diff --git a/README.md b/README.md index 2e9c5d7..9946db0 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,3 @@ # NoteNextra + static note sharing site for minmum care diff --git a/next.config.mjs b/next.config.mjs index 728a52c..590416d 100644 --- a/next.config.mjs +++ b/next.config.mjs @@ -1,11 +1,19 @@ import nextra from 'nextra' - + const withNextra = nextra({ - theme: 'nextra-theme-blog', - themeConfig: './theme.config.jsx' + theme: 'nextra-theme-docs', + themeConfig: './theme.config.jsx', + latex: { + renderer: 'katex', + // options: { + // macros: { + // '\\RR': '\\mathbb{R}' + // } + // } + } }) - + export default withNextra() - + // If you have other Next.js configurations, you can pass them as the parameter: // export default withNextra({ /* other next.js config */ }) \ No newline at end of file diff --git a/package.json b/package.json index 645f674..f7d6b74 100644 --- a/package.json +++ b/package.json @@ -6,9 +6,9 @@ }, "dependencies": { "next": "^15.0.3", - "react": "^18.3.1", - "react-dom": "^18.3.1", "nextra": "^3.2.3", - "nextra-theme-blog": "^3.2.3" + "nextra-theme-docs": "^3.2.3", + "react": "^18.3.1", + "react-dom": "^18.3.1" } } \ No newline at end of file diff --git a/pages/Math4111/Math4111_E2.md b/pages/Math4111/Exam_reviews/Math4111_E2.md similarity index 96% rename from pages/Math4111/Math4111_E2.md rename to pages/Math4111/Exam_reviews/Math4111_E2.md index 83cc115..aeb0b2c 100644 --- a/pages/Math4111/Math4111_E2.md +++ b/pages/Math4111/Exam_reviews/Math4111_E2.md @@ -1,89 +1,89 @@ -# Math 4111 Exam 2 review - -$E$ is open if $\forall x\in E$, $x\in E^\circ$ ($E\subset E^\circ$) - -$E$ is closed if $E\supset E'$ - -Then $E$ closed $\iff E^c$ open $\iff \forall x\in E^\circ, \exists r>0$ such that $B_r(x)\subset E^c$ - -$\forall x\in E^c$, $\forall x\notin E$ - -$B_r(x)\subset E^c\iff B_r(x)\cap E=\phi$ - -## Past exam questions - -$S,T$ is compact $\implies S\cup T$ is compact - -Proof: - -Suppose $S$ and $T$ are compact, let $\{G_\alpha\}_{\alpha\in A}$ be an open cover of $S\cup T$ - -(NOT) $\{G_\alpha\}$ is an open cover of $S$, $\{H_\beta\}$ is an open cover of $T$. - -... - -EOP - -## K-cells are compact - - -We'll prove the case $k=1$ and $I=[0,1]$ (This is to simplify notation. This same ideas are used in the general case) - -Proof: - -That $[0,1]$ is compact. - -(Key idea, divide and conquer) - -Suppose for contradiction that $\exists$ open cover $\{G_a\}_{\alpha\in A}$ of $[0,1]$ with no finite subcovers of $[0,1]$ - -**Step1.** Divide $[0,1]$ in half. $[0,\frac{1}{2}]$ and $[\frac{1}{2},1]$ and at least one of the subintervals cannot be covered by a finite subcollection of $\{G_\alpha\}_{\alpha\in A}$ - -(If both of them could be, combine the two finite subcollections to get a finite subcover of $[0,1]$) - -Let $I_1$ be a subinterval without a finite subcover. - -**Step2.** Divide $I_1$ in half. Let $I_2$ be one of these two subintervals of $I_1$ without a finite subcover. - -**Step3.