Unitarity of Generalized Fourier–Gauss Transforms

Abstract

A generalized Fourier–Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.     

Smoothness of Densities of Generalized Locally Non-Degenerate Wiener Functionals

Several criteria for existence of smooth densities of Wiener functionals are known in the framework of Malliavin calculus. In this article, we introduce the notion of generalized locally non-degenerate Wiener functionals and prove that they possess smooth densities. The result presented here unifies the earlier works by Shigekawa and Florit-Nualart. As an application, we prove that the law of the strong solution to a stochastic differential equation driven by Brownian motion admits a smooth density without an assumption of Lipschitz continuity for dispersion coefficients.     

Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

Random partitioning over a sparse contingency table

The present article investigates a class of random partitioning distributions of a positive integer. This class is called the limiting conditional compound poisson (LCCP) distribution and characterized by the law of small numbers. Accordingly the LCCP distribution explains the limiting behavior of counts on a sparse contingency table by the frequencies of frequencies. The LCCP distribution is constructed via some combinations of conditioning and limiting, and this view reveals that the LCCP distribution is a subclass of several known classes that depend on a Bell polynomial. It follows that the limiting behavior of a Bell polynomial provides new asymptotics for a sparse contingency table. Also the Neyman Type A distribution and the Thomas distribution are revisited as the basis of the sparsity.     

Multi-period resource allocation for estimating project costs in competitive bidding

Central European Journal of Operations Research - In competitive bidding for project contracts, contractors estimate the cost of completing a project and then determine the bid price. Accordingly,...     

Software Release Games

The software release game developed in Ref. 1 is reconsidered in the framework of a two-person nonzero-sum game of timing. More precisely, noisy-type software release strategies are derived in closed form under two different criteria as well as an alternative silent-type software release strategy. Our method overcomes the fatal problem in Ref. 1 and has an advantage on computational tractability. Also, the method can be extended directly to obtain noisy-type strategies.     

Pre-filtering Effect in an Iterative Deconvolution Method and Its Application to Signal Recovery in Fiber-Optic Distributed Temperature Sensors

The signal quality of a fiber-optic distributed temperature sensor based on optical time domain reflectometry (OTDR) is improved using a pre-filtering technique in the iterative deconvolution method. Investigation of the performance is proposed using iteration conditions in which recovery rate of the signal-component is equal to that of the unfiltering technique. The recovered signal in the pre-filtering technique gives a good signal-to-noise ratio (SNR), 3 times of the unfiltered signal. Consequently, improvements in the OTDR signal with SNR of from 10 to 100 are obtained under the iterations for both distance and temperature resolutions.     

Optical properties of organic-inorganic hybrid films prepared by the two-step growth process

Thin films of microcrystalline (C₈H₁₇NH₃)₂PbBr₄ have been prepared by the two-step growth process as follows: (1) precipitation of nanometer-sized PbBr₂ particles on substrates by vapor deposition and then (2) growth of (C₈H₁₇NH₃)₂PbBr₄ films by exposing PbBr₂ particles to C₈H₁₇NH₃Br vapor. Atomic force microscope observations reveal that the substrate is fully covered with nanometer-sized rodlike precipitates. X-ray diffraction studies suggest that (C₈H₁₇NH₃)₂PbBr₄ films are found to be microcrystalline form, single phase and highly oriented with the c-axis perpendicular to the substrate surface. (C₈H₁₇NH₃)₂PbBr₄ films show a clear exciton absorption and free-exciton emission even at room temperature. At low temperatures below 40 K, the emission band separates into three bands at 3.07 (A-band), 3.14 (B-band) and 3.20 (C-band) eV, respectively. Both A- and C-bands correspond to the free-exciton emission with large binding energies. On the contrary, time-resolved PL spectra indicate that the B-band is attributed to phosphorescence formed by the intersystem crossing.