共查询到20条相似文献,搜索用时 781 毫秒
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A 题组新编1.(1)满足条件 { 1,2 } M { 1,2 ,3,4 ,5 }的集合 M共有个 ;(2 )满足条件 M∪ { a,b,c} ={ a,b,c,d,e}的集合 M共有个 ;(3) M { 1,2 ,3,4 ,5 } ,且满足条件 :若 a∈ M,则 6 - a∈ M,这样的非空集合 M共有个 ;(4 ) A∪ B ={ a,b}的集合 A、B共有对 ;(5 ) A∪ B ={ a,b,c}的集合 A、B共有对 .2 .(1)若 f (x) =x1 x,则 f(1) f(2 ) f(3) … f(2 0 0 4 ) f(12 ) f(13) f(14 ) … f(12 0 0 4 ) =;(2 )若 f(x) =x21 x2 ,则 f (1) f(2 ) f(3) … f(2 0 0 4 ) f(12 ) f(13) f(14 ) … f(12 0 0 4 ) =;(3)若 f(x… 相似文献
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将有限集合中符合某一特性的所有子集合,称之为有限集合的子集族.在各类集合问题中,与子集族相关的问题是其中极为重要的一类.这类问题题型新颖,解答灵活,给同学们的学习造成了一定的困难.本文拟对这类问题分类进行解析.1.求有限定条件的子集个数例1(03希望杯高一竞赛题)集合S={1,2,3,4,5,6},A是S的一个子集,当x∈A时,若有x-1A,且x 1A,则称x为A的一个“孤立元素”,那么S中无“孤立元素”的4元子集族中子集的个数是.解4个元素为连续自然数的子集有{1,2,3,4},{2,3,4,5},{3,4,5,6},共3个,不都连续的子集有{1,2,4,5},{1,2,5,6},{2,3,5,6},共… 相似文献
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假设E为一致凸Banach空间,K为E的非空闭凸子集且为E的非扩张收缩,P为非扩张收缩映像.{Ti:i=1,2,…,N}:K→E为非扩张映像且F(T)=∩ from i=1 to N F(Ti)≠■.定义{xn}如下:x0∈K,xn=P(αnxn-1+(1-αn)TnP[βnxn-1+(1-βn)Tnxn]),n≥1,这里{αn},{βn}为[δ,1-δ]中的实序列,其中δ∈(0,1).若{Ti:i=1,2,…,N}满足条件(B),则{xn}强收敛于x*∈F(T). 相似文献
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题(2014年江苏预赛第9题)设集合S={1,2,…,8|,A,B是S的两个非空子集,且A中的最大数小于B中的最小数,则这样的集合对(A,B)的个数是.解当A中最大数为1时,A有2^0个,B可以是集合(2,3,…,8}任意非空子集,有2^7-1个;当A中最大数为2时,集合{1}的子集有2^1个,所以A有2^1个,B可以是集合{3,4,…,8}的任意非空子集,有2^6-1个。 相似文献
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集合问题,由于其概念抽象、题型多样、解法灵活,同学们解题时常常出错甚至感到茫然.本文试就集合学习中的几个易错问题作一归纳并加以剖析.一、误解了元素构成例1设集合A={(x,y)|2x y=4},B={(x,y)|3x 2y=7},求A∩B.误解1:由32xx 2yy==47得yx==21,∴A∩B={1,2}误解2:同上得xy==21,∴A∩B={x=1,y=2}剖析:A∩B中的元素是一个实数对,它是单元素集合.而{1,2}表示的是由两个实数组成的集合,{x=1,y=2}表示的是两个方程组成的集合.误解原因是没弄清A∩B中的元素构成.本题的正解结果为{(1,2)}.例2设集合A={y|y=x2 2x 1,x∈R},B={y|y=x2-2x,x∈… 相似文献
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幂函数、指数函数和对数函数 选择题1 定义A -B ={x|x∈A且x B} ,若I =N ,M={ 1,2 ,3,4 ,5} ,N ={ 2 ,3,6 } ,则N -M =( )(A)M . (B)N . (C) { 1,4 ,5} . (D) { 6 } .2 已知集合M ={a ,b ,c}中的三个元素可构成某一个△ABC的三边长 ,那么△ABC一定不是( )(A)直角三角形 . (B)锐角三角形 .(C)钝角三角形 . (D)等腰三角形 .3 使不等式x2 - 2 |x|- 15>0成立的负值x的范围是 ( )(A)x <- 3. (B)x <0 .(C)x <- 5. (D) - 5<x <- 3.4 从集合 {a ,b}到集合 {c,d … 相似文献
