延迟微分方程单支方法的非线性稳定性

本文讨论延迟微分方程单支方法的非线性稳定性 .对于 Kα,β,γ类非线性延迟微分方程 ,我们证明带有线性插值的 G( c,p,q) -代数稳定的单支方法当 c≤ 1时是 GR( p/2 ,q/2 ) -稳定及弱 GAR( p/2 ,q/2 ) -稳定的 ,当 c<1时是 GAR( p/2 ,q/2 ) -稳定的 .最后的数值试验表明了上述结论的正确性 .     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

Equilibrium State of Inhomogeneous Plasma

We consider the problem of a self-consistent determination of an essentially inhomogeneous equilibrium state of classical plasma. The solutions of the stationary Vlasov–Poisson equations are constructed in the form of a localized transition layer that separates the domains of homogeneous plasmas with different equilibrium parameters. The layer can also transform into a local perturbation inside a homogeneous plasma. In both cases, the solution contains neither mass currents nor electric currents, and all electrodynamic and hydrodynamic quantities and their derivatives are continuous. The parameters of the adjacent domains uniquely determine the transition layer structure.     

A statistical study of the analysis of congested spectra by total spectrum fitting

Heavily overlapped, or congested spectra often display much structure but few individual “lines.” Methods have been devised for analyzing such spectra through nonlinear least-squares fitting of the intensity as a function of wavelength or wavenumber. Such total spectrum fitting (TSF) methods are examined statistically for a simple diatomic model and compared with the standard “measure-assign-fit” (MAF) approach in use since the dawn of spectroscopy. Monte Carlo computations on typically 1000 synthetic spectra at a time verify that the predictions of the variance-covariance matrix are reliable under many circumstances. However in regions where the P and R branches double up, the predicted standard errors in the key spectroscopic constants rise sharply and greatly exceed estimates from the Monte Carlo ensemble statistics. In the same regions, the MAF method actually gives better precision. However, for imperfectly overlapped R and P branches, the MAF standard errors are typically three times larger than the TSF values; moreover, the MAF statistical errors are dwarfed by bias. The TSF approach, while clearly superior in these tests, has a practical drawback: it, too, can give significant bias if the spectra are analyzed with an incorrect model, as illustrated here through calculations employing the wrong function to describe the spectral lineshape.     

First total synthesis of the E type I phytoprostanes

The first total synthesis of two E type I phytoprostanes from furan, azelaic acid monomethyl ester and rac-1,2-epoxybutane is described. The key features of our synthetic strategy encompass an enzymatic kinetic resolution of a hydroxycyclopentenone, a Co-salen hydrolytic kinetic resolution of a terminal epoxide and a tandem conjugate addition/diastereoselective protonation sequence to construct the protected phytoprostanes. Mild cleavage of the silyl protective groups followed by enzymatic ester hydrolysis afforded the free E-type phytoprostanes.     

A method and program for mass quantum chemical calculations of protein—ligand docking complexes

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root-mean-square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 418–420, February, 2008.     

On the Solution of Discontinuous IVPs by Adaptive Runge–Kutta Codes

In this paper an automatic technique for handling discontinuous IVPs when they are solved by means of adaptive Runge–Kutta codes is proposed. This technique detects, accurately locates and passes the discontinuities in the solution of IVPs by using the information generated by the code along the numerical integration together with a continuous interpolant of the discrete solution. A remarkable feature is that it does not require additional information on the location of the discontinuities. Some numerical experiments are presented to illustrate the reliability and efficiency of the proposed algorithms.     

Optimal volume-corrected laplace-metropolis method

The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccioet al. The correction volume of probability α in DiCiccioet al. is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize the mean square relative error (MSRE). This optimal choice of α is shown to be invariant under linear transformations. The invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical use. A simulation study and a real data example are presented.     

Iterative Schemes for Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.