Related papers: Local Solutions for Generic Multidimensional Reson…
In the FIRST PART we present simple introductions to gaussian and Bessel waves, and to the Localized Waves (LW), pulses or beams, showing the important properties of the latter, and their applications whenever a role is played by a…
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations…
This letter describes a scalar curvature invariant for general relativity with a certain, distinctive feature. While many such invariants exist, this one vanishes in regions of space-time which can be said unambiguously to contain no…
We derive a canonical form for smooth vector fields on $\Re^{n+1}$. We use this to demonstrate the local multi-Hamiltonian nature of the corresponding flows. Associated with the canonical form is an inhomogenious linear PDE whose solutions…
Generalized continuum models for describing one-dimensional shear deformations of a Cosserat lattice are considered and their application to describing of structural effects essential for interfaces are discussed. The two-field…
By a generalized bidirectional decomposition method, we obtain many new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; various of them…
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an…
With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…
Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83},…
To clarify certain nonlinear properties of strong gravitational field, we investigate cylindrically symmetric gravitational waves that are localized as regular wave packets in the space of radial and time coordinates. The waves are…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail,…
A 2-dimensional framework is a straight line realisation of a graph in the Euclidean plane. It is radically solvable if the set of vertex coordinates is contained in a radical extension of the field of rationals extended by the squared edge…
The use of relativistic quark models with simple parametric wave functions for the understanding of the electromagnetic structure of nucleons together with their electromagnetic transition to resonances is discussed. The implications of…
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…
For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer…
A special conformal transformation which carries a vacuum gravitational wave into another vacuum one is built by using M\"obius-redefined time. It can either transform a globally defined vacuum wave into a vacuum sandwich wave, or carry the…
We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In…