一类含参变量积分的常差分方程计算方法

首次利用常差分方程方法计算了一类形如∫0πa+co bs cnoxs xdx(n∈N,a,b∈R)的含非负整数参数n与实数a,b的积分,且得到了完整的积分公式.     

Nondegenerate plasma with a diffusive boundary condition in a high-frequency electric field near resonance

An analytical solution of the linearized problem concerning the behavior of collisional non-degenerate plasma in an external electric field is obtained. It is assumed that the electrons are diffusively scattered from the plasma boundary. The resulting solution is used to determine the screening field. The case of a high-frequency external field with a frequency close to the plasma resonance frequency is examined.     

Second-order effects of the output resonance and frequency-locking in an electro-optic bistable system

Based on the dynamic equations of an electro-optic bistable system with delay in its feedback loop, we theoretically investigate second-order effects of the output resonance and frequency-locking of the system.     

Thermogravimetric analysis and kinetics modeling of isothermal carbonization of olive wood in inert atmosphere

The kinetics of olive wood carbonization is investigated by means of isothermal thermogravimetric analysis method. Measurements were carried out in a thermobalance for different fixed temperatures between 498 and 648 K. A two-stage semi-global kinetic model consisting of four sequential steps was proposed to derive kinetic parameters. The olive wood is classified in three pseudo-components. For the first two, similar thermal degradation mechanisms take place in a single reaction step. For the third, the thermal degradation takes place in two consecutive steps. The isothermal conditions allow the kinetic constants (activation energy and pre-exponential factors) to be estimated by means of the analytical solution of the mass conservation equations. An overall good agreement was obtained with activation energy values available in the literature.     

Entangled Porphyrins in Cyclodextrin Vesicles

The entanglement process between porphyrins and some amphiphiliccyclodextrins and the occurrence of different species have been proved by the combination of UV-Visabsorption, fluorescence anisotropy, resonance light scattering and ¹H NMR spectroscopy.     

The ν5 and 2ν9 bands of the N isotopic species of nitric acid (H15NO3): Line positions and intensities

Nitric acid (HNO₃) plays an important role in the Earth’s atmosphere as a reservoir molecule of NO_x species. It has a strong infrared signature at 11 μm which is one of the most commonly used for the infrared retrieval of this species in the atmosphere since this spectral region coincides with an atmospheric window. It is therefore essential to have high quality spectral parameters in this spectral region. For the H¹⁴NO₃ (main) isotopic species, the 11 μm bands were already the subject of numerous extensive studies which involve not only the ν₅ and 2ν₉ cold bands but also the first hot bands. The present work is the first high resolution Fourier transform analysis of the 11 μm bands for H¹⁵NO₃, which is the second most abundant isotopomer of nitric acid [a ≅ 0.00365(7)]. In this way, the analysis of the ν₅ and 2ν₉ cold bands centered at 871.0955 and 893.4518 cm⁻¹ was performed, and as for H¹⁴NO₃, these bands are significantly perturbed since rather strong resonances couple the 5¹ and 9² rotational levels. The theoretical model that we used to compute the line positions and line intensities is directly issued from the one which we used recently for H¹⁴NO₃ [A. Perrin, J. Orphal, J.-M. Flaud, S. Klee, G. Mellau, H. Mäder, D. Walbrodt, M. Winnewisser, J. Mol. Spectrosc. 228 (2004) 375-391]. Actually, for the H¹⁵NO₃ line positions, the Hamiltonian matrix accounts for the rather strong Fermi and the weaker Coriolis interactions linking the 5¹⇔9² rotational levels. Using this model which accounts correctly for the strong mixing of the 5¹ and 9² upper state energy levels, the ν₅ and 2ν₉ line intensities for H¹⁵NO₃ were satisfactorily computed using the ν₅ and 2ν₉ transition moment operators achieved previously for the ¹⁴N (main) isotopic species. In this way, the transfer of intensities from the ν₅ fundamental (and presumably strong) band to the 2ν₉ overtone (and presumably weak) band could be explained for H¹⁵NO₃ as it was done previously for the ¹⁴N (main) isotopic species. Finally, the position of the H¹⁵NO₃ν₅ + ν₉ − ν₉ hot band was identified at 875.245 cm⁻¹.     

The capture into parametric autoresonance

In this work, we show that the capture into parametric resonance may be explained as pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is descibed by the Painlevé-2 equation. We obtain connection formulae for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of asymptotic expansions.     

Interaction between α-actinin and negatively charged lipids membrane investigated by surface plasmon resonance and electrochemical methods

α-Actinin has been shown to be capable of interacting with some special membrane phospholipids directly, which is important for its function. In this study, hybrid bilayer membranes composed of negatively charged lipids are constructed on the surface plasmon resonance gold substrate and on the gold electrode, respectively, and the interaction between α-actinin and negatively charged lipids membrane is investigated by surface plasmon resonance, cyclic voltammetry and electrochemical impedance spectroscopy methods. α-Actinin is proved to be able to interact with the negatively charged lipids membrane directly. It can also insert at least partly into the membrane or lead to some defect or lesion in the membrane, which increase the permeability of the membrane. This study would bring some insight on the interaction between the α-actinin and the cell membranes in vivo.     

Collective Directional Transport in Symmetric Periodic Potentials by Breaking the Coupling Symmetry

Collective unidirectional motion of an asymmetrically coupled array of oscillators in symmetric periodic potentials is studied. A directed current is observed when the drift coupling is presented, while no external biased force is applied. Negative directed current is found when varying system parameters. An addition of a periodic rocking force may enhance the efficiency of directed transport. Resonant steps of the current are found and interpreted as the mode locking between the array and the ac force. Noise-assisted transport is observed, and an optimal noise intensity can give rise to a most efficient transport. The directed transport thus can be optimized and furthermore controlled by suitably adjusting the parameters of the system.     

General Robust-Optimization Formulation for Nonlinear Programming

Most research in robust optimization has been focused so far on inequality-only, convex conic programming with simple linear models for the uncertain parameters. Many practical optimization problems, however, are nonlinear and nonconvex. Even in linear programming, the coefficients may still be nonlinear functions of the uncertain parameters. In this paper, we propose robust formulations that extend the robust-optimization approach to a general nonlinear programming setting with parameter uncertainty involving both equality and inequality constraints. The proposed robust formulations are valid in a neighborhood of a given nominal parameter value and are robust to the first-order, thus suitable for applications where reasonable parameter estimations are available and uncertain variations are moderate. This work was supported in part by NSF Grant DMS-0405831