add convex-hull-of-stability.typ, skip-connection.typ, sabatier-princ…

…iple.typ, branch-cuts-1.typ, change-of-variables.typ and branch-and-bound.typ converted from their LaTeX sources

assets/branch-and-bound/branch-and-bound.typ

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+#import "@preview/cetz:0.3.1": canvas, draw
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#canvas({
+  import draw: line, content, circle
+
+  let node-sep = 1.5 // Horizontal separation between nodes
+  let level-sep = 1.5 // Vertical separation between levels
+  let node-radius = 0.35
+  let arrow-style = (mark: (end: "stealth", fill: black, scale: 0.2), stroke: black + 1pt)
+
+  // Helper to draw a node with label
+  let draw-node(pos, label, name: none) = {
+    circle(pos, radius: node-radius, name: name)
+    content(pos, $#label$)
+  }
+
+  // Helper to draw edge label
+  let draw-edge-label(from, to, label, left: true) = {
+    let anchor = if left { "east" } else { "west" }
+    content(
+      (rel: (if left { -0.3 } else { 0.3 }, 0), to: from + "-" + to + ".mid"),
+      $#label$,
+      anchor: anchor,
+    )
+  }
+
+  // Draw nodes level by level
+  // Root (level 0)
+  draw-node((0, 0), $P_0$, name: "p0")
+
+  // Level 1
+  draw-node((-node-sep, -level-sep), $P_1$, name: "p1")
+  draw-node((node-sep, -level-sep), $P_2$, name: "p2")
+
+  // Level 2
+  draw-node((0, -2 * level-sep), $P_3$, name: "p3")
+  draw-node((2 * node-sep, -2 * level-sep), $P_4$, name: "p4")
+
+  // Level 3
+  draw-node((-node-sep, -3 * level-sep), $P_5$, name: "p5")
+  draw-node((node-sep, -3 * level-sep), $P_6$, name: "p6")
+
+  // Draw edges
+  line("p0", "p1", ..arrow-style, name: "p0-p1")
+  line("p0", "p2", ..arrow-style, name: "p0-p2")
+  line("p2", "p3", ..arrow-style, name: "p2-p3")
+  line("p2", "p4", ..arrow-style, name: "p2-p4")
+  line("p3", "p5", ..arrow-style, name: "p3-p5")
+  line("p3", "p6", ..arrow-style, name: "p3-p6")
+
+  // Draw edge labels
+  draw-edge-label("p0", "p1", $x_1 <= 0$)
+  draw-edge-label("p0", "p2", $x_1 >= 1$, left: false)
+  draw-edge-label("p2", "p3", $x_2 <= 0$)
+  draw-edge-label("p2", "p4", $x_2 >= 1$, left: false)
+  draw-edge-label("p3", "p5", $x_3 <= 0$)
+  draw-edge-label("p3", "p6", $x_3 >= 1$, left: false)
+})

assets/branch-cuts-1/branch-cuts-1.typ

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+#import "@preview/cetz:0.3.1": canvas, draw, decorations
+
+
+#set page(width: auto, height: auto, margin: 5pt)
+
+#canvas({
+  import draw: line, content, circle
+
+  let xr = 5
+  let yr = 1
+  let arrow-style = (mark: (end: "stealth", fill: black, scale: 0.5))
+
+  // Draw axes
+  line(
+    (0, -yr),
+    (0, yr),
+    ..arrow-style,
+    name: "y-axis",
+  )
+  content(
+    (rel: (-0.7, -0.2), to: "y-axis.end"),
+    $"Im"(p_0)$,
+    name: "y-label",
+  )
+
+  // Draw branch points
+  let left-point = (-xr / 2, 0)
+  let right-point = (xr / 2, 0)
+
+  // Draw branch cut line
+  line(
+    left-point,
+    right-point,
+    name: "x-axis",
+    mark: (start: "circle", end: "circle", fill: blue, scale: 0.5),
+  )
+  // Add branch point labels
+  content(
+    (rel: (0, 0.2), to: "x-axis.start"),
+    $-sqrt(arrow(p)^2)$,
+    name: "left-label",
+  )
+  content(
+    (rel: (0, 0.2), to: "x-axis.end"),
+    $sqrt(arrow(p)^2)$,
+    name: "right-label",
+  )
+
+  // Draw zigzag lines with decorations
+  let zigzag-style = (
+    stroke: blue.darken(20%),
+    amplitude: 0.2,
+    segment-length: 0.3,
+  )
+
+  // Left zigzag
+  decorations.zigzag(
+    line(
+      (-xr - 0.5, 0),
+      "x-axis.3%",
+      ..arrow-style,
+    ),
+    ..zigzag-style,
+    name: "left-zigzag",
+  )
+
+  // Right zigzag
+  decorations.zigzag(
+    line(
+      "x-axis.end",
+      (xr, 0),
+      ..arrow-style,
+    ),
+    ..zigzag-style,
+    name: "right-zigzag",
+  )
+
+  // Add Re axis label
+  content(
+    (rel: (-0.2, 0.3), to: "right-zigzag.end"),
+    $"Re"(p_0)$,
+    name: "x-label",
+  )
+})

