diff --git a/is/UB4/Ex4.ipynb b/is/UB4/Ex4.ipynb
index 6d60849..c65cf3b 100644
--- a/is/UB4/Ex4.ipynb
+++ b/is/UB4/Ex4.ipynb
@@ -204,17 +204,22 @@
     "  0,  & \\beta_i =0\\\\\n",
     "  1, & \\beta_i \\neq 0\\\\\n",
     "\\end{cases} %0 oder eins\n",
-    "     \\\\\\frac{d \\bzero(\\lambda) }{d \\beta}&= -\\frac{2}{n} X_i^TY_i +2 \\beta_i \\overset{!}{=} 0\\\\\n",
+    "\\\\\\text{The problem  can be simplified to one}\\\\ \\text{ some element representing all others}\\\\\n",
+    "       L_i&=\\begin{cases}\n",
+    "  0,  & \\beta_i =0\\\\\n",
+    "  -\\frac{2}{n}Y^{T}_iX_i\\beta_i+\\beta_i^2+\\lambda , & \\beta_i \\neq 0\\\\\n",
+    "\\end{cases} \\\\\n",
+    "     \\\\\\frac{d L_i }{d \\beta}&= -\\frac{2}{n} X_i^TY_i +2 \\beta_i \\overset{!}{=} 0\\\\\n",
     "     \\beta_i&= \\frac{1}{n} X^T_iY_i\\\\\n",
-    "     \\text{$|\\beta_i|$ in $\\bzero(\\lambda)$,$\\beta_i \\neq 0$, determine sum element of $\\bzero(\\lambda) > 0$}\\\\\n",
-    "     0&<  -2|\\beta_i|^2+|\\beta_i|^2 +\\lambda\\\\\n",
-    "     \\lambda&<|\\beta_i|^2\\\\\n",
-    "    \\lambda &<  \\left|\\frac{1}{n} X^T_iY_i\\right|^2 \\\\\n",
-    "     \\sqrt{\\lambda} &< \\left|\\frac{1}{n} X^T_iY_i\\right| \\\\\n",
+    "     \\text{$\\beta_i$ in $L_i$,$\\beta_i \\neq 0$, determine for which $\\lambda$ $\\beta_i =0$}\\\\\n",
+    "     0&=  -2\\beta_i^2+\\beta_i^2 +\\lambda\\\\\n",
+    "     \\lambda&=|\\beta_i|^2\\\\\n",
+    "    \\lambda &=  \\left|\\frac{1}{n} X^T_iY_i\\right|^2 \\\\\n",
+    "     \\sqrt{\\lambda} &= \\left|\\frac{1}{n} X^T_iY_i\\right| \\\\\n",
     "     \\bzero(\\lambda) = \\frac{1}{n} X^T_iY_i \\cdot \n",
     "     \\begin{cases}\n",
-    "  0, & |X^T_iY_i|\\leq\\sqrt{\\lambda}\\\\\n",
-    "  1, & |X^T_iY_i|>\\sqrt{\\lambda}\\\\\n",
+    "  0, & |X^T_iY_i| =\\sqrt{\\lambda}\\\\\n",
+    "  1, & |X^T_iY_i|><\\sqrt{\\lambda}\\\\\n",
     "\\end{cases}   \n",
     "     \\end{align}   \n",
     "     Das ist etwas reverse engineered. ich bezweifle die Korrektheit aber vielleicht hilft es um zur richtigen Lösung zu kommen"
@@ -230,6 +235,15 @@
    "source": []
   },
   {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
@@ -360,9 +374,9 @@
     "\\begin{align}\\blasso(\\lambda) &:= \\mathrm{arg \\, min}_{\\beta} \\frac{1}{n} \\norm{Y - X \\beta}_2^2 + \\lambda \\norm{\\beta}_1 ,\\\\\n",
     "     &=\\mathrm{arg \\, min}_{\\beta} \\underbrace{\\frac{1}{n} Y^{T}Y}_{constant}- \\frac{2}{n}Y^{T}X\\beta+\\norm{\\beta}^2+\\lambda \\norm{\\beta}_1 \\\\\n",
     "     &=\\mathrm{arg \\, min}_{\\beta} -\\frac{2}{n}Y^{T}X\\beta+\\norm{\\beta}^2+\\lambda \\norm{\\beta}_1 \\\\\n",
-    "         &=\\mathrm{min}_{\\beta} \\sum^p_{i=1}-\\frac{2}{n}Y^{T}_iX_i\\beta_i+\\beta_i^2+\\lambda |\\beta|\\\\\n",
+    "         &=\\mathrm{min}_{\\beta} \\sum^p_{i=1}-\\frac{2}{n}Y^{T}_iX_i\\beta_i+\\beta_i^2+\\lambda |\\beta_i|\\\\\n",
     "       \\text{Minimize for a fixed i}\\\\\\text{The problem  can be simplified to the sum of its parts}\\\\\n",
-    "       L_i&=-\\frac{2}{n}Y^{T}_iX_i\\beta_i+\\beta_i^2+\\lambda |\\beta|\\\\\n",
+    "       L_i&=-\\frac{2}{n}Y^{T}_iX_i\\beta_i+\\beta_i^2+\\lambda |\\beta_i|\\\\\n",
     "       \\text{ $Y^{T}_iX_i >0$ subjects to $\\beta_i \\geq 0$}\\\\\\text{and vice versa $Y^{T}_iX_i \\leq0$ subjects to $\\beta_i \\leq 0$ }\\\\\\\\\n",
     "       \\text{Case 1: $Y^{T}_iX_i >0$ and $\\beta_i \\geq 0$}\\\\\n",
     "      \\frac{dL_i}{d\\beta} &=-\\frac{2}{n}Y^{T}_iX_i+2\\beta_i+\\lambda \\overset{!}{=} 0\\\\\n",