Although some work has been done on the metamathematics of Metamath, there has not been a clear definition of a model for a Meta-math formal system. We define the collection of models of an arbitrary Metamath formal system, both for tree-based and string-based representations. This definition is demonstrated with examples for propositional calculus, ZFC set… (More)
We present the formalization of Dirichlet's theorem on the infinitude of primes in arithmetic progressions, and Selberg's elementary proof of the prime number theorem, which asserts that the number π(x) of primes less than x is asymptotic to x/ log x, within the proof system Metamath.
microemulsion modifies the pharmacokinetic profile and cardiotoxicity of doxorubicin. The antiproliferative effect of indomethacin-loaded lipid-core nanocapsules in glioma cells is mediated by cell cycle regulation, differentiation, and the inhibition of survival pathways. Investigation of the structural organization of cationic nanoemulsion/antisense… (More)
Unlike some other formal systems, the proof system Meta-math has no built-in concept of " decimal number " in the sense that arbitrary digit strings are not recognized by the system without prior definition. We present a system of theorems and definitions and an algorithm to apply these as basic operations to perform arithmetic calculations with a number of… (More)
Surgical procedures for double-bundle reconstruction of anterior cruciate ligament, which currently use semitendinous and gracilis tendon grafts, have been described in the last decade. Most of the techniques utilize twice the hardware used in single-bundle reconstructions. We report an original anterior cruciate ligament double-bundle reconstruction… (More)
In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period N , all non-degenerate and at least one of them is hyperbolic. Moreover, the invariant curves of two hyperbolic points are transversal. We explore these properties to give some dynamical consequences specially about… (More)