Narrow Results

In the paper, we give a new non-parameter filled function method for finding global minimizer of global optimization programming problems, the filled function consists of a inverse cosine function and a logarithm function, and without parameter. Its theoretical residences are proved. A new filled function algorithm is given based on the proposed new parameterless filled function, The results of numerical with ten experiments verify the efficient and reliability for the algorithm.

We introduce and discuss the recent Agrawal–Kayal–Saxena deterministic algorithm solving primality in polynomial time.

Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a finite field ${𝔽}_{q^n}$ considered as a linear space over a subfield ${𝔽}_q$. We apply this to the recently introduced algorithmic problem of identity testing of “hidden” polynomials $f$ and $g$ over a high degree extension of a finite field, given oracle access to $f{(x)}^e$ and $g{(x)}^e$.