Convergence for a class of non-autonomous Nicholson’s blowflies model with time-varying coefficients and delays

This paper is concerned with a class of the generalized non-autonomous Nicholson’s blowflies model with time-varying coefficients and delays which is defined on the nonnegative function space. Under proper conditions, we employ a novel proof to establish some criteria to ensure that all solutions of this model converge to an equilibrium. Moreover, we give an example to illustrate our main result.     

Exponential convergence of an epidemic model with time-varying delays

In this paper the convergence behavior of an epidemic model with time-varying delays are considered. Some sufficient conditions are established to ensure that all solutions of the epidemic model with permitted initial conditions converge exponentially to zero, which are new and complement previously known results.     

A note on iterative roots of PM functions

In this paper we study iterative roots of PM functions, a special class of non-monotone functions. Problem 2 in [W. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math. LXV (1997) 119-128] is solved partly and Theorem 4 in that paper is generalized.     

Comprehension of the effects of proton on reflectivity of Mo/Si multilayer

Wavelength dependent reflectivity is crucial relationship in determining the physical property of optic system. The first object of this work is to search for the applicable method of using wavelength to predict the reflectivity of Mo/Si multilayer mirror before and after irradiation with proton. Predicated on the principle of non-linear curve fitting, a typical numerical method is highlighted because the wavelength-dependent reflectivity of Mo/Si multilayer irradiated by proton with different energies and flux are quantitative analyzed by this method. The simulations agree very well with the observed spectroscopy of 6 curves for reflectivity versus wavelength. The minimum value of correlation coefficients between actual and calculated data is 0.994. The other objects of this work are to find the optic band gap of Mo/Si multilayer and check the influences of proton on it using reflectivity spectra. In the light of the calculated results by Tauc method, the optic band gap is theoretically explained successfully via the relationship between band gap and absorption coefficient. The estimated results by both theoretical and experimental data demonstrate that the optic band gap of Mo/Si multilayer is not sensitive to proton radiation.     

Improved blowup results for the Euler and Euler–Poisson equations with repulsive forces

Some results are presented on the formation of singularities in the solutions of the radially-symmetric N-dimensional Euler or Euler–Poisson equations with repulsive forces. Based on the integration method of M.W. Yuen, we generalize the blowup results with constant compact radius R   of solutions to the case with general compact radius R(t)$R(t)$ and to the case with no compact support restriction.     

Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras*

The authors show that if Θ = (θ_jk) is a 3 × 3 totally irrational real skewsymmetric matrix, where θ_jk ∈ [0, 1) for j, k = 1, 2, 3, then for any ε > 0, there exists δ > 0 satisfying the following: For any unital C^*-algebra A with the cancellation property,strict comparison and nonempty tracial state space, any four unitaries u₁, u₂, u₃, w ∈ A such that (1) u_ku_j - e^{2πiθjk ujukk} < δ, wu_jw^-1 = u^-1_j, w² = 1_A for j, k = 1, 2, 3; (2)τ (aw) = 0 and τ ((u_ku_ju_k^*u_j^* )ⁿ ) = e^2πinθjk for all n ∈ N, all a ∈ C^*(u₁, u₂, u₃), j, k = 1, 2, 3 and all tracial states τ on A, where C^*(u₁, u₂, u₃) is the C^*-subalgebra generated by u₁, u₂ and u₃, there exists a 4-tuple of unitaries u₁, u₂, u₃, w in A such that u_ku_j = e^2πinθjk u_ku_j, w u_j w^-1 = u^-1 _j, w² = 1A and k u_j - u_jk < ε, k w - wk < ε for j, k = 1, 2, 3. The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.     

Highly Enantioselective Direct Asymmetric Aldol Reaction Catalyzed by 4,5‐Methano‐L‐proline

The 4,5‐methano‐L‐proline was used as chiral organocatalysts in direct asymmetric aldol reactions. Under the optimal conditions, excellent enantioselectivities (up to 99% ee) were obtained with high chemical yields (up to 95%) for a series of aldehydes using only 5 mol% catalyst loading. To show the practicality of the method, the reaction was tested at a large scale. The reaction was complete in 16 h, and the aldol product was obtained in 86% yield and 93% ee.     

圈积的词长度公式

利用Fordham的技巧证明了圈积群HιZ的一个词长度公式,其中H是一个有限生成群,Z是整数群.     

水平来流对扰动成长和对流周期性的影响

对Pr=0.0272的纯流体在矩形腔体外加水平来流时,进行二维流体力学基本方程组的数值模拟.研究了该纯流体Rayleigh-Benard对流的一维行波斑图的成长及时空的演化.发现对流成长过程可以划分为3个阶段,即对流发展、对流指数成长和周期变化。在对流指数成长阶段对不同相对Rayleigh(瑞利)数Ra_r的最大垂直流速场随时间变化的情况进行分析,获得了最大垂直流速场指数成长阶段的线性成长率γ_m和相对Rayleigh数Ra_r的关系公式.研究了行波周期受水平来流Reynolds(雷诺)数的影响,揭示了行波对流周期性及其对水平来流Reynolds数的依赖性.     

Positive pseudo almost periodic solutions for a class of differential iterative equations with biological background

The article considers a class of differential iterative equations with biological background. We establish some sufficient conditions for the existence of positive pseudo almost periodic solutions by applying exponential dichotomy and contraction mapping principle. The obtained results extend some known ones.