Finite nets of dimension three. I

Vapnik-Chervonenkis Dimension of Neural Nets

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Finite-State Dimension

VC Dimension, ε-nets and ε-approximation

“I’ve never touched the hard stuff, only smoked grass a few times with the boys to be polite, and that’s all, though ten is the age when the big guys come around teaching you all sorts to things. But happiness doesn’t mean much to me, I still think life is better. Happiness is a mean son of a bitch and needs to be put in his place. Him and me aren’t on the same team, and I’m cutting him dead. I...

Three-periodic nets and tilings: minimal nets.

The 15 3-periodic minimal nets of Beukemann & Klee [Z. Kristallogr. (1992), 201, 37-51] have been examined. Seven have collisions in barycentric coordinates and are self-entangled. The other eight have natural tilings. Five of these tilings are self-dual and the nets are the labyrinth nets of the P, G, D, H and CLP minimal surfaces of genus 3. Twelve ways have been found for subdividing a cube ...