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May 11

数学符号英语读法

+ : plus(positive正的)

－：minus（negative负的）

*：multiplied by

÷：divided by

＝: be equal to

≈ : be approximately equal to

() : round brackets(parenthess)

[] : square brackets

{} : braces

∵ : because

∴ : therefore

≤ : less than or equal to

≥ ：greater than or equal to

∞：infinity

f(x) : the function of x

dx : diffrencial of x

x+y : x plus y

(a+b) : bracket a plus b bracket closed

a=b : a equals b

a≠b ：a isn't equal to b

a>b : a is greater than b

a>>b : a is much greater than b

a≥b : a is greater than or equal to b

x→∞ ：x approches infinity

＜ is less than
＞ is more than
≮ is not less than  
≯ is not more than
≤ is less than or equal to 小于或等于号
- hyphen 连字符  
≥ is more than or equal to 大于或等于号
' apostrophe 省略号,英文中省略字符用的撇号;所有格符号
％ percent
－ dash 破折号
‰ per mille
∞ infinity 无限大号
∝ varies as 与…成比例
( ) parentheses 圆括号  
√ (square) root 平方根
[ ] square brackets 方括号  
∵ since; because 因为
《 》 French quotes 法文引号;书名号  
∴ hence 所以
… ellipsis 省略号
∷ equals, as (proportion) 等于，成比例
¨ tandem colon 双点号
∠ angle 角
∶ ditto 双点号
⌒ semicircle 半圆
‖ parallel 双线号
⊙ circle 圆
／ virgule 斜线号  
○ circumference 圆周
～ swung dash 代字号
△ triangle 三角形
§ section; division 分节号
⊥ perpendicular to 垂直于
→ arrow 箭号；参见号
∪ union of 并，合集
∩ intersection of 交，通集  
∫ the integral of …的积分
± plus or minus 正负号
∑ summation of 总和
× is multiplied by 乘号
° degree 度
÷ is divided by 除号  
′ minute 分
″ second 秒
≠ is not equal to 不等于号  
≡ is equivalent to 全等于号  
℃ Celsius degree 摄氏度
≌ is equal to or approximately equal to 等于或约等于号
计算机编成常用符号英语读音
` backquote 反引号
~ tilde
! exclam
@ at
# numbersign,英语国家是hash，美语是pound,音乐里作sharp,如C#
$ dollar
% percent
^ caret
& ampersand
* asterisk,star(美语),数学公式中作multiply
( parenleft,opening parentheses
) parenright,closing paretheses
- minus;hyphen连字符,不读
_ underscore
+ plus
= equal
[ bracketleft,opening bracket
] bracketright,closing bracket
{ braceleft
} braceright
; semicolon
: colon
' quote
" doublequote
/ slash
\ backslash 反斜杠
| bar
, comma
< less
> greater
. period
? question
    space 空格

希腊字母读法：

序号 大写 小写 英文注音 国际音标注音 中文注音 意义
1       Α        α       alpha        a:lf                 阿尔法 角度；系数
2       Β        β       beta         bet                贝塔 磁通系数；角度；系数
3       Γ        γ        gamma     ga:m              伽马 电导系数（小写）
4       Δ        δ       delta         delt               德尔塔 变动；密度；屈光度
5       Ε        ε        epsilon      ep`silon         伊普西龙 对数之基数
6       Ζ        ζ        zeta          zat               截塔 系数；方位角；阻抗；相对粘度；原子序数
7       Η        η       eta           eit                艾塔 磁滞系数；效率（小写）
8       Θ        θ       thet         θit                西塔 温度；相位角
9       Ι          ι        iot           aiot               约塔 微小，一点儿
10     Κ         κ       kappa       kap              卡帕 介质常数
11     Λ         λ       lambda     lambd           兰布达 波长（小写）；体积
12     Μ         μ      mu           mju              缪 磁导系数；微（千分之一）；放大因数（小写）
13     Ν         ν       nu            nju              纽 磁阻系数
14     Ξ         ξ        xi            ksi                克西
15     Ο        ο        omicron    omik`ron      奥密克戎
16     Π        π        pi            pai                派 圆周率=圆周÷直径=3.1416
17     Ρ        ρ        rho          rou                肉 电阻系数（小写）
18     Σ        σ       sigma        `sigma           西格马 总和（大写），表面密度；跨导（小写）
19     Τ        τ        tau          tau                套 时间常数
20     Υ        υ        upsilon     jup`silon         宇普西龙 位移
21     Φ       φ        phi          fai                  佛爱 磁通；角
22     Χ        χ        chi           phai               西
23     Ψ       ψ       psi            psai               普西 角速；介质电通量（静电力线）；角
24     Ω       ω        omega      o`miga           欧米伽 欧姆（大写）；角速（小写）；角

