THE CONVERGENCE OF A DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS

At recent, Hourgat et gave a domain decomposition algorithm for elliptic problems which can be implemented in parallel. Many numerical experiments have illustrated its efficiency. In the present paper, we apply this algorithm to solve the discrete parabolic problems, analyse its convergence and show that its convergence rale is about (1 - 2p + σp2 ) which is nearly optimal and independent of the parameter τ, where σ τ O((1 +H )(1 + ln(H / h))2 ). 0 < p < 1 / σ,τ,h,H are the time step size, finite element parameter and subdomain diameter, respectively.     

Density averaging for Markov processes and the invariant measures problem

A necessary and sufficient condition is given for the existence of a finite invariant measure equivalent to a given reference measure for a discrete time, general state Markov process. The condition is an extension of one given by D. Maharam in the deterministic case and involves an averaging method (called by Maraham ‘density averaging’) applied to the Radon-Nikodym derivatives with respect to the reference measure of the usual sequence of measures induced by the Markov process acting on the fixed reference     

The distribution of values of trigonometric sums with linearly independent frequencies: Kac's problem revisited

The average frequency with which a trigonometric sum having linearly independent frequencies achieves a given value in a specified time interval was solved by Kac in the form of a double integral. In the present paper, Kac's solution is generalized by allowing the amplitudes of the sinusoidal terms to be statistically independent random variables possessing compact probability density functions. The average frequency is expressed as a Fourier cosine series. Representative numerical calculations are shown. The asymptotic form of the average frequency is also discussed.     

Is the rigid-body assumption reasonable?: Insights into the effects of dynamics on the electrostatic analysis of barnase-barstar

Electrostatically-driven association of proteins is important to many biological functions, and understanding which amino acid residues contribute to these interactions is crucial to protein design. Theoretical calculations that are used to elucidate the role of electrostatics in association are typically based on a single experimentally determined protein structure, while an underlying rigid-body assumption is adopted. The goal of this study was to investigate the role of conformational fluctuations on electrostatic interaction energies, as applied to the electrostatic analysis of barnase-barstar. For our calculations, we apply theoretical alanine-scan mutagenesis to introduce charge perturbations by replacing every ionizable residue with alanine, one at a time. Electrostatic clustering and free energy calculations based on the Poisson-Boltzmann method are used to evaluate the effects of each perturbation. Molecular dynamics simulations are performed for the barnase-barstar parent complex and seven experimental alanine mutations from the literature, in order to introduce relaxation before and after mutation. We discuss the effects of dynamics, in the form of pre- and post-mutation relaxation, on electrostatic clustering and free energies of association in light of experimental data. We also examine the utility of nine electrostatic similarity methods for clustering of barnase alanine-scan mutants. Our calculations suggest that the rigid-body assumption is reasonable for electrostatic calculations of barnase-barstar.     

高压微射流制备纳米中链脂肪酸脂质体的研究

以中链脂肪酸(MCFA)为模型材料,比较了高压微射流(HPM)、超声波和微孔过滤3种方法处理后的MCFA脂质体,着重研究了HPM的处理压力和处理次数对脂质体的平均粒度、包封率和稳定性的影响。结果表明:相比超声波和微孔过滤法,HPM处理后的MCFA脂质体的平均粒度最小、包封率最高、稳定性良好;在120 MPa压力条件下处理6次时,MCFA脂质体的平均粒度达到最小,为(73.9±10.2)nm,包封率为(52.20±9.57)%;在120 MPa压力条件下处理4次时,包封率和载药量达到最高,分别为(70.64±11.25)%和(9.42±0.83)%,稳定性系数最高,为0.9990±3.6951,平均粒度为(78.9±21.5)nm。     

云层背景目标识别的匹配滤波器设计

提出一种利用最大平均相关高度(MACH)算法识别复杂云层背景目标的改进滤波器设计方法。在MACH滤波器设计中,通过对云层背景功率谱的统计特性分析,数据拟合得到云层背景功率谱的分布函数,用以代替传统的白噪声模型;提取飞行目标的姿态变化图像,并作阈值化处理,得到训练样本。对不同云层背景和姿态变化目标的相关识别结果表明:改进滤波器的平均峰值相关能量比为0.71%,峰值鉴别率为0.92,可以有效抑制云层背景的干扰,对姿态变化目标识别的鲁棒性较好。     

Energy average formula of photon gas rederived by using the generalised Hermann-Feynman theorem

By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.     

Improper choosability of graphs and maximum average degree

Improper choosability of planar graphs has been widely studied. In particular, ?krekovski investigated the smallest integer g_k such that every planar graph of girth at least g_k is k‐improper 2‐choosable. He proved [9] that 6 ≤ g₁ ≤ 9; 5 ≤ g₂ ≤ 7; 5 ≤ g₃ ≤ 6; and ? k ≥ 4, g_k = 5. In this article, we study the greatest real M(k, l) such that every graph of maximum average degree less than M(k, l) is k‐improper l‐choosable. We prove that if l ≥ 2 then . As a corollary, we deduce that g₁ ≤ 8 and g₂ ≤ 6, and we obtain new results for graphs of higher genus. We also provide an upper bound for M(k, l). This implies that for any fixed l, . © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 181–199, 2006     

Constraints on models with a break in the primordial power spectrum

One of the characteristics of the “Matter Bounce” scenario, an alternative to cosmological inflation for producing a scale-invariant spectrum of primordial adiabatic fluctuations on large scales, is a break in the power spectrum at a characteristic scale, below which the spectral index changes from ns=1$n_s=1$ to ns=3$n_s=3$. We study the constraints which current cosmological data place on the location of such a break, and more generally on the position of the break and the slope at length scales smaller than the break. The observational data we use include the WMAP five-year data set (WMAP5), other CMB data from BOOMERanG, CBI, VSA, and ACBAR, large-scale structure data from the Sloan Digital Sky Survey (SDSS, their luminous red galaxies sample), Type Ia Supernovae data (the “Union” compilation), and the Sloan Digital Sky Survey Lyman-α forest power spectrum (Lyα) data. We employ the Markov Chain Monte Carlo method to constrain the features in the primordial power spectrum which are motivated by the matter bounce model. We give an upper limit on the length scale where the break in the spectrum occurs.     

Cosmology with torsion: An alternative to cosmic inflation

We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein–Cartan–Kibble–Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems in cosmology because of an extremely small and negative torsion density parameter, ΩS≈−¹⁰⁻⁶⁹${\Omega }_S\approx -{10}^{-69}$. Thus the ECKS gravity provides a compelling alternative to speculative mechanisms of standard cosmic inflation. This scenario also suggests that the contraction of our Universe preceding the bounce at the minimum radius may correspond to the dynamics of matter inside a collapsing black hole existing in another universe, which could explain the origin of the Big Bang.