update build and types

Jenkinsfile

@@ -20,12 +20,25 @@ pipeline {
             steps {
                 script {
                     echo "Building docker image ${registry}:${version}.${env.BUILD_ID}"
-                    def customImage = docker.build("${registry}:${version}.${env.BUILD_ID}")
+                    def customImage = docker.build("${registry}:v${version}.${env.BUILD_ID}")
                     
-                    echo "Pushing docker image ${registry}:${version}.${env.BUILD_ID}"
+                    echo "Pushing docker image ${registry}:v${version}.${env.BUILD_ID}"
                     customImage.push()
                 }
             }
         }
+        stage('Deploy') {
+            steps {
+                echo "Deploying docker image ${registry}:v${version}.${env.BUILD_ID}"
+                echo "Stopping existing container"
+                sh 'docker stop notenextra'
+                echo "Removing existing container"
+                sh 'docker rm notenextra'
+                echo "Running new docker container"
+                sh 'docker run -d -p 13000:3000 --name notenextra ${registry}:v${version}.${env.BUILD_ID}'
+            }
+        }
     }
 }
+
+}

pages/CSE559A/CSE559A_L22.md

@@ -166,11 +166,11 @@ y \\
 \end{pmatrix}
 $$
 
-Constraint from a match $(x_i,x_i^′)$: $x_i^′≅Hx_i$
+Constraint from a match $(x_i,x_i^')$: $x_i^'≅Hx_i$
 
 How can we get rid of the scale ambiguity? 
 
-Cross product trick:	$x_i^′ × Hx_i=0$
+Cross product trick:	$x_i^' × Hx_i=0$
 
 The cross product is defined as:
 
@@ -181,9 +181,9 @@ $$
 Let $h_1^T, h_2^T, h_3^T$ be the rows of $H$. Then
 
 $$
-x_i^′ × Hx_i=\begin{pmatrix}
+x_i^' × Hx_i=\begin{pmatrix}
-    x_i^′ \\
+    x_i^' \\
-    y_i^′ \\
+    y_i^' \\
     1
 \end{pmatrix} \times \begin{pmatrix}
     h_1^T x_i \\
@@ -192,18 +192,18 @@ x_i^′ × Hx_i=\begin{pmatrix}
 \end{pmatrix}
 =
 \begin{pmatrix}
-    y_i^′ h_3^T x_i−h_2^T x_i \\
+    y_i^' h_3^T x_i−h_2^T x_i \\
-    h_1^T x_i−x_i^′ h_3^T x_i \\
+    h_1^T x_i−x_i^' h_3^T x_i \\
-    x_i^′ h_2^T x_i−y_i^′ h_1^T x_i
+    x_i^' h_2^T x_i−y_i^' h_1^T x_i
 \end{pmatrix}
 $$
 
-Constraint from a match $(x_i,x_i^′)$:
+Constraint from a match $(x_i,x_i^')$:
 
 $$
-x_i^′ × Hx_i=\begin{pmatrix}
+x_i^' × Hx_i=\begin{pmatrix}
-    x_i^′ \\
+    x_i^' \\
-    y_i^′ \\
+    y_i^' \\
     1
 \end{pmatrix} \times \begin{pmatrix}
     h_1^T x_i \\
@@ -212,9 +212,9 @@ x_i^′ × Hx_i=\begin{pmatrix}
 \end{pmatrix}
 =
 \begin{pmatrix}
-    y_i^′ h_3^T x_i−h_2^T x_i \\
+    y_i^' h_3^T x_i−h_2^T x_i \\
-    h_1^T x_i−x_i^′ h_3^T x_i \\
+    h_1^T x_i−x_i^' h_3^T x_i \\
-    x_i^′ h_2^T x_i−y_i^′ h_1^T x_i
+    x_i^' h_2^T x_i−y_i^' h_1^T x_i
 \end{pmatrix}
 $$
 
@@ -222,9 +222,9 @@ Rearranging the terms:
 
 $$
 \begin{bmatrix}
-    0^T &-x_i^T &y_i^′ x_i^T \\
+    0^T &-x_i^T &y_i^' x_i^T \\
-    x_i^T &0^T &-x_i^′ x_i^T \\
+    x_i^T &0^T &-x_i^' x_i^T \\
-    y_i^′ x_i^T &x_i^′ x_i^T &0^T
+    y_i^' x_i^T &x_i^' x_i^T &0^T
 \end{bmatrix}
 \begin{bmatrix}
     h_1 \\

pages/Math4121/Math4121_L35.md

@@ -0,0 +1,33 @@
+# Math4121 Lecture 35
+
+## Continue on Lebesgue Integration
+
+### Lebesgue Integration
+
+#### Definition of Lebesgue Integral
+
+For simple functions $\phi = \sum_{i=1}^{n} a_i \chi_{S_i}$, given a measure $E$, the Lebesgue integral is defined as:
+
+$$
+\int_{\mathbb{R}^n} \phi \, dm = \sum_{i=1}^{n} a_i m(S_i\cap E)
+$$
+
+
+Given a non-negative measurable function $f$ and a measurable set $E$.
+
+Define $\int_E f \, dm = \sup \left\{ \int_E \phi \, dm : \phi \text{ is a simple function and } \phi \leq f \right\}$
+
+(**We do allows $\int_E f \, dm = \infty$**)
+
+For general measurable function $f$, we can define $f^-(x)=\max\{0,-f(x)\}$, $f^+(x)=\max\{0,f(x)\}$. (The positive part of the function and the negative part of the function, both non-negative)
+
+Then $f=f^+-f^-$.
+
+We say $f$ is integrable if $\int_E f^+ \, dm < \infty$ and $\int_E f^- \, dm < \infty$. (both finite) If at least one is finite, define
+
+$$
+\int_E f \, dm = \int_E f^+ \, dm - \int_E f^- \, dm
+$$
+
+We allow for $A-\infty = -\infty$ and $A+\infty = \infty$ for any $A\in \mathbb{R}$. But not $\infty-\infty$.
+