** etc. - -We obtain a seg of intervals $I_1\subset I_2\subset \dots$ such that - -(a) $[0,1]\supset I_1\supset I_2\supset \dots$ -(b) $\forall n\in \mathbb{N}$, $I_n$ is not covered by a finite subcollection of $\{G_\alpha\}_{\alpha\in A}$ -(c) The length of $I_n$ is $\frac{1}{2^n}$ - -By (a) and **Theorem 2.38**, $\exists x^*\in \bigcap^{\infty}_{n=1} I_n$. - -Since $x^*\in [0,1]$, $\exists \alpha_0$ such that $x^*\in G_{\alpha_0}$ - -Since $G_{\alpha_0}$ is open, $\exist r>0$ such that $B_r(x^*)\subset G_{\alpha_0}$ - -Let $n\in \mathbb{N}$ be such that $\frac{1}{2^n}0$ such that $B_r(x)\subset E^c$ + +$\forall x\in E^c$, $\forall x\notin E$ + +$B_r(x)\subset E^c\iff B_r(x)\cap E=\phi$ + +## Past exam questions + +$S,T$ is compact $\implies S\cup T$ is compact + +Proof: + +Suppose $S$ and $T$ are compact, let $\{G_\alpha\}_{\alpha\in A}$ be an open cover of $S\cup T$ + +(NOT) $\{G_\alpha\}$ is an open cover of $S$, $\{H_\beta\}$ is an open cover of $T$. + +... + +EOP + +## K-cells are compact + + +We'll prove the case $k=1$ and $I=[0,1]$ (This is to simplify notation. This same ideas are used in the general case) + +Proof: + +That $[0,1]$ is compact. + +(Key idea, divide and conquer) + +Suppose for contradiction that $\exists$ open cover $\{G_a\}_{\alpha\in A}$ of $[0,1]$ with no finite subcovers of $[0,1]$ + +**Step1.** Divide $[0,1]$ in half. $[0,\frac{1}{2}]$ and $[\frac{1}{2},1]$ and at least one of the subintervals cannot be covered by a finite subcollection of $\{G_\alpha\}_{\alpha\in A}$ + +(If both of them could be, combine the two finite subcollections to get a finite subcover of $[0,1]$) + +Let $I_1$ be a subinterval without a finite subcover. + +**Step2.** Divide $I_1$ in half. Let $I_2$ be one of these two subintervals of $I_1$ without a finite subcover. + +**Step3.** etc. + +We obtain a seg of intervals $I_1\subset I_2\subset \dots$ such that + +(a) $[0,1]\supset I_1\supset I_2\supset \dots$ +(b) $\forall n\in \mathbb{N}$, $I_n$ is not covered by a finite subcollection of $\{G_\alpha\}_{\alpha\in A}$ +(c) The length of $I_n$ is $\frac{1}{2^n}$ + +By (a) and **Theorem 2.38**, $\exists x^*\in \bigcap^{\infty}_{n=1} I_n$. + +Since $x^*\in [0,1]$, $\exists \alpha_0$ such that $x^*\in G_{\alpha_0}$ + +Since $G_{\alpha_0}$ is open, $\exist r>0$ such that $B_r(x^*)\subset G_{\alpha_0}$ + +Let $n\in \mathbb{N}$ be such that $\frac{1}{2^n}0, B_r(x)\backslash\{x\}\cap E\neq\emptyset\}$ - -Closure $\overline{E}=E\cup E'=\{x\in\mathbb{R}:\forall r>0, B_r(x)\cap E\neq\emptyset\}$ - -$p_n\to p\implies \forall \epsilon>0, \exists N$ such that $\forall n\geq N, p_n\in B_\epsilon(p)$ - -### Some interesting results - -#### Lemma - -$p\in \overline{E}\iff \exists (p_n)\subseteq E$ such that $p_n\to p$ - -$p\in E'\iff \exists (p_n)\subseteq E\backslash\{p\}$ such that $p_n\to p$ (you cannot choose $p$ in the sequence) - -#### Bolzano-Weierstrass Theorem - -Let $E$ be a compact set and $(p_n)$ be a sequence in $E$. Then $\exists (p_{n_k})\subseteq (p_n)$ such