一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.     

Effect of Molecular Crowding on the Temperature–Pressure Stability Diagram of Ribonuclease A

FT‐IR spectroscopic and thermodynamic measurements were designed to explore the effect of a macromolecular crowder, dextran, on the temperature and pressure‐dependent phase diagram of the protein Ribonuclease A (RNase A), and we compare the experimental data with approximate theoretical predictions based on configuration entropy. Exploring the crowding effect on the pressure‐induced unfolding of proteins provides insight in protein stability and folding under cell‐like dense conditions, since pressure is a fundamental thermodynamic variable linked to molecular volume. Moreover, these studies are of relevance for understanding protein stability in deep‐sea organisms, which have to cope with pressures in the kbar range. We found that not only temperature‐induced equilibrium unfolding of RNase A, but also unfolding induced by pressure is markedly prohibited in the crowded dextran solutions, suggesting that crowded environments such as those found intracellularly, will also oppress high‐pressure protein unfolding. The FT‐IR spectroscopic measurements revealed a marked increase in unfolding pressure of 2 kbar in the presence of 30 wt % dextran. Whereas the structural changes upon thermal unfolding of the protein are not significantly influenced in the presence of the crowding agent, through stabilization by dextran the pressure‐unfolded state of the protein retains more ordered secondary structure elements, which seems to be a manifestation of the entropic destabilization of the unfolded state by crowding.     

Free‐energy differences between states with different conformational ensembles

Multiple conformations separated by high‐energy barriers represent a challenging problem in free‐energy calculations due to the difficulties in achieving adequate sampling. We present an application of thermodynamic integration (TI) in conjunction with the local elevation umbrella sampling (LE/US) method to improve convergence in alchemical free‐energy calculations. TI‐LE/US was applied to the guanosine triphosphate (GTP) to 8‐Br‐GTP perturbation, molecules that present high‐energy barriers between the anti and syn states and that have inverted preferences for those states. The convergence and reliability of TI‐LE/US was assessed by comparing with previous results using the enhanced‐sampling one‐step perturbation (OSP) method. A linear interpolation of the end‐state biasing potentials was sufficient to dramatically improve sampling along the chosen reaction coordinate. Conformational free‐energy differences were also computed for the syn and anti states and compared to experimental and theoretical results. Additionally, a coupled OSP with LE/US was carried out, allowing the calculation of conformational and alchemical free energies of GTP and 8‐substituted GTP analogs. © 2013 Wiley Periodicals, Inc.     

一类非牛顿流弱解的扰动

主要研究一类可压缩粘性非牛顿流方程弱解的扰动性质.在已知弱解存在的基础上,证明了选取适当范数时,沿着给定的时间序列,密度和速率的扰动趋于零.     

A new size extensive multireference perturbation theory

A new multireference perturbation series is derived based on the Rayleigh–Schrödinger perturbation theory. It is orbitally invariant. Its computational cost is comparable to the single reference Møller–Plesset perturbation theory. It is demonstrated numerically that the present multireference second‐ and third‐order energies are size extensive by two types of supermolecules composed of H₂ and BH monomers. Spectroscopic constants of as well as the ground state energies of H₂O, NH₂, and CH₂ at three bond lengths have been calculated with the second multireference perturbation theory. The dissociation behaviors of CH₄ and HF have also been investigated. Comparisons with other approximate theoretical models as well as the experimental data have been carried out to show their relative performances. © 2013 Wiley Periodicals, Inc.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.