Related papers: Questioni di Ottica Geometrica
This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results…
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of…
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus…
We give a new perspective on the Lorentzian OPE inversion formula of arXiv:1703.00278, building on arXiv:2302.06469. We introduce an ``auxiliary'' fourpoint function that can be related to the traditionally defined ones via a Radon…
Inspired by a didactic experience in an academic environment, and following the idea given by M. Villa in \cite{Villa}, we illustrate two different proofs of an important result in Euclidean geometry studied in the first two years of…
Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…
Many practical applications require the analysis of electromagnetic scattering properties of local structures using different sources of illumination. The Optical Theorem (OT) is a useful result in scattering theory, relating the extinction…
This thesis is divided into three parts. The first part deals with cylindric plane partitions. The second with lambda-determinants and the third with commutators in semi-circular systems. For more detailed abstract please see inside.…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so called gravitational optics. Besides Schr\"odinger Newton…
This thesis covers different aspects of the p-Laplace operators on Riemannian manifolds. Chapter 2. Potential theoretic aspects: the Khasmkinskii condition. Chapter 3: sharp eigenvalue estimates with Ricci curvature lower bounds. Chapter 4:…
We study the second order invariants of a Lorentzian surface in $\mathbb{R}^{2,2},$ and the curvature hyperbolas associated to its second fundamental form. Besides the four natural invariants, new invariants appear in some degenerate…
The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a…
We propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the ray's 2x2 matrix operators should be right-acting, so that the matrix product succession would…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which…
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential…