Interior peak solutions for an elliptic system of FitzHugh-Nagumo type

We consider the Dirichlet problem for an elliptic system of FitzHugh-Nagumo type. We prove that the problem has a solution with a sharp peak inside the domain.     

二茂镱,镝邻位取代苯甲酸衍生物的薄层色谱与紫外光谱的研究

用改性薄层色谱板研究了二茂镱、镝邻位取代苯甲酸衍生物的色谱行为,发现R_t值随芳环邻位取代基R的给电子能力递增而递降。初步从理论上探讨了R_t值与紫外光谱R带λ_(max)值随R基团呈相反的变化关系。     

On Positive Multipeak Solutions of a Nonlinear Elliptic Problem

In this paper we continue our investigation in [5, 7, 8] onmultipeak solutions to the problem –²u+u=Q(x)|u|^q–2u, xR^N, uH¹(R^N) (1.1) where = ^N_i=1²/x²_i is the Laplace operator in R^N, 2 < q < for N = 1, 2, 2 < q < 2N/(N–2) for N3, and Q(x)is a bounded positive continuous function on R^N satisfying thefollowing conditions. (Q₁) Q has a strict local minimum at some point x₀R^N, that is,for some > 0 Q(x)>Q(x₀) for all 0 < |x–x₀| < . (Q₂) There are constants C, > 0 such that |Q(x)–Q(y)|C|x–y| for all |x–x₀| , |y–y₀| . Our aim here is to show that corresponding to each strict localminimum point x₀ of Q(x) in R^N, and for each positive integerk, (1.1) has a positive solution with k-peaks concentratingnear x₀, provided is sufficiently small, that is, a solutionwith k-maximum points converging to x₀, while vanishing as 0 everywhere else in R^N.     

On the Superlinear Lazer–McKenna Conjecture: Part II

ABSTRACT

We prove that certain weakly nonlinear elliptic equations have many solutions when a paragraph is large. The nonlinearity grows superlinearly for y positive but grows linearly for y negative.     

Monte Carlo simulation of cutaneous reflectance and fluorescence measurements--the effect of melanin contents and localization

Melanin content and distribution in skin were studied by examining a patient with white, brown and blue skin tones expressed on skin affected by vitiligo. Both diffuse reflectance and autofluorescence spectra of the three distinction skin sites were measured and compared. Monte Carlo simulations were then performed to help explain the measured spectral differences. The modeling is based on a six-layer skin optical model established from published skin optical parameters and by adding melanin content into different locations in the model skin. Both the reflectance and fluorescence spectra calculated by Monte Carlo (MC) simulation were approximately in agreement with experimental results. The study suggests that: (1) trichrome vitiligo skin may be an ideal in vivo model for studying the effect of skin melanin content and distribution on skin spectroscopy properties. (2) Based on the skin optical model and MC simulation, the content and distribution of melanin in skin, or other component of skin could be simulated and predicted. (3) Both reflectance and fluorescence spectra provided information about superficial skin structures but fluorescence spectra are capable of providing information from deeper cutaneous structures. (4) The research method, including the spectral ratio method, the method of adding and modifying the melanin content in skin optical models, and MC simulation could be applied in other non-invasive optical studies of the skin.     

Infinitely many positive solutions for an elliptic problem with critical or supercritical growth

We prove that for some supercritical exponents and for some smooth domains D in RN there are infinitely many (distinct) positive solutions to the following Lane–Emden–Fowler equation: This seems to be the first result for such type of equations.     

Substituent Effect on 31P Chemical Shifts and Conformation of some Cyclic Phosphonates

Abstract

A series of 2-alkyl-2-oxo-1,2,3-dioxaphosphorinane (1) and some 2-alkyl-2-oxo-1,2,3-dioxaphosphepane (II) were synthesized and their NMR, IR as well as MS were reported. The substituent effect on ³¹P chemical shifts and conformations of these compounds were investigated by the molecule, mechanics calculations using Allinger's MM2 program.     

Molecular Mechanics Study of Organophosphorus Compounds

Abstract

Molecular Mechanics calculation (Allinger's force field and MM2 1985 program) was successfully applied for the structure-reactivity studies of organophosphorus compounds in our laboratory.