Related papers: Linear Orbit Parameters for the Exact Equations of…
We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta…
This lecture gives an overview of the impacts on linear machine optics of machine imperfections due to incorrect field settings and misalignments. The effects of imperfections in dipole, quadrupole, and sextupole magnets are presented,…
In this paper we study those bent functions which are linear on elements of spreads, their connections with ovals and line ovals, and we give descriptions of their dual bent functions. In particular, we give a geometric characterization of…
In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…
Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
The main object of this paper is to present a new generalized beta function which defined by three parametres Mittag-Leffler function. We also introduce new generalizations of hypergeometric and confluent hypergeometric functions with the…
Special functions are often defined as a Fourier or Laplace transform of a positive measure, and the positivity of the measure manifests as positive definiteness of certain matrices. The purpose of this expository note is to give a sample…
We demonstrate that it is possible to determine the coefficients of an all-order beta function linear in the anomalous dimensions using as data the two-loop coefficients together with the first one of the anomalous dimensions which are…
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
Orbital parameters of planets are fitted directly to an appropriate set of observations. It is shown how to use the rigorous Deming method combined with a numerical integration of gravitation equations. In all, 65 parameters of the nine…
The manner in which probability amplitudes of paths sum up to form wave functions of orbital angular momentum eigenstates is described. Using a generalization of stationary-phase analysis, distributions are derived that provide a measure of…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…
The logarithmic convexity of restrictions of the Beta functions to rays parallel to the main diagonal and the functional equation \[ \phi\left( x+1\right) =\frac{x\left( x+k\right) }{\left( 2x+k+1\right) \left( 2x+k\right) }\phi\left(…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Many advanced techniques have been developed, tested and implemented in the last decades in almost all circular accelerators across the world to measure the linear optics. However, the greater availability and accuracy of beam diagnostics…
This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic…
Limits from neutron beta decay on parameters describing physics beyond the Standard Model are presented. New Physics is described by the most general Lorentz invariant effective Hamiltonian involving vector, scalar and tensor operators and…
Measurements and analysis of orbit response matrix have been providing for decades a formidable tool in the detection of linear lattice imperfections and their correction. Basically all storage-ring-based synchrotron light sources across…
Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one…