Related papers: A proposal to characterize and quantify superoscil…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…
The work reported here originates in the discovery, four decades ago, of a previously unknown type of self-organizing interaction among oscillating systems -- so-called argumental interactions -- and of "quantized" modes of behavior in…
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…
We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…
We introduce an extension of hamiltonian dynamics, defined on hyperkahler manifolds, which we call ``hyperhamiltonian dynamics''. We show that this has many of the attractive features of standard hamiltonian dynamics. We also discuss the…
In this paper, we explore the concept of $\sigma$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
In this paper we review different expansions for neutrino oscillation probabilities in matter in the context of long-baseline neutrino experiments. We examine the accuracy and computational efficiency of different exact and approximate…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…
In this note, we present a novel measure of similarity between two functions. It quantifies how the sub-optimality gaps of two functions convert to each other, and unifies several existing notions of functional similarity. We show that it…
We derive the explicit expressions of the canonical and helicity wave functions for massive particles with arbitrary spins. Properties of these wave functions are discussed.
A definition of quantum mechanical work is introduced in this dissertation, preserving the mathematical structure of the Classical Mechanics concept of work without, however, in any way invoking the notion of trajectory. By use of Gaussian…
In this paper, we define a new type multivariable hypergeometric function. Then, we obtain some generating functions for these functions. Furthermore, we derive various families of multilinear and multilateral generating functions for these…
A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…
This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over…
I address the question whether the wave function in quantum theory exists as a real (ontic) quantity or not. For this purpose, I discuss the essentials of the quantum formalism and emphasize the central role of the superposition principle.…