embedding dimension造句

• There is no known general formula to compute the Frobenius number of numerical semigroups having embedding dimension three or more.
• Interestingly, it is known that every positive integer is the Frobenius number of some numerical semigroup with embedding dimension three.
• The zeroth deviation ? 0 is the embedding dimension of " R " ( the dimension of its tangent space ).
• By looking at a local model it is easy to see that the dimension is always less than or equal to the embedding dimension.
• It is also known that no polynomial formula can be found to compute the Frobenius number or genus of a numerical semigroup with embedding dimension three.
• The eigenfunctions of the Laplace Beltrami operator on the manifold serve as the embedding dimensions, since under mild conditions this operator has a countable spectrum that is a basis for square integrable functions on the manifold ( compare to Fourier series on the unit circle manifold ).
• Simulations can be done on a lattice of any desired geometry of embedding dimension, in fact this has been done in up to 8 dimensions, or the simulation can be done more along the lines of a standard molecular dynamics simulation where a particle is allowed to freely random walk until it gets within a certain critical range at which time it is pulled onto the cluster.