Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function...
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies.
This includes, among other lines of work, the construction of homotopical and higher-categorical models for such type theories; the use of type theory as a logic (or internal language) for abstract homotopy theory and higher category theory; the development of mathematics within a type-theoretic foundation (including both previously existing mathematics...
The Fradkin tensor, or Jauch-Hill-Fradkin tensor, named after Josef-Maria Jauch and Edward Lee Hill and David M. Fradkin, is a conservation law used in the treatment of the isotropic multidimensional harmonic oscillator in classical mechanics. For the treatment of the quantum harmonic oscillator in quantum mechanics, it is replaced by the tensor-valued Fradkin operator.
The Fradkin tensor provides enough conserved quantities to make the oscillator's equations of motion maximally superintegrable. This implies that to determine the trajectory of the system, no differential equations need to be solved...
In mathematics, a superintegrable Hamiltonian system is a Hamiltonian system on a
2
n
{\displaystyle 2n}
-dimensional symplectic manifold for which the following conditions hold:
(i) There exist
k
>
n
{\displaystyle k>n}
independent integrals
F
i
{\displaystyle F_{i}}
of motion. Their level surfaces (invariant submanifolds) form a fibered manifold
F
:...
