For the statistical stochastic models with hierarchical structure such as Deep networks, Gaussian mixture models and hidden Markov models, algebraic geometry have contributed to the performance ...

The field of algebraic geometry investigates the profound interplay between polynomial equations and geometric structures, providing a rich framework that unites abstract theory with practical ...

Considering soft computing, the Weierstrass data (ζ−1/2, ζ1/2) gives two different minimal surface equations and figures. By using hard computing, we give the family of minimal and spacelike maximal ...

Characteristic classes encapsulate intrinsic geometric information about vector bundles and, more broadly, coherent sheaves over algebraic varieties. Their formulation in algebraic geometry has ...

Journal of Commutative Algebra, Vol. 1, No. 3 (FALL 2009), pp. 361-380 (20 pages) ABSTRACT. We study Hilbert functions of quotients of the truncated polynomial ring k[ x 1 ,..., x n ]/( x 1 e 1 +1 , x ...