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内容 :1.代数 :集合、映射与函数 ; 2 .立体几何 :平面 ,空间两直线 . 选择题1 已知全集I ={ 1,2 ,3 ,4,5 } ,A∩B ={ 2 } ,A∩B ={ 1,4} ,则B等于 ( )(A) { 3} . (B) { 5 } .(C) { 1,2 ,4} .(D) { 3 ,5 } .2 设集合M ={ 1999,2 0 0 0 ,2 0 0 1} ,N ={x|x∈M } ,则M与N的关系是 ( )(A)M =N .(B)M N .(C)M N .(D)M∩N = .3 三个平面最多可把空间分成 ( )(A) 4个部分 .(B) 6个部分 .(C) 7个部分 .(D) 8个部分 .4 已知a ,b是异面直线 ,直线c平行于直线a ,那么c与b ( … 相似文献
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设E是实的一致凸Banach空间,K是E的一个非空闭凸集,P是E到K上的非扩张的保核收缩映射.设T1,T2,T3:K→E分别是具有数列{hn},{ln},{kn}[1,∞)的渐近非扩张非自映射,使得sum (hn-1) from n=1 to ∞<∞,sum ((ln-1)) from n=1 to ∞<∞及sum (n=1(kn-1) from n=1 to ∞<∞,且F=F(T1)∩F(T2)∩F(T3)={x∈K:T1x=T2x=T3x}≠Ф.定义迭代序列{xn}:x1∈K,xn+1=P((1-αn)xn+αnT1(PT1)n-1yn),yn=P((1-βn)xn+βnT2(PT2)n-1zn),zn=P((1-γn)xn+γnT3(PT3)n-1xn),其中{αn},{βn},{γn}[ε,1-ε],ε是大于零的实数.(i)如果T1,T2,T3中有一个是全连续的或者半紧的,则{xn}强收敛于某一点q∈F;(ii)如果E具有Frechet可微范数或者满足Opial’s条件或者E的对偶空间E~*具有Kadec-Klee性质,则{xn}弱收敛于某一点q∈F. 相似文献
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(2006年江苏高考第21题)设数列{an},{bn},{cn},满足:bn=an-an 2,cn=an 2an 1 3an 2(n=1,2,3,…),证明{an}为等差数列的充分必要条件是{cn}为等差数列且bn≤bn 1(n=1,2,3,…)此题的必要性易证,充分性的一个证明思路是:根据等差数列{cn}的性质有cn 2-cn为常数,结合bn≤bn 1得到bn 相似文献
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设K是一致凸Banach空间中的非空闭凸子集,T_i:K→K(i=1,2,…,N)是有限族完全渐近非扩张映象.对任意的x_0∈K,具误差的隐迭代序列{x_n}为:x_n=α_nx_n-1+β_nT_n~kx_n+γ_nu_n,n≥1,其中{α_n},{β_n},{γ_n}■[0,1]满足α_n+β_n+γ_n=1,{u_n}是K中的有界序列.在一定的条件下,该文建立了隐迭代序列{x_n}的强收敛性.得到隐迭代序列{x_n}强收敛于有限族完全渐近非扩张映象公共不动点的充要条件.所得结果改进和推广了Shahzad与Zegeye,Zhou与Chang,Chang,Tan,Lee与Chan等人的相应结果. 相似文献
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令R_k=(ak00bk)为正整数扩张矩阵,D_k={0,1,…,q_k-1}v_1+{0,1,…,q_k-1}v_2,其中v_1=(1,0)~t,v_2=(0,1)~t,q_k1为正整数.本文研究由{R_k}_(k=1)~∞和{D_}_(k=1)~∞生成的Moran测度μ{R_k},{D_k} :=δ_(R1)(-1)~D_1*δ(R_2R_1)~(-1)D_2*···*δ(R_K···R_2R_1)(-1)D_K*···的谱性,证明了当q_k|a_k且q_k|b_k时,μ{R_k},{D_k}为谱测度.这推广了文献[J.Funct,Anal.,2014,266(1):343-354]和[J.Funct.Anal.,2002,193(2):409-420]中的结论. 相似文献
