idx int64 0 750k | image unknown | latex stringlengths 2 512 | source stringclasses 8
values |
|---|---|---|---|
0 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
2,
56,
0,
0,
0,
95,
8,
2,
0,
0,
0,
106,
121,
42,
106,
0,
0,
75,
49,
73,
68,
65,
84,
120,
156,
237,
125,
119,
120,
85,
85,
186,
247,
57,
39,
14... | \begin{gathered}h^{-2\sigma}a^{-2k + \eta}= h^{-2\sigma}(h^{\frac{\sigma}{k}}(\log(h^{-1}))^{-T})^{2k - \eta}\le e^{\frac{\sigma}{k}}\log(h^{-1})^{-\frac{T}{3}}\le C \log(h^{-1})^{-\frac{T}{3}}, h^{-2\sigma}a^{-1 - 2\delta + k + \eta}\le h^{-2\sigma}a^{-2k + \eta}\le C \log(h^{-1})^{-\frac{T}{3}}. \end{gathered} | oleehyo |
1 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
180,
0,
0,
0,
66,
8,
2,
0,
0,
0,
113,
100,
107,
97,
0,
0,
14,
111,
73,
68,
65,
84,
120,
156,
237,
92,
93,
76,
92,
69,
27,
158,
115,
118,
20... | [F]=\beta, \ \chi(F)=n | oleehyo |
2 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
146,
0,
0,
0,
53,
8,
2,
0,
0,
0,
37,
0,
37,
143,
0,
0,
14,
87,
73,
68,
65,
84,
120,
156,
237,
91,
93,
108,
20,
85,
27,
158,
57,
51,
187,
... | \widehat\alpha(I_{n+1, c}) = \frac{n+1}{c}. | oleehyo |
3 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
2,
98,
0,
0,
0,
76,
8,
2,
0,
0,
0,
65,
13,
76,
222,
0,
0,
97,
128,
73,
68,
65,
84,
120,
156,
237,
125,
119,
92,
84,
103,
214,
255,
84,
170,
16... | [\sigma^i(p')+\sigma^i(j(p'))+\sigma^{-i}(p')+\sigma^{-i}(j(p')) -\sigma^i(x')-\sigma^i(j(x'))-\sigma^{-i}(x')-\sigma^{-i}(j(x'))]= [p'_i+j(p'_{d-i})+p'_{d-i}+ j(p'_{i}) - x'_i-j(x'_{d-i})-x'_{d-i}-j(x'_{i})]= (1+j)([p'_i+p'_{d-i}-x'_i-x'_{d-i}]). | oleehyo |
4 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
2,
198,
0,
0,
0,
128,
8,
2,
0,
0,
0,
135,
148,
56,
186,
0,
0,
7,
97,
73,
68,
65,
84,
120,
156,
237,
221,
235,
110,
220,
56,
12,
6,
208,
168,
2... | F:V\rightarrow V | mathwriting |
5 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
78,
0,
0,
0,
128,
8,
2,
0,
0,
0,
235,
164,
23,
78,
0,
0,
7,
158,
73,
68,
65,
84,
120,
156,
237,
157,
225,
206,
227,
40,
12,
69,
75,
212,
24... | ((\frac{495}{9})^{131}+\frac{183^{6}}{3}) | mathwriting |
6 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
50,
0,
0,
0,
128,
8,
2,
0,
0,
0,
7,
209,
114,
88,
0,
0,
4,
223,
73,
68,
65,
84,
120,
156,
237,
221,
225,
110,
227,
40,
20,
128,
209,
186,
2... | \Gamma_{1}(N) | mathwriting |
7 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
240,
0,
0,
0,
40,
8,
2,
0,
0,
0,
79,
90,
224,
135,
0,
0,
12,
209,
73,
68,
65,
84,
120,
156,
237,
155,
123,
80,
19,
103,
247,
199,
55,
9,
18... | \{Q , Q \}= P + W_{+ \infty}- W_{- \infty} | linxy_synthetic_handwrite |
8 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
200,
0,
0,
0,
40,
8,
2,
0,
0,
0,
52,
126,
34,
75,
0,
0,
14,
195,
73,
68,
65,
84,
120,
156,
