Related papers: Mother Operators and their Descendants
For any Dirac theory of quantum gravity governed by a set of well-defined quantum constraints, we discover a universal formula for the exact form of the evolution Hamiltonian operator in a variable quantum reference frame of our…
The time evolution of a simple model for crossover is discussed. A variant of this model with an improved exploration behavior in phase space is derived as a subset of standard one- and multi-point crossover operations. This model is solved…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
The goal of this paper is to set up a framework designed to take into account the characteristics of sediment particles when transported by water. Our protocol consists in describing the characteristics of sediment particles via an…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
Environmentally-induced superselection or "einselection" has been proposed as an observer-independent mechanism by which apparently classical systems "emerge" from physical interactions between degrees of freedom described completely…
The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
This paper investigates the possibility of approximating multiple mathematical operations in latent space for expression derivation. To this end, we introduce different multi-operational representation paradigms, modelling mathematical…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…