一个耦合系统自由边界问题的整体古典解

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｄｉｓｃｕｓｓｔｈｅｇｌｏｂａｌｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎｏｆａｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｑｕａｓｉｓｔａｔｉｏｎａｒｙｐｒｏｂｌｅｍ .Ｔｈｅｐｒｏｂｌｅｍｃｏｍｅｓｆｒｏｍｔｈｅｄｉｓｃｕｓｓｉｏｎｏｆａｇｒｏｗｔｈｍｏｄｅｌｏｆｓｅｌｆｍａｉｎｔａｉｎｉｎｇｐｒｏｔｏｃｅｌｌ(ｓｅｅ [1— 3])ｉｎｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｃａｓｅ .Ｔｈｅｐｒｏｔｏｃｅｌｌｃａｎｂｅｖｉｓｕａｌｉｚｅｄａｓｈａｖｉｎｇａｐｏｒｏｕｓｓｔ…     

Heegaard分解的重新分块

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＭｂｅａｃｏｍｐａｃｔ 3 ｍａｎｉｆｏｌｄ .ＩｆｔｈｅｒｅｉｓａｐｒｏｐｅｒｌｙｅｍｂｅｄｄｅｄｃｌｏｓｅｄｓｕｒｆａｃｅＳｉｎＭｗｈｉｃｈｓｅｐａｒａｔｅｓＭｉｎｔｏｔｗｏｃｏｍｐｒｅｓｓｉｏｎｂｏｄｉｅｓＨ1ａｎｄＨ2 ,ｔｈｅｎＭｃａｎｂｅｗｒｉｔｔｅｎａｓＭ =Ｈ1∪ＳＨ2 .ＴｈｉｓｓｔｒｕｃｔｕｒｅｏｎＭｉｓｃａｌｌｅｄａＨｅｅｇａａｒｄｓｐｌｉｔｔｉｎｇｏｆＭａｎｄＳｉｓａｓｐｌｉｔｔｉｎｇｓｕｒｆａｃｅ .Ｈ1∪ＳＨ2 ｉｓｓａｉｄｔｏｂｅｒｅｄｕｃｉｂｌｅ…     

ON A CLASS OF SIMPLE TABLE ALGEBRAS

§1.ＩｎｔｒｏｄｕｃｔｉｏｎＺ.ＡｒａｄａｎｄＨ.Ｂｌａｕｉｎｔｒｏｄｕｃｅｄｉｎ[1]ｔｈｅｃｏｎｃｅｐｔｏｆｔａｂｌｅａｌｇｅｂｒａｓａｎｄｕｓｅｄｔｈｉｓｔｏｄｉｓｃｕｓｓｔｈｅｃｈａｒａｃｔｅｒａｌｇｅｂｒａａｎｄｔｈｅｃｅｎｔｒａｌｃｌａｓｓａｌｇｅｂｒａｏｆａｆｉｎｉｔｅｇｒｏｕｐｉｎａｕｎｉｆｏｒｍｗａｙ.ＴｈｉｓｉｄｅａｇｏｅｓｂａｃｋｔｏＩ.Ｓｃｈｕｒ.ＡｌｉｔｔｌｅｅｘｔｅｎｄｅｄｎｏｔｉｏｎｏｆＣ-ａｌｇｅｂｒａｆｏｒｅｓｈａｄｏｗｅｄｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｃｏｍｍｕｔａ…     

关于Barge和Toledo的几个问题

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｃｈａｉｎａｂｌｅｃｏｎｔｉｎｕａｈａｖｅｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｆｏｒｍａｎｙｙｅａｒｓａｎｄｈａｖｅｇｅｎｅｒａｔｅｄｎｅｗｉｎｔｅｒｅｓｔｉｎｔｈｅｒｅｃｅｎｔｙｅａｒｓａｓｔｈｅｃｈａｉｎａｂｌｅｃｏｎｔｉｎｕｕｍｗｈｉｃｈｉｓｔｈｅｉｎｖｅｒｓｅｌｉｍｉｔｓｐａｃｅｏｆａｃｏｎｔｉｎｕｏｕｓｍａｐｆｒｏｍａｃｌｏｓｅｄｉｎｔｅｒｖａｌｉｎｔｏｉｔｓｅｌｆｃａｎｂｅｒｅａｌｉｚｅｄａｓａｇｌｏｂａｌａｔｔｒａｃｔｏｒｏｆｓｏｍｅｐｌａｎ…     