that $p_{n_k}\to p\in E$. - -Rudin Proof: - -Rudin's proof uses a fact from Chapter 2. - -If $E$ is compact, and $S\subseteq E$ is infinite, then $S$ has a limit point in $E$ ($S'\cap E\neq\emptyset$). - -## Examples of Cauchy sequence that does not converge - -> Cauchy sequence in $(X,d),\forall \epsilon>0, \exists N$ such that $\forall m,n\geq N, d(p_m,p_n)<\epsilon$ - -Let $X=\mathbb{Q}$ and $(p_q)=\{1,1.4,1.41,1.414,1.4142,1.41421,\dots\}$ The sequence is Cauchy but does not converge in $\mathbb{Q}$. - -This does not hold in $\mathbb{R}$ because compact metric spaces are complete. - -Fact: Every Cauchy sequence is bounded. - -## Proof that $e$ is irrational - -> $e=\sum_{n=0}^\infty \frac{1}{n!}$ - -Let $s_n=\sum_{k=0}^n \frac{1}{k!}$ - -So $e-s_n=\left(\sum_{k=n+1}^\infty \frac{1}{k!}\right)<\frac{1}{n!n}$ - -If $e$ is rational, then $\exists p,q\in\mathbb{Z}$ such that $e=\frac{q}{p}$ and $q!s_q\in\mathbb{Z}$, $q!e=q!\frac{p}{q}\in \mathbb{Z}$, so $q!(e-s_q)\in\mathbb{Z}$ - -$0s^*,\{n:a_n>x\}$ is finite. $\exists N$ such that $\forall n\geq N, a_n\leq x$ - -$\forall xx\}$ is infinite. - -One example is $(a_n)=(-1)^n\frac{n}{n+1}$ - -$\limsup a_n=1$ and $\liminf a_n=-1$ - -So the size of set of elements of $a_n$ that are greater than any $x<1$ is infinite. and the size of set of elements of $a_n$ that are greater than any $x>1$ is finite. - -#### $\limsup(a_n+b_n)\leq \limsup a_n+\limsup b_n$ - -One example for smaller than is $(a_n)=(-1)^n$ and $(b_n)=(-1)^{n+1}$ - -$\limsup(a_n+b_n)=0$ and $\limsup a_n+\limsup b_n=2$ - -## ($\forall n,s_n\leq t_n$) $\implies \limsup s_n\leq \limsup t_n$ - -One example of using this theorem is $(s_n)=\left(\sum_{k=1}^n\frac{1}{k!}\right)$ and $(t_n)=\left(\frac{1}{n}+1\right)^n$ - -## Rearrangement of series - -Will not be tested. - -_infinite sum is not similar to finite sum. For infinite sum, the order of terms matters. But for finite sum, the order of terms does not matter, you can rearrange the terms as you want._ - -## Ways to prove convergence of series - -### n-th term test (divergence test) - -If $\lim_{n\to\infty}a_n\neq 0$, then $\sum a_n$ diverges. - -### Definition of convergence of series (convergence and divergence test) - -If $\sum a_n$ converges, then $\lim_{n\to\infty}\sum_{k=1}^n a_k=0$. - -Example: Telescoping series and geometric series. - -### Comparison test (convergence and divergence test (absolute convergence)) - -Let $(a_n)$ be a sequence in $\mathbb{C}$ and $(c_n)$ be a non-negative sequence in $\mathbb{R}$. Suppose $\forall n, |a_n|\leq c_n$. - -(a) If the series $\sum_{n=1}^{\infty}c_n$ converges, then the series $\sum_{n=1}^{\infty}a_n$ converges. -(b) If the series $\sum_{n=1}^{\infty}a_n$ diverges, then the series $\sum_{n=1}^{\infty}c_n$ diverges. - -### Ratio test (convergence and divergence test (absolute convergence)) - -> $$ \left|\frac{a_{n+1}}{a_n}\right| \leq \alpha \implies |a_n|\leq \alpha^n$$ - -Given a series $\sum_{n=0}^{\infty} a_n$, $a_n\in\mathbb{C}\backslash\{0\}$. - -Then - -(a) If $\limsup_{n\to\infty} \left|\frac{a_{n+1}}{a_n}\right| < 1$, then $\sum_{n=0}^{\infty} a_n$ converges. -(b) If $\left|\frac{a_{n+1}}{a_n}\right| \geq 1$ for all $n\geq n_0$ for some $n_0\in\mathbb{N}$, then $\sum_{n=0}^{\infty} a_n$ diverges. - - -### Root test (convergence and divergence test (absolute convergence)) - -> $$ \sqrt[n]{|a_n|} \leq \alpha \implies |a_n|\leq \alpha^n$$ - -Given a series $\sum_{n=0}^{\infty} a_n$, put $\alpha = \limsup_{n\to\infty} \sqrt[n]{|a_n|}$. - -Then - -(a) If $\alpha < 1$, then $\sum_{n=0}^{\infty} a_n$ converges. -(b) If $\alpha > 1$, then $\sum_{n=0}^{\infty} a_n$ diverges. -(c) If $\alpha = 1$, the test gives no information - - -### Cauchy criterion - -### Geometric series - -### P-series - - -(a) $\sum_{n=0}^{\infty}\frac{1}{n}$ diverges. -(b) $\sum_{n=0}^{\infty}\frac{1}{n^2}$ converges. - -### Cauchy condensation test (convergence test) - -Suppose $(a_n)$ is a non-negative sequence. The series $\sum_{n=1}^{\infty}a_n$ converges if and only if the series $\sum_{k=0}^{\infty}2^ka_{2^k}$ converges. - -### Dirichlet test (convergence test) - -Suppose - -(a) the partial sum $A_n$ of $\sum a_n$ form a bounded sequence. -(b) $b_0\geq b_1\geq b_2\geq \cdots$ (non-increasing) -(c) $\lim_{n\to\infty}b_n=0$. - -Then $\sum a_nb_n$ converges. - -Example: $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}$ converges. - -### Abel's test (convergence test) - -Let $(b_n)^\infty_{n=0}$ be a sequence such that: - -(a) $b_0\geq b_1\geq b_2\geq \cdots$ (non-increasing) -(b) $\lim_{n\to\infty}b_n=0$ - -Then if $|z|=1$ and $z\neq 1$, $\sum_{n=0}^\infty b_nz^n$ converges. +# Exam 3 Review session + +## Relations between series and topology (compactness, closure, etc.) + +Limit points $E'=\{x\in\mathbb{R}:\forall r>0, B_r(x)\backslash\{x\}\cap E\neq\emptyset\}$ + +Closure $\overline{E}=E\cup E'=\{x\in\mathbb{R}:\forall r>0, B_r(x)\cap E\neq\emptyset\}$ + +$p_n\to p\implies \forall \epsilon>0, \exists N$ such that $\forall n\geq N, p_n\in B_\epsilon(p)$ + +### Some interesting results + +#### Lemma + +$p\in \overline{E}\iff \exists (p_n)\subseteq E$ such that $p_n\to p$ + +$p\in E'\iff \exists (p_n)\subseteq E\backslash\{p\}$ such that $p_n\to p$ (you cannot choose $p$ in the sequence) + +#### Bolzano-Weierstrass Theorem + +Let $E$ be a compact set and $(p_n)$ be a sequence in $E$. Then $\exists (p_{n_k})\subseteq (p_n)$ such that $p_{n_k}\to p\in E$. + +Rudin Proof: + +Rudin's proof uses a fact from Chapter 2. + +If $E$ is compact, and $S\subseteq E$ is infinite, then $S$ has a limit point in $E$ ($S'\cap E\neq\emptyset$). + +## Examples of Cauchy sequence that does not converge + +> Cauchy sequence in $(X,d),\forall \epsilon>0, \exists N$ such that $\forall m,n\geq N, d(p_m,p_n)<\epsilon$ + +Let $X=\mathbb{Q}$ and $(p_q)=\{1,1.4,1.41,1.414,1.4142,1.41421,\dots\}$ The sequence is Cauchy but does not converge in $\mathbb{Q}$. + +This does not hold in $\mathbb{R}$ because compact metric spaces are complete. + +Fact: Every Cauchy sequence is bounded. + +## Proof that $e$ is irrational + +> $e=\sum_{n=0}^\infty \frac{1}{n!