Related papers: Differential and integral invariants under Mobius …
Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this…
We develop the method of regularized moving frames of Fels and Olver to obtain explicit general formulas for the basis invariants that generate all the joint differential invariants, under gauge transformations, for the operators…
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
We show that Maxwell's electrodynamics in vacuum is invariant under active transformations of the metric. These metrics are related by disformal mappings induced by derivatives of the gauge vector $A_{\mu}$ such that the gauge symmetry is…
A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and…
A fundamental theorem of Liouville asserts that positive entire harmonic functions in Euclidean spaces must be constant. A remarkable Liouville-type theorem of Caffarelli-Gidas-Spruck states that positive entire solutions of $-\Delta u=u^{…
The main aim of this paper is to investigate the nature of invariancy of rectifying curve under conformal transformation and obtain a sufficient condition for which such a curve remains conformally invariant. It is shown that the normal…
Within the Hamiltonian formulation of diffeomorphism invariant theories we address the problem of how to determine and how to reduce diffeomorphisms outside the identity component.
We compute the Hilbert polynomial and the Poincare function counting the number of fixed jet-order differential invariants of conformal metric structures modulo local diffeomorphisms, and we describe the field of rational differential…
We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background $\mathcal{Q}$-curvature charge and an exponential…
This paper presents an invariant under scaling and linear brightness change. The invariant is based on differentials and therefore is a local feature. Rotationally invariant 2-d differential Gaussian operators up to third order are proposed…
Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to…
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
Producing spatial transformations that are diffeomorphic is a key goal in deformable image registration. As a diffeomorphic transformation should have positive Jacobian determinant |J| everywhere, the number of voxels with |J|<0 has been…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
A 'Liouville structure' is a structure isomorphic to a cotangent vector fibration. A Liouville structure is an essential ingredient of every variational formulation of a physical theory. For reasons of interpretation the Liouville structure…
In this article we discuss a weaker version of Liouville's theorem on the integrability of Hamiltonian systems. We show that in the case of Tonelli Hamiltonians the involution hypothesis on the integrals of motion can be completely dropped…
Construction and classification of 2D superintegrable systems (i.e. systems admitting, in addition to two global integrals of motion guaranteeing the Liouville integrability, the third global and independent one) defined on 2D spaces of…
The Moyal momentum algebra is, once again, used to discuss some important aspects of NC integrable models and 2d conformal field theories. Among the results presented, we setup algebraic structures and makes useful convention notations…