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在“2005年地方联考题”中有这样一题:对于集合N={1,2,…,n}及它的每一个非空子集,定义一个“交替和”如下:按照递减的次序重新排列该子集元素,然后从最大数开始交替地减、加后继的数,例如集合{1,2,4,6,9}的“交替和”是9-6+4-2+1=6,集合{5}的“交替和”为5, 相似文献
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在上世纪初前后,有一类自相矛盾的语句引起了数学家们的关注.他们为了在数学的基础性研究中避免类似的矛盾而煞费苦心,从而促进了数学基础及数理逻辑的发展.这类语句称为悖论,现在举几个例子.1罗素悖论哲学家兼数学家罗素(B.Russell)在考虑集合的理论时,想到了“所有的集合”,以及“所有的集合”是否也能组成一个集合呢?如果能,记它为A,则应有:(集合)A∈(所有的集合组成的)A.但我们日常所见到的集合并不如此,例如集合{a},它只有1个元素a,而{a}就不是{a}的元素了.所以,我们日常见到的任一集合S,都具有S S这样的性质.现在考虑“所有适合S … 相似文献
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选择题 (第 1— 10题每题 4分 ,第 11— 14题每题 5分 ,共 6 0分 )1 已知集合I ={1,2 ,3,4 ,5},A ={1,2 ,3},B ={3,4 ,5},则A∩B = ( )(A) {3}. (B) {4,5}. (C) {1,2 }. (D) .2 已知元素 (x ,y)在映射 f下的像是 (x -y ,x y) ,那么 ( 2 ,- 4)在 f下的原象为 ( )(A) ( 1,3) . (B) ( - 1,3) .(C) ( 1,- 3) . (D) ( - 1,- 3) .3 函数 f(x) =1 sinx -cosx的最小正周期为( )(A) π2 . (B)π . (C) 2π . (D) 3π .4 函数 f(x) =2 x a2 x-a为奇函数 ,则实数a… 相似文献
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The present paper is concerned with the nonlinear elliptic system of second order.
Firstly, we shall establish a complex form of the system. Secondly .we shall consider the solvability of some boundary value problems for tbe complex equation of second order.
let
(1) \[{\Phi _j}(x,y,U,V,{U_x},{U_y},...,{U_{xx}},{U_{yy}},{V_{xx}},{V_{xy}},{V_{yy}}) = 0,j = 1,2\] be the I. G. Petrowkii’s nonlinear elliptic system of second Qrder in the botinded domain G, where \[{\Phi _j}(x,y,{z_1},...,{z_{12}})(j = 1,2)\]) are continuous real functions of
the variables \[x,y[(x,y) \in G],{z_1},...,{z_{12}} \in R\], (the real axis), and contiriupusly
differentiable for \[{z_1},...,{z_{12}} \in R\]. The solutions \[[U(x,y),V(x,y)]\], F(a?, y)] of the system are understood in the generalized sense.
THEOBEM I. i) If the I. G. Petrovskii;s nonlinear system of equations (1) satisfies the M. I. visik-D. Xiagi’s uniformly elliptic condition for any solutions
U(x,y),V(x,y) of (1) in G, then it can be written as the following complex equation?