assets/change-of-variables/change-of-variables.typ

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+#import "@preview/cetz:0.3.1": canvas, draw
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#canvas({
+  import draw: line, content, rect
+
+  let arrow-style = (mark: (end: "stealth", fill: black, scale: 0.5))
+  let plot-size = 6
+  let plot-sep = 8
+
+  // Helper to draw coordinate axes
+  let draw-axes(origin, label) = {
+    // Draw axes
+    line(
+      (origin.at(0) - plot-size / 2, origin.at(1)),
+      (origin.at(0) + plot-size / 2, origin.at(1)),
+      ..arrow-style,
+      name: label + "-x",
+    )
+    line(
+      (origin.at(0), origin.at(1) - plot-size / 2),
+      (origin.at(0), origin.at(1) + plot-size / 2),
+      ..arrow-style,
+      name: label + "-y",
+    )
+
+    // Add axis labels
+    content((rel: (0, -0.3), to: label + "-x.end"), eval(lower(label) + "_1", mode: "math"), name: label + "-x-label")
+    content((rel: (0.3, 0), to: label + "-y.end"), eval(lower(label) + "_2", mode: "math"), name: label + "-y-label")
+
+    // Add plot label
+    content(
+      (origin.at(0) - plot-size / 2, origin.at(1) + plot-size / 2),
+      text(size: 1.2em)[$#label$],
+      anchor: "south-west",
+      name: label + "-title",
+    )
+  }
+
+  // Draw left plot (Z space)
+  let z-origin = (0, 0)
+  draw-axes(z-origin, "Z")
+
+  // Draw blue square in Z space
+  rect(
+    (z-origin.at(0), z-origin.at(1)),
+    (z-origin.at(0) + 1, z-origin.at(1) + 1),
+    fill: blue.transparentize(60%),
+    name: "z-square",
+  )
+
+  // Draw right plot (X space)
+  let x-origin = (plot-sep, 0)
+  draw-axes(x-origin, "X")
+
+  // Draw transformed squares in X space
+  rect(
+    (x-origin.at(0), x-origin.at(1)),
+    (x-origin.at(0) + 2, x-origin.at(1) + 2),
+    fill: red.transparentize(60%),
+    name: "x-square-1",
+  )
+  rect(
+    (x-origin.at(0), x-origin.at(1)),
+    (x-origin.at(0) + 2, x-origin.at(1) - 2),
+    fill: green.transparentize(60%),
+    name: "x-square-2",
+  )
+
+  // Draw mapping arrows
+  let mid-x = plot-sep / 2
+  line(
+    (mid-x - 0.3, 2.7),
+    (mid-x + 0.3, 2.7),
+    ..arrow-style,
+    name: "f-arrow",
+  )
+  content("f-arrow.mid", $f$, name: "f-label", anchor: "south", padding: (bottom: 4pt))
+  line(
+    (mid-x + 0.3, -2.5),
+    (mid-x - 0.3, -2.5),
+    ..arrow-style,
+    name: "f-inv-arrow",
+  )
+  content("f-inv-arrow.mid", $f^(-1)$, name: "f-inv-label", anchor: "north", padding: (top: 4pt))
+
+  // Draw dotted transformation arrows with determinant labels
+  line(
+    "z-square.north-east",
+    "x-square-1.north-east",
+    ..arrow-style,
+    stroke: (dash: "dotted", paint: red),
+    name: "det-arrow-1",
+  )
+  content(
+    (rel: (0.2, -0.2), to: "det-arrow-1.mid"),
+    [#text(red, $det J_f^(-1) = mat(delim: "|", 2, 0; 0, 2)^(-1) = 1 / 4$)],
+    anchor: "north",
+    angle: 5deg,
+    name: "det-label-1",
+  )
+
+  line(
+    "z-square.north-east",
+    "x-square-2.south-east",
+    ..arrow-style,
+    stroke: (dash: "dotted", paint: green),
+    name: "det-arrow-2",
+  )
+  content(
+    (rel: (0.2, -0.3), to: "det-arrow-2.mid"),
+    [#text(green, $det J_f^(-1) = mat(delim: "|", 2, 0; 0, -2)^(-1) = -1 / 4$)],
+    anchor: "north",
+    angle: -19deg,
+    name: "det-label-2",
+  )
+})