Related papers: A smooth introduction to the wavefront set
This chapter contains a short discussion of some fundamental plasma phenomena. In section 2 we introduce key plasma properties like quasi-neutrality, shielding, particle transport processes and sheath formation. In section 3 we describe the…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
In this work we consider the Conical Radon Transform, which integrates a function on $\R^n$ over families of circular cones. Transforms of this type are known to arise naturally as models of Compton camera imaging and single-scattering…
In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential…
We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with repsect to a…
Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the…
We investigate wavefront solutions in a nonlinear system of two coupled reaction-diffusion equations with degenerate diffusivity: \[n_t = n_{xx} - nb, \quad b_t = [D nbb_x]_x + nb,\] where $t\geq0,$ $x\in\mathbb{R}$, and $D$ is a positive…
The term wavefront sensor refers to the entire class of devices capable of measuring the optical wavefront of the incoming beam. Although numerous solutions have been proposed so far, recent advances in structured light have opened new…
Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are…
The global approach to control systems which we have been pursuing in other work favours the study of dynamics achievable through control. It employs certain globally defined geometric objects and attempts to describe them in the general…
In a recent paper a mathematical model for quantum measurement was presented. The phenomenon of wave particle duality, which is introduced in every beginning course of quantum theory, can be explained using this model. Although it is a…
The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The…
We clarify the meaning of spatial densities of hadrons. A physical density is given by the expectation value of a local operator for a physical state, and depends on both internal structure and the hadron's wave packet. In some particular…
Using the vehicle of resolving an apparent paradox, a discussion of quantum interference is presented. The understanding of a number of different physical phenomena can be unified, in this context. These range from the neutral kaon system…
The aim of this review is twofold. First, a general approach is presented allowing for a unified description of dynamics in radiating systems of different nature. Both atomic systems as well as spin assemblies can be treated in the frame of…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…