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April 20

非线性方程求根

                     
 
二分法:          
function root=MultiRoot(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fun=diff(sym(f));
    ddf=diff(sym(fun));
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    dfa=subs(sym(fun),findsym(sym(fun)),a);
    dfb=subs(sym(fun),findsym(sym(fun)),b);
    if(dfa>dfb)
        root=a;
    else
        root=b;
    end
    while(tol>eps)
        r1=root;
        fx=subs(sym(f),findsym(sym(f)),r1);
        dfx=subs(sym(fun),findsym(sym(fun)),r1);
        ddfx=subs(sym(ddf),findsym(sym(ddf)),r1);
        root=r1-fx*dfx/(dfx*dfx-fx*ddfx);
        tol=abs(root-r1);
    end
end
Example:
>> HalfInterval('x^3-3*x+1',0,1)
 
ans =
 
    0.3473
黄金分割法:
function root=hj(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else  
    t1=a+(b-a)*0.382;
    t2=a+(b-a)*0.618;
    f_1=subs(sym(f),findsym(sym(f)),t1);
    f_2=subs(sym(f),findsym(sym(f)),t2);
    tol=abs(t1-t2);
    while(tol>eps)                           %精度控制
        if(f_1*f_2<0)
            a=t1;
            b=t2;
        else
            fa=subs(sym(f),findsym(sym(f)),a);        
            if(f_1*fa>0)
                a=t2;
            else
                b=t1;
            end
        end
        t1=a+(b-a)*0.382;
        t2=a+(b-a)*0.618;
        f_1=subs(sym(f),findsym(sym(f)),t1);
        f_2=subs(sym(f),findsym(sym(f)),t2);
        tol=abs(t2-t1);
    end
    root=(t1+t2)/2;                             %输出根
end
 
>> hj('x^3-3*x+1',0,1)
 
ans =
 
    0.3473
不动点迭代:
function [root,n]=StablePoint(f,x0,eps)
if(nargin==2)
    eps=1.0e-4;
end
 
tol=1;
root=x0;
n=0;
while(tol>eps)
    n=n+1;
    r1=root;
    root=subs(sym(f),findsym(sym(f)),r1)+r1;
    tol=abs(root-r1);
end
>> [r,n]=StablePoint('1/sqrt(x)+x-2',0.5)
 
r =
 
    0.3820
 
 
n =
 
     4
Atken加速迭代法：
function [root,n]=AtkenStablePoint(f,x0,eps)
if(nargin==2)
    eps=1.0e-4;
end
 
tol=1;
root=x0;
x(1:2)=0;
n=0;
m=0;
a2=x0;
while(tol>eps)
    n=n+1;
    a1=a2;
    r1=root;
    root=subs(sym(f),findsym(sym(f)),r1)+r1;
    x(n)=root;
    if(n>2)
        m=m+1;
        a2=x(m)-(x(m+1)-x(m))^2/(x(m+2)-2*x(m+1)+x(m));
        tol=abs(a2-a1);
    end  
end
root=a2;
>> [r,n]=AtkenStablePoint('1/sqrt(x)+x-2',0.5)
 
