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.     

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.     

Ricci curvature and monotonicity for harmonic functions

In this paper we generalize the monotonicity formulas of “Colding (Acta Math 209:229–263, 2012)” for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., “Almgren (Preprint)”, “Colding and Minicozzi II (PNAS, 2012)”, “Garofalo and Lin (Indiana Univ Math 35:245–267, 1986)” for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green’s function on open manifolds with nonnegative Ricci curvature are asymptotically umbilic.     

Collisional broadening of Ba I line (553.5 nm) by He or Ar

The Doppler-free line shape of the 6s ^{2 1} S ₀ – 6s ¹6p ^{1 1} P ₁ transition at 553.5 nm in natural Ba in the presence of an argon or helium buffer gas has been measured at 744 K for gas pressures from 0.2 to 100 Torr. Using the measured data for pressures above 5 Torr, the broadening rate coefficients for the half width at half maximum (HWHM) are determined to be (4.9±0.5)10^–9 and (5.0±0.5)10^–9 s^–1 cm^–3 for helium and argon respectively.     

Chlorine nuclear quadrupole coupling in chlorodifluoroacetyl chloride: Theory and experiment

A potential energy scan of chlorodifluoroacetyl chloride, CF₂ClC(O)Cl, at the MP2/6-311+G(d) level of theory predicts stable gauche and trans conformers, with E_gauche<E_trans. Ab initio calculations were made of approximate equilibrium structures of these and, on these structures, calculations were made of ³⁵Cl and ³⁷Cl nuclear quadrupole coupling constant tensors. Coupling constants here predicted, as well as rotational constants and molecular dipole moments, are applied to aid analyses of experimental microwave spectra. Chirped pulse Fourier transform microwave spectroscopy has been used to rapidly record the rotational spectra of four isotopologues of the title molecule, CClF₂C(O)Cl, namely ³⁵Cl³⁵Cl, ³⁵Cl³⁷Cl, ³⁷Cl³⁵Cl, and ³⁷Cl³⁷Cl. Only the gauche conformer was observed under the experimental conditions. For the four isotopologues a total of 464, 219, 197, and 77 transitions have been recorded, respectively. With the exception of the ³⁷Cl³⁷Cl isotopologue sufficient data was available to determine all Cl quadrupole coupling tensors. Comparisons between the theoretical and experimental results are made.