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Sets the initial point in the line to (x, y), leaving the end point unchanged.
In all tests we take μ = 0.5, C = rand ( n ) and ( X 0, Y 0, Z 0 ) = ( I n × n, I n × n, 0 n × n ) as the initial point in the test.
Where τ i are the PL decay lifetimes and α i are the corresponding pre-exponential factors, taking into account the normalization of the initial point in the decay to unity.
Hence, the truncation of the infinite precision solution can be set as a good initial point and we are required to search the neighborhood of the initial point in the integer space.
Our result shows that the unique solution exists in a product set and can be approximated by making an iterative sequence for any initial point in the product set.
The existence of a unique closed finite limiting sequence on any sequence of iterations from any initial point in the union of the subsets is proven if X is a uniformly convex Banach space and all the subsets of X are nonempty, convex and closed.
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We then generate at least 20 samples, each taken from the end of a single Markov chain initialized from different random initial points in the state space.
Uniform design method is used to choose the initial points in the feasible region.
Algorithm 1 converges to a Nash equilibrium of with sufficient small δ b and δ s for any initial points in the mixed strategies except the initial points in the pure strategies.
With this convention, the initial points in the arc ℒ are parameterized as γ ( s ) for s ∈ [ π, 2 π ] (s is the angle) with γ = P −, γ ( 2 π ) = P + and γ ( 3 π / 2 ) = R.
However, it is conjectured that the set of initial points in the state space exhibiting this behavior is a set of measure zero, meaning, in this context, that although there are an infinite number of points exhibiting this behavior, this set represents zero percent of the number of points composing the attractor.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com