r =
 
    0.3820
 
 
n =
 
     4
Steffensen加速迭代：
function [root,n]=StevenStablePoint(f,x0,eps)
if(nargin==2)
    eps=1.0e-4;
end
 
tol=1;
root=x0;
n=0;
while(tol>eps)
    n=n+1;
    r1=root;
    y=subs(sym(f),findsym(sym(f)),r1)+r1;
    z=subs(sym(f),findsym(sym(f)),y)+y;
    root=r1-(y-r1)^2/(z-2*y+r1);
    tol=abs(root-r1);
end
>> [r,n]=StevenStablePoint('1/sqrt(x)+x-2',0.5)
 
r =
 
    0.3820
 
 
n =
 
     4
弦截法：       
function root=Secant(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b); 
    root=a-(b-a)*fa/(fb-fa);
    while(tol>eps)
        r1=root;
        fx=subs(sym(f),findsym(sym(f)),r1);
        s=fx*fa;
        if(s==0)
            root=r1;
        else
            if(s>0)
                root=b-(r1-b)*fb/(fx-fb);
            else
                root=a-(r1-a)*fa/(fx-fa);
            end
        end
        tol=abs(root-r1);
    end
end
>> Secant('x^3-3*x+1',0,1)
 
ans =
 
    0.3473
Steffensen弦截法：
function root=StevenSecant(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    faa=subs(sym(f),findsym(sym(f)),fa+a);
    root=a-fa*fa/(faa-fa);
    while(tol>eps)
        r1=root;
        fx=subs(sym(f),findsym(sym(f)),r1);
        v=fx+r1;
        fxx=subs(sym(f),findsym(sym(f)),v);
        root=r1-fx*fx/(fxx-fx);
        tol=abs(root-r1);
    end
end
>> StevenSecant('x^3-3*x+1',0,1)
 
ans =
 
    0.3473
抛物线法：
function root=Parabola(f,a,b,x,eps)
if(nargin==4)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    fx=subs(sym(f),findsym(sym(f)),x);
    d1=(fb-fa)/(b-a);
    d2=(fx-fb)/(x-b);
    d3=(d2-d1)/(x-a);
    B=d2+d3*(x-b);
    root=x-2*fx/(B+sign(B)*sqrt(B^2-4*fx*d3));
    t=zeros(3);
    t(1)=a;
    t(2)=b;
    t(3)=x;
    while(tol>eps)
        t(1)=t(2);
        t(2)=t(3);
        t(3)=root;
        f1=subs(sym(f),findsym(sym(f)),t(1));
        f2=subs(sym(f),findsym(sym(f)),t(2));
        f3=subs(sym(f),findsym(sym(f)),t(3));
        d1=(f2-f1)/(t(2)-t(1));
        d2=(f3-f2)/(t(3)-t(2));
        d3=(d2-d1)/(t(3)-t(1));
        B=d2+d3*(t(3)-t(2));
        root=t(3)-2*f3/(B+sign(B)*sqrt(B^2-4*f3*d3)); 
        tol=abs(root-t(3));
    end
end
>> Parabola('sqrt(x)+log(x)-2',1,4,2)
 
ans =
 
    1.8773
Newton法：
function root=NewtonRoot(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fun=diff(sym(f));
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    dfa=subs(sym(fun),findsym(sym(fun)),a);
    dfb=subs(sym(fun),findsym(sym(fun)),b);
    if(dfa>dfb)
        root=a-fa/dfa;
    else
        root=b-fb/dfb;
    end
    while(tol>eps)
        r1=root;
        fx=subs(sym(f),findsym(sym(f)),r1);
        dfx=subs(sym(fun),findsym(sym(fun)),r1);
        root=r1-fx/dfx;
        tol=abs(root-r1);
    end
end
>> NewtonRoot('sqrt(x)-x^3+2',0.5,2)
 
ans =
 
    1.4759
简化Newton法：
function root=SimpleNewton(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fun=diff(sym(f));
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    dfa=subs(sym(fun),findsym(sym(fun)),a);
    dfb=subs(sym(fun),findsym(sym(fun)),b);
 