(2)\[{W_{z\overline z }} = F(z,W,{W_z},\overline {{W_z}} ,{W_{zz}},{\overline W _{zz}})\]
where W=U+iV, z=x+iy, \[{W_z} = \frac{1}{2}[{W_x} - i{W_y}],...,\],
ii) If the I. G. Petrovskii's nonlinear elliptic system (1) satisfies the condition that there exist two positive constants \[\delta \] and K, such that
(3) \[|{\Phi _{j{U_{xx}}}}|,|{\Phi _{j{U_{xy}}}}|,|{\Phi _{j{U_{yy}}}}|,|{\Phi _{j{V_{xx}}}}|,|{\Phi _{j{V_{xy}}}}|,|{\Phi _{j{V_{yy}}}}| \leqslant K,j = 1,2\]
\[|det(A)| \geqslant \delta > 0\], in G, then by a suitable linear trans-formation of the variables (x,y)into variables \[(\xi ,\eta )\], system (1) can be written as the following coinplex equation
⑷ \[{W_{\xi \xi }} = F(\xi ,W,{W_\xi },{\overline W _\xi },{W_{\xi \xi }},{\overline W _{\xi \xi }}),\varsigma = \xi + i\eta \]
In the following section, we discuss the complex equation (2) of the following
form:
,We^B(z9 Wee)x .\[(5)\left\{ \begin{gathered}
{W_{zz}} = F(z,W,{W_z},{\overline W _z},{W_{zz}},{\overline W _{zz}}) \hfill \ F = {Q_1}{W_{zz}} + {Q_2}\overline {{W_{\overline z \overline z }}} + {Q_4}{W_{zz}} + {A_1}{W_z} + {A_2}{\overline W _{\overline z }} \hfill \ + {A_3}\overline {{W_z}} + {A_4}{W_{\bar z}} + {A_5}W + {A_6}\bar W + {A_7}, \hfill \ {Q_j} = {Q_j}(z,W,{W_{\bar z}},{\overline W _{\bar z}},{W_{zz}},{\overline W _{zz}}),j = 1,...,4 \hfill \ {A_j} = {A_j}(z,W,{W_z},{\overline W _z}),j = 1,...,7 \hfill \\
\end{gathered} \right.\]
1) \[{Q_j}(z,W,{W_z},{\overline W _z},U,V),j = 1,...,4.{A_j} = (z,W,{W_z},{\overline W _z}),j = 1,...,7\] are measurable functions of z for any continuously differentiable functions W(z) and measurable functions U(z), V(z) in G, Furthermore they satisfy
(6)\[{\left\| {{A_j}} \right\|_{{L_p}(\overline {G)} }} \leqslant {K_0},j = 1,2,{\left\| {{A_j}} \right\|_{{L_p}(\overline {G)} }} \leqslant {K_1},j = 3,...,7\]
where\[{K_0},{K_1}( \leqslant {K_0}),p( > 2)\] are constants:
2) Qj, Aj are continuous for \[W,{W_z},{\overline W _z} \in E\](the whole plane) and the continuity is uniform with respect to almost every point \[z \in G\] and \[U,V \in E\]
3) \[F(z,W,{W_z},{\overline W _z},U,V)\] satisfies the following Lipschitz's condition, i.e. for
almost every point \[z \in G\], and for all \[W,{W_z},{\overline W _z}{U_1},{U_2},{V_1},{V_2} \in E\], the inequality
(7)\[\begin{gathered}
|F(z,W,{W_z},{\overline W _z},{U_1},{V_1}) - F(z,W,{W_z},{\overline W _z},{U_2},{V_2})| \hfill \ \leqslant {q_0}|{U_1} - {U_2}| + q_0^'|{V_1} - {V_2}|,{q_0} + q_0^' < 1 \hfill \\
\end{gathered} \] holds where \[{q_0},q_0^'\] are two nonnegative constants.
In this paper, let G be a simply connected domain with boundary \[\Gamma \in C_\mu ^2(0 < \mu < 1)\]; without loss of geaerality, we may assume that G is the unit disk |z|<1. Now
we, describe the results of the solvability of Riemann-Hilbert botindary value problem (Problem R-H) and the oblique derivative problem (Problem P) for Eq. (5) in the unit disk G: |z| <1.