滋长阶小于1的亚纯函数唯一性

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＢｙａｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｗｅａｌｗａｙｓｍｅａｎａｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｉｎｔｈｅｃｏｍｐｌｅｘｐｌａｎｅＣ .ＷｅａｓｓｕｍｅｔｈａｔｔｈｅｒｅａｄｅｒｉｓｆａｍｉｌｉａｒｗｉｔｈＮｅｖａｎｌｉｎｎａｔｈｅｏｒｙｔｈａｔｃａｎｂｅｆｏｕｎｄ ,ｆｏｒｉｎｓｔａｎｃｅ ,ｉｎ [1 ] .Ｗｅｓａｙｔｈａｔｔｗｏｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓｆａｎｄ ｇｓｈａｒｅｔｈｅｖａｌｕｅａ∈ Ｃｐｒｏｖｉｄｅｄｔｈ…     

INSTRUCTIONS TO AUTHORS

1.ＴｈｅＣｈｉｎｅｓｅＡｎｎａｌｓｏｆＭａｔｈｅｍａｔｉｃｓ(ＣＡＭ)Ｓｅｒ.Ｂｉｓａｃｏｍｐｒｅｈｅｎｓｉｖｅｍａｔｈｅｍａｔｉｃａｌｊｏｕｒｎａｌｃａｒｒｙｉｎｇｏｒｉｇｉｎａｌｐａｐｅｒｓｏｎｐｕｒｅａｎｄａｐｐｌｉｅｄｍａｔｈｅｍａｔｉｃｓ.Ｉｔａｉｍｓａｔｐｒｅｓｅｎｔｉｎｇｔｈｅｌａｔｅｓｔａｃｈｉｅｖｅｍｅｎｔｓｉｎｍａｔｈｅｍａｔｉｃａｌｒｅｓｅａｒｃｈｅｓａｎｄｐｒｏｍｏｔｉｎｇｄｏｍｅｓｔｉｃａｎｄｉｎｔｅｒｎａｔｉｏｎａｌａｃａｄｅｍｉｃｅｘｃｈａｎｇｅｓ.2.ＣＡＭＳｅｒ.Ｂｉｓ…     

一道三角习题的多解与多变

高中《代数》上册 (必修 )Ｐ1 50第 1 7题 :已知ｔａｎα =2 ,求ｓｉｎα +ｃｏｓαｓｉｎα -ｃｏｓα的值 .此题虽浅显简单 ,但若能正确使用 ,对同学们培养能力 ,发展智力 ,引起兴趣 ,确能起到一定的作用 .1　一题多解解法 1　ｔａｎα =2 ｓｉｎα =2 55,ｃｏｓα =55.或　ｓｉｎα =- 2 55,ｃｏｓα =- 55.∴ ｓｉｎα +ｃｏｓαｓｉｎα -ｃｏｓα=3 .解法 2　∵ｔａｎα =2 ｓｉｎαｃｏｓα=2 ,即ｓｉｎα =2ｃｏｓα ,∴ ｓｉｎα +ｃｏｓαｓｉｎα -ｃｏｓα=2ｃｏｓα +ｃｏｓα2ｃｏｓα -ｃｏｓα=3 .解法 3　ｔａｎα=2 ｓ…     

Genus Distribution for Circular Ladders

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎｔｏｐｏｌｏｇｉｃａｌｇｒａｐｈｔｈｅｏｒｙ ,ａｇｒａｐｈｍａｙｈａｖｅｍｕｌｔｉｐｌｅａｄｊａｃｅｎｔｉｅｓａｎｄｓｅｌｆｌｏｏｐｓ.Ａｇｒａｐｈｉｓｃａｌｌｅｄｓｉｍｐｌｉｃｉａｌｉｆｉｔｈａｓｎｏｍｕｌｔｉｐｌｅａｄｊａｃｅｎｃｉｅｓａｎｄｓｅｌｆｌｏｏｐｓ .Ａｓｕｒｆａｃｅｈｅｒｅｉｓａｃｏｍｐａｃｔ2 ｍａｎｉｆｏｌｄｗｉｔｈｏｕｔｂｏｕｎｄａｒｙ .Ａｎｅｍｂｅｄｄｉｎｇｏｆａｇｒａｐｈｉｓｃｅｌｌｕｌａｒｉｆｅａｃｈｃｏｍｐｏｎｅｎｔｏｆｔｈｅｓｕｒ…     