    if(dfa>dfb)
        df0=1/dfa;
        root=a-df0*fa;
    else
        df0=1/dfb;
        root=b-df0*fb;
    end
    while(tol>eps)
        r1=root;  
        fx=subs(sym(f),findsym(sym(f)),r1);
        root=r1-df0*fx;
        tol=abs(root-r1);
    end
end
>> SimpleNewton('sqrt(x)-x^3+2',1.2,2)
 
ans =
 
    1.4759
Newton下山法：
function root=NewtonDown(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fun=diff(sym(f));
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    dfa=subs(sym(fun),findsym(sym(fun)),a);
    dfb=subs(sym(fun),findsym(sym(fun)),b);
    if(dfa>dfb)
        root=a;
    else
        root=b;
    end
    while(tol>eps)
        r1=root;  
        fx=subs(sym(f),findsym(sym(f)),r1);   
        dfx=subs(sym(fun),findsym(sym(fun)),r1);
        toldf=1;
        alpha=2;
        while toldf>0
            alpha=alpha/2;
            root=r1-alpha*fx/dfx;
            fv=subs(sym(f),findsym(sym(f)),root);
            toldf=abs(fv)-abs(fx);
        end
        tol=abs(root-r1);
    end
end
>> NewtonDown('sqrt(x)-x^3+2',1.2,2)
 
ans =
 
1.4759
 
两步迭代法：
function root=TwoStep(f,a,b,type,eps)
if(nargin==4)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fun=diff(sym(f));
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    dfa=subs(sym(fun),findsym(sym(fun)),a);
    dfb=subs(sym(fun),findsym(sym(fun)),b);
    if(dfa>dfb)
        root=a;
    else
        root=b;
    end
    while(tol>eps)
        if(type==1)
            r1=root;
            fx1=subs(sym(f),findsym(sym(f)),r1);
            dfx=subs(sym(fun),findsym(sym(fun)),r1);
            r2=r1-fx1/dfx;
            fx2=subs(sym(f),findsym(sym(f)),r2);
            root=r2-fx2/dfx;
            tol=abs(root-r1);
        else
            r1=root;
            fx1=subs(sym(f),findsym(sym(f)),r1);
            dfx=subs(sym(fun),findsym(sym(fun)),r1);
            r2=r1-fx1/dfx;
            fx2=subs(sym(f),findsym(sym(f)),r2);
            root=r2-fx2*(r2-r1)/(2*fx2-fx1);
            tol=abs(root-r1);
        end
    end
end
>> Two_Step('log(x)-sin(x)+1',0.1,3,1)
 
ans =
 
    0.7013
重根的迭代法：
function root=MultiRoot(f,a,b,eps)
if(nargin==3)
    eps=1.0e-4;
end
 
f1=subs(sym(f),findsym(sym(f)),a);
f2=subs(sym(f),findsym(sym(f)),b);
if(f1==0)
    root=a;
end
if(f2==0)
    root=b;
end
 
if(f1*f2>0)
    disp('两端点函数值乘积大于0!');
    return;
else
    tol=1;
    fun=diff(sym(f));
    ddf=diff(sym(fun));
    fa=subs(sym(f),findsym(sym(f)),a);
    fb=subs(sym(f),findsym(sym(f)),b);
    dfa=subs(sym(fun),findsym(sym(fun)),a);
    dfb=subs(sym(fun),findsym(sym(fun)),b);
    if(dfa>dfb)
        root=a;
    else
        root=b;
    end
    while(tol>eps)
        r1=root;
        fx=subs(sym(f),findsym(sym(f)),r1);
        dfx=subs(sym(fun),findsym(sym(fun)),r1);
        ddfx=subs(sym(ddf),findsym(sym(ddf)),r1);
        root=r1-fx*dfx/(dfx*dfx-fx*ddfx);
        tol=abs(root-r1);
    end
end
>> MultiRoot('(sin(x)-x+2)*x*x',-2,3,1e-8)
 
ans =
 
     0
 
非线性方程组的数值解法
 
不动点迭代：
function [r,n]=mulStablePoint(myf,x0,eps)
if nargin==1
    eps=1.0e-4;
end
 
r=myf(x0);
n=1;
tol=1;
while tol>eps
    x0=r;
    r=myf(x0);
    tol=norm(r-x0);
    n=n+1;
    if(n>100000)
        disp('迭代步数太多，可能不收敛！');
        return;
    end
end
Newton法：
function [r,n]=mulNewton(myf,dmyf,x0,eps)
if nargin==1
    eps=1.0e-4;
end
 
r=x0-myf(x0)/dmyf(x0);
n=1;
tol=1;
while tol>eps
    x0=r;
    r=x0-myf(x0)/dmyf(x0);
    tol=norm(r-x0);
    n=n+1;
    if(n>100000)
        disp('迭代步数太多，可能不收敛！');
        return;
    end
end
简化Newton法：
function [r,n]=mulSimNewton(myf,dmyf,x0,eps)
if nargin==1
    eps=1.0e-4;
end
 
r=x0-myf(x0)/dmyf(x0);
c=dmyf(x0);
n=1;
tol=1;
while tol>eps
    x0=r;
    r=x0-myf(x0)/c;
    tol=norm(r-x0);
    n=n+1;
    if(n>100000)
        disp('迭代步数太多，可能不收敛！');
        return;
    end
end
Newton下山法：
function [r,n]=mulDNewton(myf,dmyf,x0,eps)
if nargin==1
    eps=1.0e-4;
end
 
r=x0-myf(x0)/dmyf(x0);
n=1;
tol=1;
while tol>eps
    x0=r;
    ttol=1;
    w=1;
    F1=norm(myf(x0));
    while ttol>=0
        r=x0-w*myf(x0)/dmyf(x0);
        ttol=norm(myf(r))-F1;
        w=w/2;
    end
    tol=norm(r-x0);
    n=n+1;
    if(n>100000)
        disp('迭代步数太多，可能不收敛！');
        return;
    end
end
拟Newton法：
function [r,n]=mulVNewton(myf,x0,A,eps)
if nargin==1 
    A=eye(length(x0));
else
    if nargin==2
        eps=1.0e-4;
    end
end
 
r=x0-myf(x0)/A;
n=1;
tol=1;
while tol>eps
    x0=r;
    r=x0-myf(x0)/A;
    y=r-x0;
    z=myf(r)-myf(x0);
    A1=A+(z-y*A)'*y/norm(y);
    A=A1;
    n=n+1;
    if(n>100000)
        disp('迭代步数太多，可能不收敛！');
        return;
    end
    tol=norm(r-x0);
end                                       
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April 13

总算有点眉目了

     当一个动态的协同节点上有某存储的消息与查询消息匹配时，生成的响应消息要在传统意义上原路返回几乎不可能，所以可以采取基于梯度场的机制。梯度值的如何计算是一个问题（跳数、延迟应该是主要考虑因素）。此外，有多个查询消息匹配同一个目标消息时，如何优化传输？若一个查询得到多个响应，如何过滤？整个过程的模型如何建立呢？
     先找全所有变量再说吧！HOHOHOOH。。

 

 

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March 02

说点啥？！

     弹指一挥间罢了～
     想说的很多，却也不知道从何说起……
     等到可说的时候再说罢，呵呵！
    
    
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February 25

Pleasant Memories

     The leaving day is coming.
     Living together in past nearly three weeks made us be taken more with both sides.
     We did all what we could do.
     I cann't forget those pictures representing your smile,worry,animation,lose...which will be stored in my mind forever.
     You said you would wait for me.
     You said you grown up.
     You said you loved me.
     You said you expected to marry me.
     Yup,you trust me and gave a so great wish to me.
     Well. Well. It's a circinal credible chain, isn't it? Thus.
     There's no doubt I will also abide by my promise with no any hesitancy.
     In other words, you inspired me and upgraded my confidence.
     Please remember the ideality I've told you ever before.
     The style of that life is what I'm most willing to strive for my whole life and, from now on hand in hand with you.
     I believe confirmedly, the leaving is a beginning of the next meeting.
     I'm waiting...
    
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