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• Metric tensor
  ...ample, here we have deformed the $x$-axis and changed the concavity of the graph at $x=1$: Concavity is an important concept that captures the shape of the graph of a function in calculus as well as the acceleration in physics. The upwar
  42 KB (7,131 words) - 17:31, 30 November 2015
• Geometry
  ...ample, here we have deformed the $x$-axis and changed the concavity of the graph at $x=1$: Concavity is an important concept that captures the shape of the graph of a function in calculus as well as the acceleration in physics. The upwar
  41 KB (6,928 words) - 17:31, 26 October 2015
• Linear operators: part 4
  '''Example:''' Suppose $G$ is a directed graph. *$\ker D = $ all cycles of the graph.
  13 KB (2,067 words) - 01:11, 12 September 2011
• Applications of ODEs
  *3. directed along the segment between them. ...an just the gravity. The gravity is a ''central force'', i.e., one that is directed along the line between the location and the origin. Then the recursive form
  50 KB (8,692 words) - 14:29, 24 November 2018
• PageRank as a solution of a matrix equation
  Suppose $p_1,...,p_N$ are the $N$ pages/nodes in the graph (of the World Wide Web). Suppose also that $R(p_i)$ is the PageRank of node where $A$ is the [[adjacency matrix]] of the graph and $K$ is the diagonal matrix with the [[outdegree]]s $L(p_j)$ in the diag
  5 KB (811 words) - 18:36, 28 November 2012
• Social choice
  The simple formula fails when there are loops in the graph of links: '''Example.''' Consider the propagation of PageRank through this simple graph:
  47 KB (8,030 words) - 18:48, 30 November 2015
• ODEs
  ...''' Provide an analog of this iterative procedure for an IVP with domain a graph $K$ and find out under what circumstances this procedure works or fails. '''Exercise.''' (a) Explain how an arbitrary directed graph gives rise to advection and find its ODE. (b) What if, in addition to carry
  47 KB (8,415 words) - 15:46, 1 December 2015
• Metric complexes
  Suppose $K$ is a graph and its vertex $A$ has three adjacent edges $AB,AC,AD$. Then, in the dual c '''Proposition.''' If the complex $K$ is a directed graph with unit edges, the matrix $D$ of the second derivative is given by its el
  35 KB (5,871 words) - 22:43, 7 April 2016
• Calculus Illustrated -- preface
  ...s, etc.). However, a large proportion of time and effort can and should be directed elsewhere: ...shortest step from pen and paper: one cell - one number - one point on the graph. For more advanced tasks such as modelling, spreadsheets were chosen over o
  17 KB (1,758 words) - 13:57, 25 August 2019
• Conferences and workshops
  ..., geographical information systems, protein folding, statistical analysis, graph drawing, visualization, circuit design, etc. ...has published over 30 articles on knot theory and related subjects. He has directed over 40 undergraduate students on research in knot theory and co-authored p
  8 KB (1,122 words) - 02:52, 24 October 2011
• Second derivative and the Laplacian
  ...ntial forms]] of order $0$ and $1$. So the formula applies to a directed [[graph]]. In that case, the matrix $L$ of $\Delta$ can be computed directly: for e
  4 KB (608 words) - 13:13, 28 August 2015
• Web search
  That's why the web can be treated as [[directed graph]]s. So web search can be analyzed [[mathematics|mathematically]]. For how n
  469 bytes (65 words) - 14:50, 24 August 2011
• More ODEs
  '''Exercise.''' (a) Explain how an arbitrary directed graph gives rise to advection and present its ODE. (b) What if, in addition to ca
  26 KB (4,649 words) - 12:43, 7 April 2016

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