关于不变集的一个注记

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＲｎｂｅｎｄｉｍｅｎｓｉｏｎａｌＥｕｃｌｉｄｅａｎｓｐａｃｅ,ａｎｄ (ｆ1,… ,ｆｍ,Ｒｎ)ａｃｏｎｔｒａｃｔｉｏｎｉｔｅｒａｔｅｄｆｕｎｃｔｉｏｎｓｙｓｔｅｍ .Ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｒｅｅｘｉｓｔｓａｕｎｉｑｕｅｎｏｎ ｅｍｐｔｙｃｏｍｐａｃｔｓｅｔＥｓｕｃｈｔｈａｔＥ =∪ｍｉ=1 ｆｉ(Ｅ) .ＷｅｃａｌｌｔｈｅｓｅｔＥｉｎｖａｒｉｎｔｓｅｔｆｏｒ (ｆ1,… ,ｆｍ,Ｒｎ) .　Ｌｅｔ (ｆ1,… ,ｆｍ,Ｒｎ)ｂｅａｃｏｎｔｒａｃｔｉｏｎｉｔｅｒａｔｅｄｆｕｎｃｔ…     

Chromatic Uniqueness of a Family of K_4-Homeomorphs

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ａｌｌｇｒａｐｈｓｃｏｎｓｉｄｅｒｅｄｉｎｔｈｉｓｐａｐｅｒａｒｅｆｉｎｉｔｅ,ｕｎｄｉｒｅｃｔｅｄ ,ｕｎｌｏｏｐｅｄａｎｄｓｉｍｐｌｅｇｒａｐｈｓ.ＷｅｄｅｎｏｔｅｔｈｅｃｈｒｏｍａｔｉｃｐｏｌｙｎｏｍｉａｌｏｆａｇｒａｐｈＧｂｙＰ(Ｇ ,λ)ｏｒＰ(Ｇ) .ＷｅｓａｙｇｒａｐｈｓＧａｎｄＨｔｏｂｅｃｈｒｏｍａｔｉａｌｌｙｅｑｕｉｖａｌｅｎｔｉｆＰ(Ｇ) =Ｐ(Ｈ) .ＴｈｅｃｈｒｏｍａｔｉｃｕｎｉｑｕｅｎｅｓｓｏｆａｇｒａｐｈＧｉｓｅｓｔａｂｌｉｓｈｅｄｉｆｉｔｃａｎｂｅｄｅｄ…     

具有四个时滞的平面系统的周期解的存在性

The sufficient condition for the existence of non-constant periodic solutions of the following planar system with four delays are obtained:     

Periodicity in a Nonlinear Predator-prey System with State Dependent Delays

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system where a_i(t),c_j(t),d_i(t) are continuous positive periodic functions with periodic ω>0, b_1(t),b_2(t) are continuous periodic functions with periodic ωand ∫_0~ωbi(t)dt>0. T_i,σ_j, p_i (i=1,2,…,n, j=1, 2,…,m) are continuous and ω-periodic with respect to their first arguments, respectively, α_i, β_j,γ_i(i=1,2,…,n, j=1,2, …, m) are positive constants.     

Periodic solution of a neutral delay competition model

1.IntroductionNeutraldelayffereatialequationsinpopulationdynamicshavebeenstudiedextensivelyforthep88tfewyears.However,onlyafewpapersll--5]havebeenpublishedontheexistencesofperiodicsolutionsoftheneutraldelaypopulationmodels.In[6,7],Kuangproposedtoinve...     

Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model

By using the continuation theorem of Mawhin's coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition modelwhere ri and r2 are continuous w-periodic functions in R+=[0,∞) with ,ai,ci(i =1,2) are positive continuous w-periodic functions in R+=[0,∞),bi (i = 1,2) is nonnegative continuous w-periodic function in R+=[0,∞), w and T are positive constants. Ki,Lt ∈ C([-T,0], (01 88)) and Ki(s)ds = 1,ds - 1. i = 1,2. Some known results are improved and extended.     

Small prime solutions of some additive equations

Essentially sharp bounds for small prime solutionsp _j ,q _i of the following two different types of equations are obtained.

Multiple rational trigonometric sums and multiple integrals

We obtain an estimate of the modulus of a complete multiple rational trigonometric sum: $$\left| {\sum {_{x_{1, \ldots ,} x_r = 1^{\exp \left( {{{2\pi if\left( {x_{1, \ldots ,} x_r } \right)} \mathord{\left/ {\vphantom {{2\pi if\left( {x_{1, \ldots ,} x_r } \right)} q}} \right. \kern-\nulldelimiterspace} q}} \right)} }^q } } \right| \ll q^{{{r - 1} \mathord{\left/ {\vphantom {{r - 1} {n + \varepsilon }}} \right. \kern-\nulldelimiterspace} {n + \varepsilon }}} ,$$ where $$\begin{gathered} f\left( {x_{1, \ldots ,} x_r } \right) = \sum {_{0 \leqslant t_1 , \ldots ,t_r \leqslant n^a t_1 , \ldots ,t_r x_1^{t_1 } \ldots x_r^{t_r } ,} } \hfill \\ a_{0, \ldots ,0} = 0,\left( {a_{0, \ldots ,0,1} , \ldots ,a_{n, \ldots ,n,} q} \right) = 1 \hfill \\ \end{gathered} $$ , and an estimate of the modulus of a multiple trigonometric integral.     

