Killed Random Processes and Heat Kernels

Let V(x) ≥ 0 be a given function tending to a constant at infinity. It is well known that the density of the Brownian motion B_t killed at the infinitesimal rate V is a Green's function for the heat operator with such a potential. With an appropriate generalization, its Laplace transform also gives the density of ∫ ₀ ^t V(B_s)ds. We construct such a Green's function via spectral analysis of the classical one-dimensional stationary Schrodinger operator. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 423–432, August, 2005. An erratum to this article is available at .     

Conditioned stochastic differential equations: theory, examples and application to finance

We generalize the notion of Brownian bridge. More precisely, we study a standard Brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations that we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general presentation several examples are studied: the conditioning of a standard Brownian motion (and more generally of a Markov diffusion) by its value at a given date, the conditioning of a geometric Brownian motion with negative drift by its quadratic variation and finally the conditioning of a standard Brownian motion by its first hitting time of a given level. As an application, we introduce the notion of weak information on a complete market, and we give a “quantitative” value to this weak information.     

Various types of stochastic integrals with respect to fractional Brownian sheet and their applications

In this paper, we develop a stochastic calculus related to a fractional Brownian sheet as in the case of the standard Brownian sheet. Let be a fractional Brownian sheet with Hurst parameters H=(H₁,H₂), and (²[0,1],B(²[0,1]),μ) a measure space. By using the techniques of stochastic calculus of variations, we introduce stochastic line integrals along all sufficiently smooth curves γ in ²[0,1], and four types of stochastic surface integrals: , i=1,2, , , , . As an application of these stochastic integrals, we prove an Itô formula for fractional Brownian sheet with Hurst parameters H₁,H₂∈(1/4,1). Our proof is based on the repeated applications of Itô formula for one-parameter Gaussian process.     

A Second Main Theorem of Nevanlinna Theory for Meromorphic Functions on Complex Submanifolds in C<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We show a second main theorem of Nevalinna theory for meromorphic functions on complex submanifolds in C ⁿ . This has a similar form to the classical one and has a remainder term including Ricci curvature. We also give a concrete computation of the remainder term in the case of nonsingular algebraic submanifolds. Partially supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.     

Higher order PDE's and iterated processes

We introduce a class of stochastic processes based on symmetric -stable processes, for . These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric -stable process. We call them -time processes. They generalize Brownian time processes studied in Allouba and Zheng (2001), Allouba (2002), (2003), and they introduce new interesting examples. We establish the connection of -time processes to some higher order PDE's for rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.

     

A new solid-phase extraction disk based on a sheet of single-walled carbon nanotubes

A new kind of solid-phase extraction disk based on a sheet of single-walled carbon nanotubes (SWCNTs) is developed in this study. The properties of such disks are tested, and different disks showed satisfactory reproducibility. One liter of aqueous solution can pass through the disk within 10–100 min while still allowing good recoveries. Two disks (DD-disk) can be stacked to enrich phthalate esters, bisphenol A (BPA), 4-n-nonylphenol (4-NP), 4-tert-octylphenol (4-OP) and chlorophenols from various volumes of solution. The results show that SWCNT disks have high extraction ability for all analytes. The SWCNT disk can extract polar chlorophenols more efficiently than a C₁₈ disk from water solution. Unlike the activated carbon disk, analytes adsorbed by the new disks can be eluted completely with 8–15 mL of methanol or acetonitrile. Finally, the DD-disk system is used to pretreat 1000-mL real-world water samples spiked with BPA, 4-OP and 4-NP. Detection limits of 7, 25, and 38 ng L⁻¹ for BPA, 4-OP, and 4-NP, respectively, were achieved under optimized conditions. The advantages of this new disk include its strong adsorption ability, its high flow rate and its easy preparation. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Quadrupole versus dipole photomotors: Symmetry constraints and operating properties

The operating properties of different-type Brownian photomotors have been compared in relation to the symmetry interplay between their moving (particle/molecule) and immovable (substrate) units. As found, essentially different symmetry constraints and hence different motor behavior are characteristic of molecules if their electron density redistribution on excitation involves only odd-order or only even-order multipole moments. The two respective types of molecules give rise to dipole and quadrupole photomotors. Purely dipole photomotors can operate only on substrates with symmetric charge distribution and their ensemble with random molecular orientations undergoes equidirectional diffusion rather than directed motion. Contrary to this, purely quadrupole photomotors need substrates with antisymmetric charge distribution for directed motion to occur and they can move directionally in an ensemble. Also, quadrupole photomotors provide much smaller velocities of directed motion than their dipole counterparts (as a result of the much weaker interaction of quadrupoles than dipoles with an electric field). The generic distinctions between the two photomotor types are exemplified by donor-acceptor-substituted stilbenoids (dipole molecules) and symmetric squaraines (quadrupole molecules). The model used affords the rational design of photomotors by the selection of promising moving molecules and by the continuous wide-range tuning of charge-distribution symmetry in substrates.     

Nuclear reactor application on Jeffrey fluid flow with Falkner-skan factor,Brownian and thermophoresis,non linear thermal radiation impacts past a wedge

In this paper, an impact of non-linear thermal radiation, Brownian and thermophoresis on an MHD through a wedge with dissipative impacts for Jeffrey fluid is investigated. In addition, heat transport analysis is carried out. This work's originality is attributable to the Jeffrey fluid formulation, nonlinear thermal radiation, Brownian and Thermophoresis. The boundary layer approximations are examined, to transform the governing equations into partial differential equations. Utilizing appropriate similarity transformations, the boundary value issue is expressed in ordinary differential form. BVP4C, a nonlinear numerical method, was utilized to determine the outcomes of velocity, concentration and temperature fields at multiple points of the measured quantities. The skin friction term, Sherwood and Nusselt numbers were analyzed in depth, and the findings are achieved graphically and tabularly. A comparison via the previously published data reveals a good degree of concordance. This research focuses mostly on the modelling of flow in a nuclear reactor. The boundary layer flow caused by a wedge surface play s a crucial role the aspects of geothermal and heat exchangers systems.     

基于静电纺丝工艺的LED远程荧光片制备技术

首次提出了一种基于静电纺丝工艺以柔性PET为基底的新型LED远程荧光片的制备方法,实现了蓝色LED芯片与荧光粉层相分离的免封装器件结构。采用静电纺丝工艺制备了黄色荧光片和红色荧光片,并研究了黄色荧光片的透射率、吸收率、PL谱及红色荧光片对白光LED的光学性能参数的影响,包括光通量、相关色温、光效。实验结果表明,所制备黄色荧光片在可见光波段具有良好的透光性,荧光片的光谱完全由荧光粉来决定,不需要考虑复杂工艺的影响;使用红色荧光片可以在保持高光效的同时将球泡灯的相关色温由5 595 K降低为3 214 K,这在曲面发光及色温调节方面为灯具设计提供了广阔的空间。