237,
92,
121,
76,
84,
215,
247,
191,
111,
157,
5... | \gamma_{1}( \alpha_{1}\beta_{2}- \alpha_{2}\beta_{1}) - \gamma_{1}\frac{\partial \gamma_{1}}{\partial \theta}= 0 | linxy_full |
9 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
252,
0,
0,
0,
40,
8,
2,
0,
0,
0,
85,
102,
0,
9,
0,
0,
21,
108,
73,
68,
65,
84,
120,
156,
237,
92,
121,
76,
84,
103,
215,
191,
203,
44,
160,... | q(u)=\exp_{A}(u-K_{p}(u)+\log_{A}p) | oleehyo |
10 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
186,
0,
0,
0,
53,
8,
2,
0,
0,
0,
121,
138,
102,
171,
0,
0,
16,
141,
73,
68,
65,
84,
120,
156,
237,
91,
107,
108,
84,
85,
215,
62,
103,
206,
... | \overline{\beta_{jk}\left(\left|\eta\right|\right)}=\beta_{jk}\left(-\left|\eta\right|\right). | oleehyo |
11 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
154,
0,
0,
0,
51,
8,
2,
0,
0,
0,
224,
142,
134,
102,
0,
0,
13,
226,
73,
68,
65,
84,
120,
156,
237,
90,
107,
76,
92,
213,
22,
62,
143,
57,
5... | D_t=\left(\begin{smallmatrix}\cos t -\sin t \sin t \cos t\end{smallmatrix}\right). | oleehyo |
12 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
237,
0,
0,
0,
128,
8,
2,
0,
0,
0,
104,
69,
121,
92,
0,
0,
4,
137,
73,
68,
65,
84,
120,
156,
237,
157,
235,
110,
164,
48,
12,
70,
39,
104,
2... | \overline{P_{1}P_{2}} | mathwriting |
13 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
200,
0,
0,
0,
40,
8,
2,
0,
0,
0,
52,
126,
34,
75,
0,
0,
12,
162,
73,
68,
65,
84,
120,
156,
237,
91,
125,
76,
83,
103,
23,
127,
238,
87,
75,... | \Delta_{R}\{\theta_{1}, \theta_{2}\}_{\mathrm{c . b .}}= \{\theta_{1}, \theta_{2}\}_{\mathrm{c . b .}}\otimes I | linxy_full |
14 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
128,
0,
0,
0,
128,
8,
2,
0,
0,
0,
76,
92,
246,
156,
0,
0,
2,
203,
73,
68,
65,
84,
120,
156,
237,
157,
203,
114,
195,
48,
12,
3,
197,
140,
2... | \frac{-1}{\sqrt{2}} | mathwriting |
15 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
3,
32,
0,
0,
0,
100,
8,
2,
0,
0,
0,
241,
51,
195,
216,
0,
0,
53,
127,
73,
68,
65,
84,
120,
156,
237,
221,
121,
60,
84,
251,
255,
56,
240,
209,
... | {\frac{\partial}{\partial r}}\left[ ( r^{2}+ A^{2}- 2 M r ){\frac{\partial G}{\partial r}}\right] +{\frac{1}{s i n \theta}}{\frac{\partial}{\partial \theta}}\left[ s i n \theta{\frac{\partial G}{\partial \theta}}\right] = - \delta ( r - r_{o}) \delta ( c o s \theta - c o s{\theta}_{o}) \delta ( \varphi -{\varphi}_{o}) | linxy_synthetic_handwrite |
16 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
245,
0,
0,
0,
44,
8,
2,
0,
0,
0,
50,
226,
105,
213,
0,
0,
25,
162,
73,
68,
65,
84,
120,
156,
237,
92,
123,
112,
84,
229,
249,
62,
103,
207,
... | \lim_{n\to \infty}|\phi(\Delta_n)|=\lim_{n\to \infty}|\psi(\Delta_n)|=1 | oleehyo |
17 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
