Related papers: Determination and Reduction of Large Diffeomorphis…
The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
We propose an integral transform, called metamorphism, which allow us to reduce the order of a differential equation. For example, the second order Helmholtz equation is transformed into a first order equation, which can be solved by the…
In this short note we perform canonical analysis of the theory invariant under restricted diffeomorphism so that the action contains kinetic term for determinant of metric. We find corresponding Hamiltonian and determine structure of…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…
We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal…
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of…
This paper presents invariants under gamma correction and similarity transformations. The invariants are local features based on differentials which are implemented using derivatives of the Gaussian. The use of the proposed invariant…
A new analysis of the gauge invariances and their unity with diffeomorphism invariances in second order metric gravity is presented which strictly follows Dirac's constrained Hamiltonian approach.
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
In this paper, we construct infinitely many bi-invariant metrics on the Hamiltonian diffeomorphism group and study their basic properties and corresponding generalizations of the Hofer inequality and Sikorav one.
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction…
In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of…
A new analytical formulation is prescribed to solve the Helmholtz equation in 2D with arbitrary boundary. A suitable diffeomorphism is used to annul the asymmetries in the boundary by mapping it into an equivalent circle. This results in a…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials…