本刊英文版2015年58卷第2期(221–458)摘要(英文)

<正>Objective triangle functors RINGEL Claus MichaelZHANG Pu Abstract An additive functor F:A→B between additive categories is said to be objective,provided any morphism f in A with F(f)=0 factors through an object K with F(K)=0.We concentrate on triangle functors between triangulated categories.The first aim of this paper is to characterize objective triangle functors F in several ways.Second,we are interested in the corresponding Verdier quotient functors VF:A→A/Ker F,in particular we want to know under what conditions VF is full.The third question to be considered concerns     

New Solutions for (1+1)-Dimensional and (2+1)-Dimensional Kaup–Kupershmidt Equations

In this paper, using the exp-function method we obtain some new exact solutions for (1+1)-dimensional and (2+1)-dimensional Kaup–Kupershmidt (KK) equations. We show figures of some of the new solutions obtained here. We conclude that the exp-function method presents a wider applicability for handling nonlinear partial differential equations.     

试题研讨(10)

题1 (2003年元月湖北省八校高三第一次联考)设P是直线x-y+9=0上的一点,过P点的椭圆以双曲线4x2-5y2=20的焦点为焦点,试求P点在什么位置时,所求椭圆的长轴最短,并写出这个具有最短长轴的椭圆方程.     

本刊英文版2015年58卷第1期摘要(英文)

<正>On the lower bounds of the curvatures in a bounded domain LU Qi Keng Abstract Let KD(z,z)be the Bergman kernel of a bounded domain D in Cnand Sect D(z,ξ)and Ricci D(z,ξ)be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2=TD(z,z)dzαdzβrespectivelyαβat the point z∈D with tangent vectorξ.It is proved by constructing suitable minimal functions that     

不等式研究成果集锦(10)

１１６ 设任意△ＨＢＣ中,Ｄ、Ｅ、Ｆ分别是△ＡＢＣ的边ＢＣ、ＣＡ、ＡＢ上的内点,△ＤＥＦ、△ＡＥＦ、△ＢＤＦ、△ＣＥＤ 的周长分别记为ｍ０、ｍ１、ｍ２。ｍ３,　＝ｍｉｎ｛Ａ、Ｂ、Ｃ｝,则 上述命题可向平面ｎ边形推广,另猜测,在任意△ＡＢＣ中,有 （吴善和．１９９９,４） １１７ 如果△ＡＢＣ内的三个圆都与三角形的内切圆相切,并且每个圆与△ＡＢＣ的两边相切,设ｒ、ｒａ．ｒｂ、ｒｃ分别为内切圆及其余三个圆的半径,则 （赵长健．１９９９,４） １１８ 在交叉四边形 ＡＢＣＤ中,ａ、ｂ、ｃ／及Ｓ分别表示其边长和面…     

New Runge–Kutta–Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form y″ = f(x,y)

For initial value problems in ordinary second-order differential equations of the special form y″ = f(x, y), mew explicit, direct Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) are presented using the mode of Bettis, Dormand and Prince. Two numerical examples demonstrate the efficiency of the new formula-pairs.     

(-1)~(k 1)=1(k∈Z)

解方程 sin5x=sin4x。解法一:因为与a有相同的正弦值的弧度数x的集合是{x|x=kπ (-1)~ka,k∈Z},所以原方程可以化成 5x=kπ (-1)4x (k∈Z) 解之得:x=kπ/5 (-1)~(k 1) 所以原方程的解集是{x|2= 解法二:原方程等价为sin4x=sin5x,m同解法一得:4x=kπ (-1)~k5x 解之得:x=kπ/4 (-1)~(k 1)5(k∈z)