Metric results on the approximation of zero by linear combinations of independent and of dependent rationals

We give some “rational analoga” to metric results in the classical theory of the diophantine approximation of zero by linear forms. That is: we study the behaviour of expressions of the form $$\begin{gathered} \lim _{m \to \infty } \frac{1}{{\left| {P_s (m)} \right|}}|\{ (x_1 , \ldots ,x_s ) \in P_s (m): \hfill \\ \parallel a_1 \frac{{x_1 }}{m} + \ldots + a_s \frac{{x_s }}{m}\parallel _m \geqslant \psi (a_1 , \ldots ,a_s ,m) \hfill \\ for all - \frac{m}{2}< a_1 , \ldots ,a_s \leqslant \frac{m}{2}, \hfill \\ with (a_1 , \ldots ,a_s ) \ne (0, \ldots ,0)\} |, \hfill \\ \end{gathered} $$ whereP _s (m) is a certain subset of {1, …,m} ^s , ψ is a certain nonnegative function, and ‖ · ‖ _m means the maximum of 1/m and the distance to the nearest integer. Some of the investigations are also motivated by problems in the theory of uniform distribution and of pseudo-random number generation. The results partly depend on the validity of the generalized Riemann hypothesis.     

Determination of the infinite Jacobi matrix with respect to two-spectra

The inverse problem about two-spectra for the equation (1) $$\begin{gathered} b_0 y_0 + a_0 y_1 = \lambda y_0 , \hfill \\ a_{n - 1} y_{n - 1} + b_n y_n + a_n y_{n + 1} = \lambda y_n \left( {n = 1, 2, 3, ...} \right), \hfill \\ \end{gathered} $$ where {y_n} ₀ ^∞ is the desired solution, λ is a complex parameter and $$a_n > 0, \operatorname{Im} b_n = 0 \left( {n = 0, 1 ,2, ...} \right)$$ is studied. Necessary and sufficient conditions for the solvability of the inverse problem about two-spectrafor Eq. (1) are established and also the procedure of reconstruction of the equation from its two-spectra is indicated.     

On a periodic prey-predator system with infinite delays

§1　IntroductionAnvarovandLarinov[1]introducedthefollowingprey-predatorsystem:x(t)=x(t)[α-γy(t)-γ∫∞0K1(s)y(t-s)ds-∫∞0∫∞0R1(s,θ)y(t-s)y(t-θ)dθds],y(t)=y(t)[-β μx(t) μ∫∞0K2(s)x(t-s)ds ∫∞0∫∞0R2(s,θ)x(t-θ)x(t-s)dθds],(1)whereα,γ,βandμarepositiveconstants,Ki∈C([0,∞),(0,∞))andRi∈C([0,∞)×[0,∞),(0,∞)),i=1,2.Fortheecologicalsenseofsystem(1),wereferto[1,2]andrefer-encescitedtherein.Sincerealisticmodelsrequiretheinclusionoftheeffectofchangingen-vironment,itmot…     

Hyperbolic stochastic differential equations: Absolute continuity of the LKW of the solution at a fixed point

LetW be the Wiener process onT=[0, 1]². Consider the stochastic integral equation $$\begin{gathered} X_\zeta = x_0 + \int_{R_\zeta } {a_1 (\zeta \prime )X(s\prime ,dt\prime )ds\prime + } \int_{R_\zeta } {a_2 (\zeta \prime )X(ds\prime ,t\prime )dt\prime } \hfill \\ + \int_{R_\zeta } {a_3 (X_{\zeta \prime , } \zeta \prime )W(ds\prime ,dt\prime ) + } \int_{R_\zeta } {a_4 (X_{\zeta \prime , } \zeta \prime )ds\prime ,dt\prime ,} \hfill \\ \end{gathered} $$ whereR _ζ =(s, t) ∈ T, andx ₀ ∈ ?. Under some assumptions on the coefficients a_i, the existence and uniqueness of a solution for this stochastic integral equation is already known (see [6]). In this paper we present some sufficient conditions for the law ofX _ζ to have a density.