BOUNDEDNESS OF INFINITE DELAY DIFFERENCE SYSTEMS IN TERMS OF TWO MEASURES

1 PreliminariesLet R (R--), Z (Z--) denote the sets of non-negative (non-positive) realnumbers and nonnegative (nonpositive) integers, respectively, X= {of: { --r,'' 1--2, --1, 0} - Rk}, where r is a non-negative integer or r = oo. DenoteF == {h: Z X Rk - R , h(n, x) is continuous in x, and inf{h(n, x)} = 0},K = {a E C(R ,R ) t a(u) is strictly increasing in u and a(0) = 0},n LQ = {ry E C(R , R ): there are constants a, L 2 1 such that Z n(s) < a,s=n 1for all n E Z }, and in this …     

关于对流差分格式有界性与CBC准则的讨论

通常认为CBC准则是差分格式有界性的充分条件。本文采用满足与不满足CBC准则的两种高阶差分格式对非线性问题进行了求解,重新讨论了格式有界性与CBC准则的关系,得出结论如下：在数值方法稳定的前提下,CBC准则下的有界模式是求解有界的充分条件,而非必要条件;此外,文章还分析了张涵信三阶精度格式的特点。     

Liénard系统的比较定理

研究了Liénard方程的一类新的等价系统解的有界性与周期解的存在性.证明了几个比较定理,使传统Liénard方程等价系统解的有界性和周期解的存在性可用于判定新等价系统解的有界性与周期解的存在性.     

Discussions on the correspondence of dissipative particle dynamics and Langevin dynamics at small scales

We investigate the behavior of dissipative particle dynamics(DPD) within different scaling regimes by numerical simulations. The paper extends earlier analytical findings of Ripoll, M., Ernst, M. H., and Espa?nol, P.(Large scale and mesoscopic hydrodynamics for dissipative particle dynamics. Journal of Chemical Physics, 115(15),7271–7281(2001)) by evaluation of numerical data for the particle and collective scaling regimes and the four different subregimes. DPD simulations are performed for a range of dynamic overlapping parameters. Based on analyses of the current auto-correlation functions(CACFs), we demonstrate that within the particle regime at scales smaller than its force cut-off radius, DPD follows Langevin dynamics. For the collective regime,we show that the small-scale behavior of DPD differs from Langevin dynamics. For the wavenumber-dependent effective shear viscosity, universal scaling regimes are observed in the microscopic and mesoscopic wavenumber ranges over the considered range of dynamic overlapping parameters.     

Boundedness of semilinear Duffing equations with singularity

We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.     

Boundedness and persistence and global asymptotic stability for a class of delay difference equations with higher order

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｄｅｌａｙｄｉｆｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈｈｉｇｈｅｒｏｒｄｅｒｘｎ+1=Ａ0ｘｐ0ｎ+ Ａ1ｘｐ1 ｎ- 1+… + Ａｋｘｐｋｎ-ｋ　　 (ｎ=0 ,1 ,2 ,… ) ,( 1 )ｗｈｅｒｅＡｉ,ｐｉ ∈ [0 ,∞ )　　 (ｉ=0 ,1 ,2 ,…ｋ;ｋ∈ 1 ,2 ,… ) ( 2 )ａｎｄｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｓｘ-ｋ,ｘ-ｋ+1,… ,ｘ- 1,ｘ0 ａｒｅａｒｂｉｔｒａｒｙｐｏｓｉｔｉｖｅｎｕｍｂｅｒｓ.Ｓｏｍｅｓｐｅｃｉａｌｃａｓｅｓｏｆｋ=1ｆｏｒＥｑ .( 1 )ｈａｖｅｂｅｅｎ…     

沿曲线的超奇性奇异积分算子的Lp有界性

定义R^2中超奇性奇异积分算子Ha、βf（x,y）=p·v·∫-1^1f（x-t,y-γ（t））e^-i｜t｜^-βdt/t｜t｜^a（a,β＞0）,其中（t,γ（t））是R^2上的某类曲线,当γ″（t）和γ″′（t）在（0,∞）上非负（或非正）时,Ha、β为L^p（R^2）有界。     

L^P-REGULARITY FOR A CLASS OF PSEUDODIFFERENTIAL OPERATORS IN R^n

We study here a class of pseudodifferential operators with weighted symbols of Shubin type. First, we develop the basic elements of the pseudodifferential calculus for these operators, proving in particular a result of L^p-boundedness. Then we derive regularity results in the frame of suitably defined functional spaces of Sobolev type.     

THE TRANSFORMATION Φ AND GENERAL PYTHAGORAS’THEOREM ON THE LINEAR MANIFOLD

The primary aim of this paper is to describe the transformation function Φ^[1]. to extend the conclusion of Pythagoras’ theorem for "squared length" of any triangle and to study some geometrical significance of its application     

Uniform boundedness and eventual Hölder continuity to a cancer invasion model with remodeling of ECM and nonlinear diffusion

This paper is concerned with a class of cancer invasion model with nonlinear diffusion and remodeling of ECM. The primary difficulty that arises here is that due to nonlinear diffusion, the good coupling structure between the diffusion term and haptotactic term is destroyed, rendering the effective methods used in the linear diffusion model no longer applicable. Fortunately, we have found a new effective combination between the diffusion term and the haptotactic term, which allows the diffusion term to dominate the haptotactic term, thus preliminarily improving the regularity of the weak solution. Based on these results, we can prove part of long-time asymptotic behavior of the solution, thereby finally proving the uniform boundedness of the weak solution. Subsequently, by improving the convergence of cancer cells u from $L^p$-norm to $L^{\infty }$-norm, it is also proved that after a long time, the weak solution will eventually be Hölder continuous for some slow diffusion cases.