1 citations · 2 across the 5 of their papers we have counts for
6 papers
Formalizing Elements of Probabilistic Mechanics
Farida Kachapova, Ilias Kachapov
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the pa…
Formalizing groups in type theory
Farida Kachapova
In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory w…
Formalizing relations in type theory
Farida Kachapova
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking…
Alternative proof of existence of Gibbs measure at high temperature
Farida Kachapova, Ilias Kachapov
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a f…
Comparison of constructive multi-typed theory with subsystems of second order arithmetic
Farida Kachapova
This paper describes an axiomatic theory BT for constructive mathematics. BT has a predicative comprehension axiom for a countable number of set types and usual combinatorial opera…
Application of semi-invariants to proof of the central limit theorem on a lattice
Farida Kachapova, Ilias Kachapov
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied a…