Related papers: Determining the Qibla Direction by Astronomical an…
The Lambert problem is to determine the gravitational orbit between two points that has a specified time of flight, allowing the second point to be a moving target such as a satellite. After a review of gravitational orbits, a solution of…
Methods for measuring an integral of a classical field via local interaction of classical bits or local interaction of qubits passing through the field one at a time are analyzed. A quantum method, which has an exponentially better…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
For quantum systems, we expect to see the classical behaviour at the limit of large quantum numbers. Hence, we apply Bohmian approach for describing the evolution of Earth around the Sun. We obtain possible trajectories of the Earth system…
In this paper, we give a geometric approach to the cubic oscillator with three distinct turning points based on the $\mathcal{D\diagup SG}$\emph{\ correspondence }introduced in \cite{Thabet+al}. The existence of quantization conditions,…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…
Advancement in astronomical observations and technical instrumentation requires coding light propagation at high level of precision; this could open a new detection window of many subtle relativistic effects suffered by light while it is…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational…
Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form.…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed : 1) improvement of observational means (ground-based radio and optical…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
Accurate measurement of relative distance and orientation of two nearby quantum particles is discussed. We are in particular interested in a realistic description requiring as little prior knowledge about the system as possible. Thus,…
Various models of structure formation can account for various aspects of the galaxy formation process on different scales, as well as for various observational features of structures. Thus, the investigation of galaxies orientation…