}$ + +Let $s_n=\sum_{k=0}^n \frac{1}{k!}$ + +So $e-s_n=\left(\sum_{k=n+1}^\infty \frac{1}{k!}\right)<\frac{1}{n!n}$ + +If $e$ is rational, then $\exists p,q\in\mathbb{Z}$ such that $e=\frac{q}{p}$ and $q!s_q\in\mathbb{Z}$, $q!e=q!\frac{p}{q}\in \mathbb{Z}$, so $q!(e-s_q)\in\mathbb{Z}$ + +$0s^*,\{n:a_n>x\}$ is finite. $\exists N$ such that $\forall n\geq N, a_n\leq x$ + +$\forall xx\}$ is infinite. + +One example is $(a_n)=(-1)^n\frac{n}{n+1}$ + +$\limsup a_n=1$ and $\liminf a_n=-1$ + +So the size of set of elements of $a_n$ that are greater than any $x<1$ is infinite. and the size of set of elements of $a_n$ that are greater than any $x>1$ is finite. + +#### $\limsup(a_n+b_n)\leq \limsup a_n+\limsup b_n$ + +One example for smaller than is $(a_n)=(-1)^n$ and $(b_n)=(-1)^{n+1}$ + +$\limsup(a_n+b_n)=0$ and $\limsup a_n+\limsup b_n=2$ + +## ($\forall n,s_n\leq t_n$) $\implies \limsup s_n\leq \limsup t_n$ + +One example of using this theorem is $(s_n)=\left(\sum_{k=1}^n\frac{1}{k!}\right)$ and $(t_n)=\left(\frac{1}{n}+1\right)^n$ + +## Rearrangement of series + +Will not be tested. + +_infinite sum is not similar to finite sum. For infinite sum, the order of terms matters. But for finite sum, the order of terms does not matter, you can rearrange the terms as you want._ + +## Ways to prove convergence of series + +### n-th term test (divergence test) + +If $\lim_{n\to\infty}a_n\neq 0$, then $\sum a_n$ diverges. + +### Definition of convergence of series (convergence and divergence test) + +If $\sum a_n$ converges, then $\lim_{n\to\infty}\sum_{k=1}^n a_k=0$. + +Example: Telescoping series and geometric series. + +### Comparison test (convergence and divergence test (absolute convergence)) + +Let $(a_n)$ be a sequence in $\mathbb{C}$ and $(c_n)$ be a non-negative sequence in $\mathbb{R}$. Suppose $\forall n, |a_n|\leq c_n$. + +(a) If the series $\sum_{n=1}^{\infty}c_n$ converges, then the series $\sum_{n=1}^{\infty}a_n$ converges. +(b) If the series $\sum_{n=1}^{\infty}a_n$ diverges, then the series $\sum_{n=1}^{\infty}c_n$ diverges. + +### Ratio test (convergence and divergence test (absolute convergence)) + +> $$ \left|\frac{a_{n+1}}{a_n}\right| \leq \alpha \implies |a_n|\leq \alpha^n$$ + +Given a series $\sum_{n=0}^{\infty} a_n$, $a_n\in\mathbb{C}\backslash\{0\}$. + +Then + +(a) If $\limsup_{n\to\infty} \left|\frac{a_{n+1}}{a_n}\right| < 1$, then $\sum_{n=0}^{\infty} a_n$ converges. +(b) If $\left|\frac{a_{n+1}}{a_n}\right| \geq 1$ for all $n\geq n_0$ for some $n_0\in\mathbb{N}$, then $\sum_{n=0}^{\infty} a_n$ diverges. + + +### Root test (convergence and divergence test (absolute convergence)) + +> $$ \sqrt[n]{|a_n|} \leq \alpha \implies |a_n|\leq \alpha^n$$ + +Given a series $\sum_{n=0}^{\infty} a_n$, put $\alpha = \limsup_{n\to\infty} \sqrt[n]{|a_n|}$. + +Then + +(a) If $\alpha < 1$, then $\sum_{n=0}^{\infty} a_n$ converges. +(b) If $\alpha > 1$, then $\sum_{n=0}^{\infty} a_n$ diverges. +(c) If $\alpha = 1$, the test gives no information + + +### Cauchy criterion + +### Geometric series + +### P-series + + +(a) $\sum_{n=0}^{\infty}\frac{1}{n}$ diverges. +(b) $\sum_{n=0}^{\infty}\frac{1}{n^2}$ converges. + +### Cauchy condensation test (convergence test) + +Suppose $(a_n)$ is a non-negative sequence. The series $\sum_{n=1}^{\infty}a_n$ converges if and only if the series $\sum_{k=0}^{\infty}2^ka_{2^k}$ converges. + +### Dirichlet test (convergence test) + +Suppose + +(a) the partial sum $A_n$ of $\sum a_n$ form a bounded sequence. +(b) $b_0\geq b_1\geq b_2\geq \cdots$ (non-increasing) +(c) $\lim_{n\to\infty}b_n=0$. + +Then $\sum a_nb_n$ converges. + +Example: $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}$ converges. + +### Abel's test (convergence test) + +Let $(b_n)^\infty_{n=0}$ be a sequence such that: + +(a) $b_0\geq b_1\geq b_2\geq \cdots$ (non-increasing) +(b) $\lim_{n\to\infty}b_n=0$ + +Then if $|z|=1$ and $z\neq 1$, $\sum_{n=0}^\infty b_nz^n$ converges. diff --git a/pages/Math4111/_meta.js b/pages/Math4111/_meta.js new file mode 100644 index 0000000..b088f16 --- /dev/null +++ b/pages/Math4111/_meta.js @@ -0,0 +1,48 @@ +export default { + Exam_reviews: "Exam reviews", + Math4111_L1: "Lecture 1", + Math4111_L2: "Lecture 2", + Math4111_L3: "Lecture 3", + Math4111_L4: "Lecture 4", + Math4111_L5: "Lecture 5", + Math4111_L6: "Lecture 6", + Math4111_L7: "Lecture 7", + Math4111_L8: "Lecture 8", + Math4111_L9: "Lecture 9", + Math4111_L10: "Lecture 10", + Math4111_L11: "Lecture 11", + Math4111_L12: "Lecture 12", + Math4111_L13: "Lecture 13", + Math4111_L14: "Lecture 14", + Math4111_L15: "Lecture 15", + Math4111_L16: "Lecture 16", + Math4111_L17: "Lecture 17", + Math4111_L18: "Lecture 18", + Math4111_L19: "Lecture 19", + Math4111_L20: "Lecture 20", + Math4111_L21: "Lecture 21", + Math4111_L22: { + display: 'hidden' + }, + Math4111_L23: { + display: 'hidden' + }, + Math4111_L24: { + display: 'hidden' + }, + Math4111_L25: { + display: 'hidden' + }, + Math4111_L26: { + display: 'hidden' + }, + Math4111_L27: { + display: 'hidden' + }, + Math4111_L28: { + display: 'hidden' + }, + index: { + display: 'hidden' + } +} diff --git a/pages/Math4111/index.mdx b/pages/Math4111/index.mdx new file mode 100644 index 0000000..e69de29 diff --git a/pages/_app.jsx b/pages/_app.jsx index ddba3be..8237e7c 100644 --- a/pages/_app.jsx +++ b/pages/_app.jsx @@ -1,3 +1,9 @@ +import { ThemeProvider } from 'next-themes' + export default function App({ Component, pageProps }) { - return + return ( + + + + ) } \ No newline at end of file diff --git a/pages/_meta.js b/pages/_meta.js index fe6e765..6a35253 100644 --- a/pages/_meta.js +++ b/pages/_meta.js @@ -1,5 +1,30 @@ export default { - index: 'My Homepage', - contact: 'Contact Us', - about: 'About Us' + index: { + title: 'Home', + type: 'menu', + items: { + index: { + title: 'Home', + href: '/' + }, + about: { + title: 'About', + href: '/about' + }, + contact: { + title: 'Contact Me', + href: '/contact' + } + } + }, + Math4111: { + title: 'Math 4111', + type: 'page' + }, + about: { + display: 'hidden' + }, + contact: { + display: 'hidden' + } } \ No newline at end of file diff --git a/pages/about.mdx b/pages/about.mdx new file mode 100644 index 0000000..301c508 --- /dev/null +++ b/pages/about.mdx @@ -0,0 +1,4 @@ +# About + +## + diff --git a/pages/contact.mdx b/pages/contact.mdx new file mode 100644 index 0000000..55716f4 --- /dev/null +++ b/pages/contact.mdx @@ -0,0 +1,4 @@ +# contact + +## + diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml index 39c6c90..8694f51 100644 --- a/pnpm-lock.yaml +++ b/pnpm-lock.yaml @@ -14,7 +14,7 @@ importers: nextra: specifier: ^3.2.3 version: 3.2.3(@types/react@18.3.12)(acorn@8.14.0)(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(react-dom@18.3.1(react@18.3.1))(react@18.3.1)(typescript@5.6.3) - nextra-theme-blog: + nextra-theme-docs: specifier: ^3.2.3 version: 3.2.3(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(nextra@3.2.3(@types/react@18.3.12)(acorn@8.14.0)(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(react-dom@18.3.1(react@18.3.1))(react@18.3.1)(typescript@5.6.3))(react-dom@18.3.1(react@18.3.1))(react@18.3.1) react: @@ -694,6 +694,9 @@ packages: resolution: {integrity: sha512-e2i4wANQiSXgnrBlIatyHtP1odfUp0BbV5Y5nEGbxtIrStkEOAAzCUirvLBNXHLr7kwLvJl6V+4V3XV9x7Wd9w==} engines: {node: ^12.20.0 || >=14} + compute-scroll-into-view@3.1.0: + resolution: {integrity: sha512-rj8l8pD4bJ1nx+dAkMhV1xB5RuZEyVysfxJqB1pRchh1KVvwOv9b7CGB8ZfjTImVv2oF+sYMUkMZq6Na5Ftmbg==} + confbox@0.1.8: resolution: {integrity: sha512-RMtmw0iFkeR4YV+fUOSucriAQNb9g8zFR52MWCtl+cCZOFRNL6zeB395vPzFhEjjn4fMxXudmELnl/KF/WrK6w==} @@ -972,6 +975,9 @@ packages: fault@2.0.1: resolution: {integrity: sha512-WtySTkS4OKev5JtpHXnib4Gxiurzh5NCGvWrFaZ34m6JehfTUhKZvn9njTfw48t6JumVQOmrKqpmGcdwxnhqBQ==} + flexsearch@0.7.43: + resolution: {integrity: sha512-c5o/+Um8aqCSOXGcZoqZOm+NqtVwNsvVpWv6lfmSclU954O3wvQKxxK8zj74fPaSJbXpSLTs4PRhh+wnoCXnKg==} + format@0.2.2: resolution: {integrity: sha512-wzsgA6WOq+09wrU1tsJ09udeR/YZRaeArL9e1wPbFg3GG2yDnC2ldKpxs4xunpFF9DgqCqOIra3bc1HWrJ37Ww==} engines: {node: '>=0.4.x'} @@ -1387,6 +1393,14 @@ packages: react-cusdis: optional: true + nextra-theme-docs@3.2.3: + resolution: {integrity: sha512-kRhnLxbAbD3FgR93yLbu6Iz6XvErka3I5CcVo3VobLuV1mefbZ1T6DfiY6q0KJoHLGRrJESsFSarIqPjKOx00g==} + peerDependencies: + next: '>=13' + nextra: 3.2.3 + react: '>=18' + react-dom: '>=18' + nextra@3.2.3: resolution: {integrity: sha512-MyNA2kPvDyJK1trjFkwpTdMOKJu/MIueENHtmLoxPnyOi3fxtk9H5k6b5WdMGBibsyFeXqTz9REnz7d1/xL9Hg==} engines: {node: '>=18'} @@ -1570,6 +1584,9 @@ packages: scheduler@0.23.2: resolution: {integrity: sha512-UOShsPwz7NrMUqhR6t0hWjFduvOzbtv7toDH1/hIrfRNIDBnnBWd0CwJTGvTpngVlmwGCdP9/Zl/tVrDqcuYzQ==} + scroll-into-view-if-needed@3.1.0: + resolution: {integrity: