High-spectral-resolution rayleigh-mie lidar measurement of vertical aerosol and atmospheric profiles

A new two-channel ground-based high-spectral-resolution Rayleigh-Mie lidar and its operation is described. Upon the inversion of data collected during the night of August 14–15, 1990, with this unique lidar system (553.7 nm), vertical profiles of atmospheric parameters including temperature, potential temperature, pressure and density, as well as aerosol parameters including backscatter-ratio, extinction coefficient and backscatter phase function are determined.     

Minimal Submanifolds

This paper provides a survey of both old and new results aboutminimal surfaces and submanifolds. 2000 Mathematics SubjectClassification 54C40, 14E20 (primary), 46E25, 20C20 (secondary).     

BKP方程族的Pfaffian解

本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解.     

Dibenzothiophene Sulfone Derivatives as Plasma Membrane Dyes

Dibenzothiophene 5,5-dioxide (DBTOO) derivatives have recently been shown to processes utility as fluorescent cell dyes. In an effort to extend the functionality of DBTOO-based dyes to include the visualization of cellular membranes, two lipophilic DBTOO were synthesized and their ability to incorporate into the plasma membrane of HeLa cells was examined by fluorescent microscopy. The photophysical properties of the two new DBTOO derivatives were determined and both have good fluorescent quantum yields and a visible blue emission. Due to agreeable wavelengths of excitation and emission, a standard 4′,6-diamindino-2-phenylindole (DAPI) filter set worked well with these dyes. After co-staining, it was confirmed that both DBTOO dyes localized in the plasma membrane. The quality of the overlap was quantified using Pearson correlation coefficient, which indicated a strong overlap between the DBTOO dyes and the standard plasma membrane dye. The novel dyes also displayed relatively low toxicity to the HeLa cells with IC₅₀ between 10 and 100 µm . Thus, this work reports a new use of DBTOO derivatives as fluorescent microscopy stains.     

Using the complex polynomial method with Mathematica to model problems involving the Laplace and Poisson equations

The complex polynomial method variant of the well‐known complex variable boundary element method (CVBEM) is reexamined in its utility in solving Partial Differential Equations (PDE) of the Poisson and Laplace type. Because the CVBEM was recently extended to three and higher dimensions, the use of complex polynomials to solve higher dimension PDE becomes apparent and therefore the advantages afforded by the use of complex polynomials can be brought to focus on higher dimension problems. Because complex polynomials involve use of computational algorithms that require high accuracy in numerical precision, including the solution of fully populated nonsymmetric matrices, the computer program Mathematica is evaluated for use as the underlying computational engine. Furthermore, Mathematica is evaluated for its internal high‐accuracy computational features and algorithms, including ease of program setup. In this research, the new program is found to provide at least a 5‐fold increase in complex polynomial degree utilization (from degree 10 to degree 50), with computational speed less than was involved in the original degree 10 approximation of Hromadka and Guymon [ASCE J Hydraulic Eng 110 (1984), 329–339], and with exceptional computational accuracy and reporting features. The Mathematica program is quite small and is provided to the reader as freeware and can be obtained from the first author. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

A molecule with small rotational constants containing an atom with a large nuclear quadrupole moment: The microwave spectrum of trans-1-iodoperfluoropropane

Using pulsed jet chirped-pulse, and cavity-based Fourier transform microwave spectroscopies over 900 transitions have been recorded for the title molecule in the 1–4 GHz and 8–18 GHz regions. The C₁,C₂ and C₃ carbon-13 species have been observed in natural abundance allowing a substitution structure for the CCC backbone to be determined. Nearly all the transitions observed were either a-type R branches or b-type Q branches. No c-type transitions were observed consistent with only the trans conformer being present under our experimental conditions. The χ_aa,χ_bb,χ_cc and χ_ab components of the iodine nuclear quadrupole coupling tensor have been determined. Of note, several forbidden, ΔJ±2 transitions, and one ΔJ±3 transition were observed with quite reasonable intensity. These observations have been rationalized through considerations of near degeneracies between energy levels connected via a large χ_ab value (≈1 GHz).     

Population models with diffusion, strong Allee effect, and nonlinear boundary conditions

We consider a population model with diffusion, a strong Allee effect per capita growth function, and constant yield harvesting. In particular, we focus our study on a population living in a patch, Ω⊆Rⁿ with n≥1, that satisfies a certain nonlinear boundary condition. We establish our existence results by the method of sub-supersolutions.     

Modeling potential flow using Laurent series expansions and boundary elements

The fundamental underpinnings of the well‐known Bernoulli's Equation, as used to describe steady state two‐dimensional flow of an ideal incompressible irrotational flow, are typically described in terms of partial differential equations. However, it has been shown that the Cauchy Integral Theorem of standard complex variables also explain the Bernoulli's Equation and, hence, can be directly used to model problems of ideal fluid flow (or other potential problems such as electrostatics among other topics) using approximation function techniques such as the complex variable boundary element method (CVBEM). In this article, the CVBEM is extended to include Laurent Series expansions about singular points located outside of the problem domain union boundary. It is shown that by including such negatively powered complex monomials in the CVBEM formulation, considerable power is introduced to model potential flow problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 573–586,2012     

Integral transform and convolution of analytic functionals on abstract Wiener space

Yeh defined a convolution of functionals on classical Wiener space and investigated the relationship between the Fourier-Wiener transforms of functionals in certain classes and the Fourier-Wiener transform of their convolution. Yoo extended Yeh's results to abstract Wiener space. In this paper, we introduce the intergal transform and convolution of analytic functionals on abstract Wiener space. And we establish the relationship between the integral transforms of exponential type of analytic functionals and the integral transform of theor convolution. Also we obtain Parseval's and Plancherel's relations for those functionals from this relationship. The main results of Yeh and Yoo then follow from our results as corollaries.