary chains are formed consecutively, and the number of heterochain types, N, is extrapolated to infinity. Practically, such extrapolation can be conducted on the basis of the calculated values for only three different N values with sufficient accuracy. This matrix formula is valid regardless of the chemical and reactor systems used, as long as the primary chain‐connection statistics is considered Markovian. The gel point can be determined simply by solving an equation det( I ? M ) = 0. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2791–2800, 2004     

Structural stability of vector fields with shadowing

Let X be a C¹ vector field without singularities. In this paper, we show that X is in the C¹ interior of the set of vector fields with the shadowing property if and only if X satisfies both Axiom A and the strong transversality condition; that is, X is structurally stable.     

Optical transfer function analysis of Lau-Type grating atom interferometer

A grating interferometer composed of two transmission gratings in tandem irradiated incoherently was studied for an atom interferometer. Determination of its interference effect was made with consideration of the optical transfer function. An atom beam had a velocity distribution, which made the influence on the interference phenomenon. The calculated results show that the fringe (grating image) with relatively high contrast is obtained under a certain grating arrangement even if the interferometer is irradiated by a spatially incoherent polychromatic atom beam.     

Universal scaling law in human behavioral organization

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.     

Resonant waveguide device with vertical gratings

Transmission resonant filters in a waveguide with vertical gratings have been realized in silicon on insulator wafers. Experimental studies of fabricated devices show a broad stopband of approximately 19 nm in the center of which exists a narrow transmission band of approximately 0.5 nm with a quality factor of approximately 3000. These resonant cavities are useful for laser cavities, switches, modulators, detectors, and tunable filters.     

Compact, filtered diode laser system for precision spectroscopy

Stable, narrow-linewidth optical sources are necessary in modern atomic physics. An appealing approach to achieving approximately 10 kHz frequency stability is optical feedback. We have designed a compact external cavity diode laser with optical feedback to a filter cavity mounted on a single baseplate and enclosed inside a vacuum sealed box. The design was implemented for three wavelengths addressing the 422 nm cooling, 1091 nm repumping, and 674 nm clock transition lines of Sr(+). We are able to cool a single, trapped strontium ion to approximately 2 mK and observe motional sidebands of the 5S(1/2) <--> 4D(5/2) transition.     

Pyrene aromatic arrays on RNA duplexes as helical templates

RNA oligomers having multiple (2 to 4) pyrenylmethyl substituents at the 2'-O-sugar residues were synthesized. UV-melting studies showed that the pyrene-modified RNAs could form duplexes with complementary RNA sequences without loss of thermal stability. Absorption, fluorescence, and circular dichroism (CD) spectra revealed that the incorporated pyrenes projected toward the outside of A-form RNA duplexes and assembled in helical aromatic arrays along the minor grooves of the RNA duplexes. Results of computer simulations agreed with the assembled structures of the pyrenes. The helical pyrene arrays exhibited remarkably strong excimer fluorescence, which was dependent on the sequence contexts of RNA duplexes.     

High-throughput screening using porous photoelectrode for the development of visible-light-responsive semiconductors

A high-throughput screening system for new visible-light-responsive semiconductors for photoelectrodes and photocatalysts was developed in this study. Photoelectrochemical measurement was selected to evaluate visible-light responsiveness, and an automated semiconductor synthesis system that can be used to prepare porous thin-film photoelectrodes of various materials was also developed. As an example application of our system, iron-based binary oxides were selected as target materials for n-type semiconductors. Fe-Ti, Fe-Nb, and Fe-V with various composition ratios were synthesized. Fe-Ti and Fe-Nb binary oxide systems have been studied previously, and our results showed good consistency with previous reports, demonstrating the capability of our system. In the Fe-V system, the highest photocurrent was observed with 50% vanadium. This ratio corresponds to FeVO4, which is expected to be a new visible-light-responsive material. As another example, screening targets of bismuth-based binary oxides were investigated for p-type semiconductor photoelectrodes, and CuBi2O4 was found as a new visible-light-responsive p-type semiconductor.