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Simplicial Continuation, or Piecewise Linear Continuation (Allgower and Georg) is based on three basic results. The first is If F(x) maps IR^n into IR^(n-1), there is a unique linear interpolant on an (n-1)-dimensional simplex which agrees with the function values at the vertices of the simplex.
The primary computational method used in numerical algebraic geometry is homotopy continuation, in which a homotopy is formed between two polynomial systems, and the isolated solutions (points) of one are continued to the other. This is a specialization of the more general method of numerical continuation.
The real part of every nontrivial zero of the Riemann zeta function is 1/2. The Riemann hypothesis is that all nontrivial zeros of the analytical continuation of the Riemann zeta function have a real part of 1 / 2 . A proof or disproof of this would have far-reaching implications in number theory, especially for the distribution of prime ...
A potential problem of this analytic continuation along a curve strategy is there are usually many curves which end up at the same point in the larger set. The monodromy theorem gives sufficient conditions for analytic continuation to give the same value at a given point regardless of the curve used to get there, so that the resulting extended ...
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The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
For every 3 non-theme words you find, you earn a hint. Hints show the letters of a theme word. If there is already an active hint on the board, a hint will show that word’s letter order ...
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