2,
86,
0,
0,
0,
128,
8,
2,
0,
0,
0,
70,
63,
176,
83,
0,
0,
10,
141,
73,
68,
65,
84,
120,
156,
237,
221,
237,
142,
228,
40,
12,
133,
225,
102,
... | \pi_{3}(SL(2,\mathbb{R})) | mathwriting |
18 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
2,
253,
0,
0,
0,
128,
8,
2,
0,
0,
0,
23,
135,
65,
117,
0,
0,
11,
187,
73,
68,
65,
84,
120,
156,
237,
221,
217,
82,
195,
58,
18,
0,
80,
114,
13... | y_{n+1}=y_{n}(\frac{3}{2}-\frac{x}{2}y_{n}^{2})=\frac{y_{n}(3-xy_{n}^{2})}{2}. | mathwriting |
19 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
73,
0,
0,
0,
63,
8,
2,
0,
0,
0,
226,
228,
173,
151,
0,
0,
37,
144,
73,
68,
65,
84,
120,
156,
237,
93,
123,
84,
213,
85,
246,
255,
222,
23,
... | u\frac{\partial R(u,g)}{\partial u}= \beta (g^2)\frac{\partial R(u,g)}{\partial g^2}+\gamma (g^2)R(u,g), | oleehyo |
20 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
3,
183,
0,
0,
0,
128,
8,
2,
0,
0,
0,
95,
145,
9,
220,
0,
0,
12,
151,
73,
68,
65,
84,
120,
156,
237,
221,
235,
150,
171,
168,
22,
6,
208,
202,
... | D=\frac{C\cdot A}{B}=\frac{1.63m\cdot180m}{2m}=146.7m | mathwriting |
21 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
2,
121,
0,
0,
0,
128,
8,
2,
0,
0,
0,
248,
105,
232,
14,
0,
0,
10,
58,
73,
68,
65,
84,
120,
156,
237,
221,
237,
142,
155,
58,
16,
0,
208,
82,
2... | (\sum_{i=1}^{3}\sqrt{a_{i}x+b_{i}}-\sum_{i=4}^{6}\sqrt{a_{i}x+b_{i}})=0 | mathwriting |
22 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
0,
255,
0,
0,
0,
128,
8,
2,
0,
0,
0,
75,
30,
40,
137,
0,
0,
5,
146,
73,
68,
65,
84,
120,
156,
237,
157,
219,
142,
27,
33,
16,
68,
141,
229,
25... | N_{2}(c) | mathwriting |
23 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
125,
0,
0,
0,
128,
8,
2,
0,
0,
0,
104,
96,
46,
117,
0,
0,
6,
196,
73,
68,
65,
84,
120,
156,
237,
221,
237,
142,
227,
32,
12,
133,
225,
178,
... | x_{j}\in\frac{[b_{i}]-\sum_{k\ne j}[a_{ik}]\cdot[x_{k}]}{[a_{ii}]} | mathwriting |
24 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
74,
0,
0,
0,
128,
8,
2,
0,
0,
0,
226,
79,
183,
52,
0,
0,
6,
88,
73,
68,
65,
84,
120,
156,
237,
157,
225,
110,
236,
42,
12,
6,
151,
106,
223... | \rho^{\prime}\equiv\rho+\frac{\Lambda}{8\pi G} | mathwriting |
25 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
204,
0,
0,
0,
128,
8,
2,
0,
0,
0,
9,
84,
206,
114,
0,
0,
8,
77,
73,
68,
65,
84,
120,
156,
237,
221,
237,
110,
156,
48,
16,
133,
225,
82,
22... | U_{el}(x)=\frac{1}{2}kx^{2} | mathwriting |
26 | [
137,
80,
78,
71,
13,
10,
26,
10,
0,
0,
0,
13,
73,
72,
68,
82,
0,
0,
1,
114,
0,
0,
0,
128,
8,
2,
0,
0,
0,
153,
107,
117,
248,
0,
0,
5,
149,
73,
68,
65,
84,
120,
156,
237,
221,
225,
110,
219,
58,
12,
6,
208,
105,
... | \beta=\frac{E}{RT_{f}}\frac{T_{f}-T_{o}}{T_{f}} | mathwriting |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- -