Problem R-H. We try to find a solution W(z)of Eq. (5) which is continuonsly differentiable on \[G\], and satisfies the boundary conditions:
(8) \[\operatorname{Re} [{{\bar z}^{{\chi _1}}},{W_z}] = {r_1}(z),Re[{{\bar z}^{{\chi _2}}}\overline {W(z)} ] = {r_2}(z),z \in \Gamma \]?
where \[{\chi _1},{\chi _2}\] are two integers, and \[{r_j} \in C_v^{j - 1}(\Gamma ),j = 1,2,\frac{1}{2} < v < 1\]
Problem P. we try to find a solution W(z) of Eq. (5) which is continuously
diffierentiabfe on \[\overline G \] and satisfies the boundaory conditions:
(9) \[\operatorname{Re} [{{\bar z}^{{\chi _1}}}{W_z}] = {r_1}(z),Re[{{\bar z}^{{\chi _2}}}\overline {W(z)} ] = {r_2}(z),z \in \Gamma \],
Where \[{\chi _1},{\chi _2},{r_1}(z),{r_2}(z)\] are the same as in (8), but \[{r_2}(z) \in {C_v}(\Gamma )\].
Theorem II. Suppose that Eq. (5) satisfies the condition C and the constants \[q_0^'\] and K1 are adequately small; then the solvability of Problem R-H is as follows:
1) When \[{\chi _1} \geqslant 0,{\chi _2} \geqslant 0\] Problem R-H is solvable;
2) When \[{\chi _1} < 0,{\chi _2} \geqslant 0(or{\kern 1pt} {\kern 1pt} {\chi _1} \geqslant 0,{\chi _2} < 0){\kern 1pt} \] there are \[2|{\chi _1}| - 1(or2|{\chi _2}| - 1)\] solvable
conditions for Problem R-H;
3) WHen \[{\chi _1} < 0,{\chi _2} < 0\], there are \[2(|{\chi _1}| + |{\chi _2}| - 1)\] solvable conditions for Problem
R-H.
Theorem III Let Eq (5) satisf the condition C and the constants \[q_0^'\] and \[{K_1}\] are adequately small, then tbe solvability of Problem P is as follows:
1) When \[{\chi _1} \geqslant 0,{\chi _2} \geqslant 0\] Problem P is solvable;
2) When \[{\chi _1} < 0,{\chi _2} \geqslant 0(or{\kern 1pt} {\kern 1pt} {\chi _1} \geqslant 0,{\chi _2} < 0){\kern 1pt} {\kern 1pt} {\kern 1pt} \], there are \[2|{\chi _1}| - 1(or2|{\chi _2}| - 1)\] solvable conditions for Problem P;
3) When \[{\chi _1} < 0,{\chi _2} < 0\]; there are \[2|{\chi _1}|{\text{ + }}|{\chi _2}| - 1)\] solvable conditions for Problem P.
Furthermore, the solution W(z) of Problem P for Eq. (5) may be expressed as
\[{g_j}(\xi ,z) = \left\{ \begin{gathered}
\int_0^z {\frac{{{z^{2{\chi _j} + 1}}}}{{1 - \bar \xi z}}dz,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} for{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\chi _j} \geqslant 0} \hfill \ \int_0^z {\frac{{{\xi ^{ - 2{\chi _j} - 1}}}}{{1 - \bar \xi z}}dz,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} for{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\chi _j} < 0} \hfill \\
\end{gathered} \right.j = 1,2\]
where \[{\Phi _0}(z) = a + ib\] is a complex constant,and \[{\Phi _1}(z),{\Phi _2}(z)\] are two analytic functions.
The proofs of the above stated theorems are based on a prior estimates for the bounded solutes of these boundary value problems and Leray-Schander theorem.
Besides, we have considered also the solvability of Problem R-H and Problem P for Eq. (6) in the multiply connected domain. 相似文献