sha512-49oNpRjWRvnU8NyGVmUaYG4jtTkNonFZI86MmGRDqBphEK2EXT9gdEUoQPZhuBM8yWHxCWbobltqYO5M4XrUvQ==} + section-matter@1.0.0: resolution: {integrity: sha512-vfD3pmTzGpufjScBh50YHKzEu2lxBWhVEHsNGoEXmCmn2hKGfeNLYMzCJpe8cD7gqX7TJluOVpBkAequ6dgMmA==} engines: {node: '>=4'} @@ -2501,6 +2518,8 @@ snapshots: commander@9.2.0: {} + compute-scroll-into-view@3.1.0: {} + confbox@0.1.8: {} cose-base@1.0.3: @@ -2817,6 +2836,8 @@ snapshots: dependencies: format: 0.2.2 + flexsearch@0.7.43: {} + format@0.2.2: {} get-stream@3.0.0: {} @@ -3629,6 +3650,20 @@ snapshots: react: 18.3.1 react-dom: 18.3.1(react@18.3.1) + nextra-theme-docs@3.2.3(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(nextra@3.2.3(@types/react@18.3.12)(acorn@8.14.0)(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(react-dom@18.3.1(react@18.3.1))(react@18.3.1)(typescript@5.6.3))(react-dom@18.3.1(react@18.3.1))(react@18.3.1): + dependencies: + '@headlessui/react': 2.2.0(react-dom@18.3.1(react@18.3.1))(react@18.3.1) + clsx: 2.1.1 + escape-string-regexp: 5.0.0 + flexsearch: 0.7.43 + next: 15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1) + next-themes: 0.4.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1) + nextra: 3.2.3(@types/react@18.3.12)(acorn@8.14.0)(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(react-dom@18.3.1(react@18.3.1))(react@18.3.1)(typescript@5.6.3) + react: 18.3.1 + react-dom: 18.3.1(react@18.3.1) + scroll-into-view-if-needed: 3.1.0 + zod: 3.23.8 + nextra@3.2.3(@types/react@18.3.12)(acorn@8.14.0)(next@15.0.3(react-dom@18.3.1(react@18.3.1))(react@18.3.1))(react-dom@18.3.1(react@18.3.1))(react@18.3.1)(typescript@5.6.3): dependencies: '@formatjs/intl-localematcher': 0.5.7 @@ -3964,6 +3999,10 @@ snapshots: dependencies: loose-envify: 1.4.0 + scroll-into-view-if-needed@3.1.0: + dependencies: + compute-scroll-into-view: 3.1.0 + section-matter@1.0.0: dependencies: extend-shallow: 2.0.1 diff --git a/theme.config.jsx b/theme.config.jsx index b532daf..4c6e62f 100644 --- a/theme.config.jsx +++ b/theme.config.jsx @@ -1,21 +1,54 @@ +import { useRouter } from 'next/router' +import { useConfig } from 'nextra-theme-docs' + export default { - footer:

MIT 2023 © Nextra.

, - head: ({ title, meta }) => ( + footer: { + content: ( + + MIT {new Date().getFullYear()} ©{' '} + + Trance-0 + + . + + ) + }, + head() { + const { asPath, defaultLocale, locale } = useRouter() + const { frontMatter } = useConfig() + const url = + 'https://vercel.com/notenextra' + + (defaultLocale === locale ? asPath : `/${locale}${asPath}`) + + return ( <> - {meta.description && ( - - )} - {meta.tag && } - {meta.author && } + + + - ), - readMore: 'Read More →', - postFooter: null, - darkMode: false, - navs: [ - { - url: 'https://github.com/shuding/nextra', - name: 'Nextra' - } - ] - } \ No newline at end of file + ) + }, + + logo: ( + <> + + + + + NoteNextra + + + ), + readMore: 'Read More →', + postFooter: null, + darkMode: false, + navs: [ + { + url: 'https://github.com/Trance-0/NoteNextra', + name: 'Source' + } + ] +} \ No newline at end of file