Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.     

Measurements of self-broadening and self-pressure-induced shift parameters of the methane spectral lines in the 5556-6166 cm range

The absorption spectra of methane at different path lengths and different pressures for three temperatures 180, 240 and 296 K have been recorded in the 5556-6166 cm⁻¹ region using the Bruker IFS 120 HR and 125 HR high-resolution Fourier transform spectrometers. The multispectrum fitting procedure has been applied to these spectra to recover the spectral line parameters. The main goal of this procedure was the determination of self-broadening and self-pressure-induced shift coefficients and the exponents of their temperature dependences. These parameters have been derived for 406 assigned lines with good values of the signal to noise ratio. The rotational dependence of these parameters is discussed.     

Evaluation of eigenvalues of a smooth potential via Schroedinger transmission across multi-step potential

In a one-dimensional quantal solution of Schroedinger equation, the general expressions for reflection and transmission coefficients are derived for a potential constituting n number of rectangular wells and barriers. These expressions are readily used for the estimation of eigenvalues of a smooth potential which is simulated by a multi-step potential. The applicability of this method is demonstrated with success in potentials with different forms including the most versatile Ginocchio potential where the widely used numerical method like Runge-Kutta integration algorithm fails to yield the result. Accurate evaluation of eigenvalues free from numerical problem for any form of potentials, whether analytically solvable or not, is the highlight of the present multi-step approximation method in the theory of potential scattering.      

Analysis of price fluctuations in futures exchange markets

We show that the fluctuations of the tick-by-tick logarithmic price in a futures market can be described in terms of the Fokker-Planck equation (FPE). We calculate the corresponding drift and diffusion coefficients and argue that these values can contain some information pertaining to the market state. It is particularly showed that the Korean treasury bond (KTB) futures is well described by a FPE and has a similar structure to turbulence.     

Analytical evaluation of cylindrical exponential integrals arising in radiative transfer

New analytical results are presented performing to cylindrical exponential integral (CEI) functions for integer and noninteger values of parameter n. These integrals are often employed of two-dimensional radiative transfer in an absorbing-emitting medium and determination of the radiative flux in cylindrical media. The simple and efficient algorithm for the calculation of these functions is developed. The series expansion relations established in this work are accurate enough in the whole range of parameters.     

Temperature Effect on Drying and Swelling of Kappa Carrageenan Gels: A Steady State Fluorescence Study

Summary: A novel technique based on in situ steady state fluorescence (SSF) measurements is introduced for studying drying and swelling of κ- carrageenan (kappa carrageenan) gels at various temperatures. κ- carrageenan gels were completely dried and then swelled in water vapor. Pyranine was embedded in κ- carrageenan and used as a fluorescence probe. Scattered light intensities, I_sc and fluorescence intensities, I were monitored during the drying and swelling of κ- carrageenan gels. It was observed that the fluorescence intensity decreased linearly as drying time was increased. A simple model consisting of Case II diffusion was used to quantify the drying processes of the κ- carrageenan gels. This moving boundary model provided packing constant, k₀. During swelling, fluorescence intensity increased exponentially as time is increased. The increase in I, was modeled using Li-Tanaka equation from which swelling time constants, τ_c and cooperative diffusion coefficients, D_c were determined. It was observed that swelling time constants, τ_c decreased and diffusion coefficients, D_c increased as the swelling temperature was increased. Activation energies for drying and swelling were also obtained and found to be 53.9 and 47.2 kJ mol⁻¹, respectively.     

New Exact Solutions to （2＋1）-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.     

On the structure of the class A(ϕ)

In this paper, we study whether the set A(?) is closed under multiplication f · g, where f and g belong to the class A(?). We also study the problem of the existence of a solution of the equation Bx = C (where B,C ∈ A(?) and B ≠ 0) on the set A(?).