你说得对，但是$Goldstone$场通常取为归一化的赝标量介子场，即有：

$$\sum_{a=1}^{8}\lambda_a\xi_a=\frac{F}{\sqrt{2}} \begin{pmatrix} \frac{1}{\sqrt{2}}\pi^0+\frac{1}{\sqrt{6}}\eta^0 & \pi^+ & K^+ \\ \pi- & -\frac{1}{\sqrt{2}}\pi^0+\frac{1}{\sqrt{6}}\eta^0 & K^0 \\ \bar{K}^- & \bar{K}^0 & -\sqrt{\frac{2}{3}}\eta^0 \end{pmatrix} =\frac{F}{\sqrt{2}}B $$

但是同时，

$$\widetilde{\Delta}_ku_0=F^{-1}(1_{\zeta\in V_k}\hat{u_0}(\zeta))\text{ },\text{ }\sum_{k\in N}\begin{Vmatrix}\widetilde{\Delta}_ku_0\end{Vmatrix}^2_{H^s}<+\infty $$$$\tiny{(分微乱入?)}$$

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你说得对，但是如果随机变量$h^i_k$都是标准的实的$Gauss$随机变量或者$Bernoulli$随机变量，则存在某个$C>0,c>0$使得

$$P(\Omega_{\infty,s})\ge1-Ce^{\frac{-c}{\begin{Vmatrix}(1-e^{-a|k|^{2a}T})^{\frac{1}{a}}|k|^s\alpha^i_k\end{Vmatrix}^2_{l^2_{k,i}}}} $$

以及考虑到

$$\lVert u\rVert_{\alpha,\beta}=\sup_{x\in\mathbf{R}^n}|x^\alpha\partial^\beta u(x)| $$

我们得出结论$:$你说的是废话$.$

---

你说得对，但是由于$F(a)$为自由循环$\mathfrak{B}-$模,所以对于任一个右$\mathfrak{B}-$模,有右正和列

$$\oplus_\Lambda\mathbf{F}(A)\xrightarrow{\text{ }f\text{ }}\oplus_\Omega\mathbf{F}(A)\twoheadrightarrow W $$

//written by blue_239k

#include<iostream>
#include<conio.h>
#include<Windows.h>
#include<string.h>
#include<iomanip>
#include<math.h>

using namespace std;

#define handle GetStdHandle(STD_OUTPUT_HANDLE)
#define f_int FOREGROUND_INTENSITY
#define f_r FOREGROUND_RED
#define f_g FOREGROUND_GREEN
#define f_b FOREGROUND_BLUE
#define b_int BACKGROUND_INTENSITY
#define b_r BACKGROUND_RED
#define b_g BACKGROUND_GREEN
#define b_b BACKGROUND_BLUE
#define f_white f_r | f_g | f_b
#define b_white b_r | b_g | b_b
#define settext SetConsoleTextAttribute

#define decision_eps 0.0001

//int maxlength = 0;
string number[128] = {"7", "7", "4", "4"};  
long double numop1, numop2;
short op;

void color(bool flip){
	if(flip){
		settext(handle, 0);
		settext(handle, b_int | b_r | b_g | b_b);
	}
	else{
		settext(handle, 0);
		settext(handle, f_int | f_r | f_g | f_b);
	}
}

void number_out(short row, string* text, short pos, int maxlength){//output the current number situation
	system("cls");
	for(short i = 0; i < row; i++){
		color(i == pos);
		cout << stold(text[i]);
		for(int j = 0; j < maxlength - (int)(log(stold(text[i]))/log(10)); j++){
			cout << " ";
		}
		color(0);
//		cout << "\n";
	}
}

void botton_out(short row, string* text, short pos, int maxlength){//output the current button situation
	system("cls");
	for(short i = 0; i < row; i++){
		color(i == pos);
		cout << text[i];
		for(int j = 0; j < maxlength + 1 - (int)text[i].length(); j++){
			cout << " ";
		}
		color(0);
//		cout << "\n";
	}
}

int numplat(short row, string* text, bool afterop);

void operplat(short row, string* text, short pos){
	short operrow = 4;
	string opertext[128] = {"+", "-", "*", "/"};
	short operpos = 0;
	botton_out(operrow, opertext, 0, 1);
	while(1){
		if(_kbhit()){
			int ch = getch();
			switch(ch){
				case 75://left
					if(operpos == 0){
						operpos = row;
					}
					operpos--;
					botton_out(operrow, opertext, operpos, 1);
					break;
				case 77:
					if(operpos == operrow - 1){
						operpos = -1;
					}
					operpos++;
					botton_out(operrow, opertext, operpos, 1);
					break;
				case 32://space
//				case 13://enter
					string textselect[row - 1];
					for(int i = 0; i < row - 1; i++){
						if(i < pos){
							textselect[i] = text[i];
						}
						if(i >= pos){
							textselect[i] = text[i + 1];
						}
					}
					op = operpos;
					numplat(row - 1, textselect, 1);
					break;
			}
		}
		Sleep(20);
	}
}

int numplat(short row, string* text, bool afterop){
	short pos = 0;
	int maxlength = 0;
	for(short j = 0; j < row; j++){
		maxlength = max(maxlength, 1 + (int)(log(stold(text[j]))/log(10)));
	}
	number_out(row, text, 0, maxlength);
	while(1){
		if(_kbhit()){
			int ch = getch();
			switch(ch){
				case 75://left
					if(pos == 0){
						pos = row;
					}
					pos--;
					number_out(row, text, pos, maxlength);
					break;
				case 77:
					if(pos == row - 1){
						pos = -1;
					}
					pos++;
					number_out(row, text, pos, maxlength);
					break;
				case 32://space
//				case 13://enter
					if(!afterop){
						numop1 = stold(text[pos]);
						operplat(row, text, pos);
					}
					if(afterop){
						numop2 = stold(text[pos]);
						long double replacenum;
						switch(op){
							case 0:
								replacenum = numop1 + numop2;
								break;
							case 1:
								replacenum = numop1 - numop2;
								break;
							case 2:
								replacenum = numop1 * numop2;
								break;
							case 3:
								replacenum = numop1 / numop2;
								break;
						}
						text[pos] = to_string(replacenum);
						if(row == 1 && stold(text[row - 1]) - 24 < decision_eps){
							system("cls");
							cout << "You win!" << endl;
							return 1;
						}
						else{
							if(row == 1){
								system("cls");
								cout << "You lost!" << endl;
								return 0;
							}
							numplat(row, text, 0);
						}
					}
					break;
			}
		}
		Sleep(20);
	}
} 

int main(){
	cout << setprecision(3);
	CONSOLE_CURSOR_INFO CursorInfo;
	GetConsoleCursorInfo(handle, &CursorInfo);
	CursorInfo.bVisible = false;
	SetConsoleCursorInfo(handle, &CursorInfo);
	numplat(4, number, 0);
	return 0;
}