固定化酶的反应扩散过程的靶波解

通过固定化酶的数学模型的数值模拟，发现其反应扩散过程是以靶波形式出现的     

PROPAGATION OF A L0NG WAVE IN A CURVED DUCT(I) BASIC ANALYSIS OF LONG WAVE PROPAGATION IN A CURVED DUCT WITH VARIABLE CROSS SECTION

The propagation of a long wave in a three-dimensional curvedduct with variable cross section is studied in this paper.It isshown that a three-dimensional Helmholtz equation can be decom-posed into a two-dimensional Laplace(or Poisson)equation and aone-dimensional Webster equation by the curvilinear orthogonalcoordinate system,non-dimensionization of reduced wave equationand regular perturbation with small parameter ka,where k isthe wave number and a is the characteristic radius of the duct.The influences of the duct’s geometric parameters(the area varia-tion of the cross section,the curvature and torsion of the cen-tral line)on the asymptotic expansion of the solution are analy-sed.It is concluded that the effects of the variation of thecross sectional area first appear in the first term of the asym-ptotic ezpansion,and when the cross section shape has certainsymmetric properties,the effects of the curvature and torsion ofthe central line first appear in the third and the fourth terms,respectively.An e     

长波在弯曲管道中的传播——Ⅰ变截面弯管中长波传播的基本分析

本文研究长波在三维变截面弯管中的传播问题.通过建立正交曲线坐标系,以波数k和管道横截面的特征半径a的乘积ka作为小参数,对波动方程进行无量纲处理,用正则摄动法,把三维的Helmholtz方程化为二维的Laplace(或Poisson)方程和一维的Webster方程.并分析了管道的几何参数(横截面面积、管道中心线的曲率和挠度)对复速度势渐近展开的各阶项的影响.文中指出,横截面面积的变化首先影响浙近解的零阶项.在横截面的形状具有某种对称性时,管道中心线的曲率首先影响渐近解的二阶项,而挠度首先影响渐近解的三阶项.最后,给出了长波在弯曲圆管中传播的实例.     

PROPAGATION OF A LONG WAVE IN A CURVED DUCT (Ⅱ)APPLICATIONS OF MATCHED EXPANSION TO LONG WAVE PROPAGATION THROUGH A HOLE WITH VARIABLE CROSS-SECTION

Only the case in which the parameterε=ka《1 is considered in this paper,where k is the wave number and a is the characteris-tic radius of the cross-section of the hole.The general asymp-totic expansion of the complex velocity potential of a long wave propagating in the hole with variable cross-section is obtained by regular perturbation:The methods of matched asymptotic ex-pansion are employed to calculate the reflection coefficients,scattering coefficients and radiation coefficients at the open ends of the hole when a long wave propagates through it,which may be open at both ends or only at one end.Three examples of different kinds of holes are given to show the way to solve such two-dimensional or three-dimensional problems.     

THE TARGET WAVE PATTERNS OF A REACTION-DIFFUSION PROCESS IN AN IMMOBILIZED ENZYME

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｎｚｙｍｅｉｓａｃｏｎｃｅｎｔｒａｔｅｄａｎｄｓｐｅｃｉｆｉｃａｌｂｉｏ＿ｃａｔａｌｙｓｔ．Ｉｔｓｅｓｅｎｃｅｉｓａｐｒｏｔｅｉｎａｎｄｉｔｓａｐｐｌｉｃａｔｉｏｎｉｓｖｅｒｙｅｘｔｅｎｓｉｖｅ．Ｈｏｗｅｖｅｒｉｔｈａ...     

BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE

Ｃｏｎｓｉｄｅｒｐｌａｎａｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂｅｄｓｙｓｔｅｍ ｘ=ｆ(ｘ) +εｇ(ｔ,ｘ,ε ,δ) ,　　ｘ∈Ｒ2 ,( 1 )ｗｈｅｒｅε∈Ｒ ,δ∈Ｄ ＲｎｗｉｔｈＤｃｏｍｐａｃｔ,ａｎｄｆ,ｇａｒｅＣ3ｆｕｎｃｔｉｏｎｓａｎｄｇｉｓＴ＿ｐｅｒｉｏｄｉｃｉｎｔ,Ｔ >0 .Ｌｅｔｓｙｓｔｅｍ ( 1 )ｈａｓａｌｉｍｉｔｃｙｃｌｅＬ0 :ｘ =ｕ(ｔ) ,0 ≤ｔ≤Ｔ0 ｆｏｒε =0ｗｉｔｈＴ0 ｔｈｅｐｅｒｉｏｄｏｆＬ0 .ＳｕｐｐｏｓｅＴ0 /Ｔｉｓｒａｔｉｏｎａｌ,ｔｈａｔｉｓＴ0 /Ｔ=ｍ/ｋ,　　 (ｍ ,ｋ) =1 . ( 2 )Ａｓｗｅｋｎｏ…     

THE FRACTAL RESEARCH AND PREDICATING ON THE TIME SERIES OF SUNSPOT RELATIVE NUMBER

IntroductionThesunspotnumberisanindexwhichnsummarizestheactivitiesofthesun.IthasbeenusedsinceWolfadvanceditin1949.Inreality,yet,onlyitsmonthlymeanvariation,monthlyslipvariationandannuallymeanvariationarevaluable.Intheearlyworksofresearch,Peopletriedtodescribethelawofitsprocessbysomekindsofmodeling,whichturnedouttobeofgreatdifficultybecauseofthechaoticvaluesofthosesuchasthemonthlymeanvariationofthesunspotnumber.Thisfactindicatedthattheprocessofthesunspotnumberishighlycomplicated.Withthedevelo…     

双曲极限环在周期扰动下次调和解的分支

研究了一给定平面自治系统的双曲极限环在周期扰动下m阶次调和解的分支问题 ,用Poincar啨映射 ,通过变尺度方法 ,获得了判别m阶次调和解的存在条件 ,最后给出了一个实例     

长波在弯曲管道中的传播——Ⅱ长波在变截面孔洞中传播时匹配方法的应用

以k表示波数,a表示孔洞横截面的特征半径,本文只研究参数ε=ka《1(即长波)的情况,本文用正则摄动的方法,给出了长波在变截面孔洞中传播时,其复速度势函数渐近展开的一般表达式;论述了长波在两端开口或一端开口一端封闭的变截面孔洞中传播时,如何用匹配方法求得波在洞口反射、散射和辐射的系数;以三个不同的孔洞作为实例,具体说明三维或二维此类问题的求解方法.     

GLOBAL BIFURCATIONS OF LIMIT CYCLES FOR A CUBIC SYSTEM

1MainResultsConsiderthecubicsystemwheree>Oissmall,parametersa=(a,,a,)EDCR2withDboundedandcl)cz)bl?bzareconstants.LetWesupposep'(y)2ofory/oorequivalentlyoscf53c2.(1.3)Assumethatg(x)hasonlysimplezeroswith6152/o.Withoutlossofgene-ralitywecansuppose610,5z<0(onecenterandtwosaddles);(3)5l-46z<0,bz>0(twocentersandonesaddle),Inthispaperweonlyconsiderthefirsttwocases.Obviously,(1'1).=ohasafamily0fperiodicorbitswhe…