Differential Equation Invariance Axiomatization

Differential Equation Axiomatization: The Impressive Power of Differential Ghosts

We prove the completeness of an axiomatization for differential equation invariants. First, we show that the differential equation axioms in differential dynamic logic are complete for all algebraic invariants. Our proof exploits differential ghosts, which introduce additional variables that can be chosen to evolve freely along new differential equations. Cleverly chosen differential ghosts are...

Strong Addition Invariance and axiomatization of the weighted Shapley value

This paper shows a new axiomatization of the Shapley value by using two axioms. First axiom is Dummy Player Property and second axiom is Strong Addition Invariance. Strong Addition Invariance states that the payoff vector of a game does not change even if we add some specific games to the game. By slightly changing the definition of Strong Addition Invariance, we can also axiomatize the weighte...

Who Cares about Axiomatization? Representation, Invariance, and Formal Ontologies *

Invariance of the Schrödinger Equation

We study a model for quantum gravity on a circle in which the notion of a classical metric tensor is replaced by a quantum metric with an inhomogeneous transformation law under diffeomorphisms. This transformation law corresponds to the co–adjoint action of the Virasoro algebra, and resembles that of the connection in Yang–Mills theory. The transformation property is motivated by the diffeomorp...

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...