相关论文: Polar coordinates, special relativity and CAS

Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…

A challenging problem related to the design of polar codes is "robustness against channel parameter variations" as stated in Ar{\i}kan's original work. In this paper, we describe how the problem of robust polar code design can be viewed as…

The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…

This paper proposes an approach for the adaptation of spatial or temporal cases in a case-based reasoning system. Qualitative algebras are used as spatial and temporal knowledge representation languages. The intuition behind this adaptation…

We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…

Starting from the description of space-time as a curved four-dimensional manifold, null Gaussian coordinates systems as appropriate for relativistic positioning will be discussed. Different approaches and strategies will be reviewed,…

We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.

Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…

The two-dimensional (2D) offset linear canonical transform (OLCT) in polar coordinates plays an important role in many fields of optics and signal processing. This paper studies the 2D OLCT in polar coordinates. Firstly, we extend the 2D…

Observations of the apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change…

Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of…

It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The…

Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…

Computer codes are widely used to describe physical processes in lieu of physical observations. In some cases, more than one computer simulator, each with different degrees of fidelity, can be used to explore the physical system. In this…

Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…

A coordinate system is proposed that replaces the usual three-dimensional Cartesian x,y,z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and,…

Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…

We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…

Computer simulations that demonstrate the valueof novel approaches are crucial to developing more flexibleand robust power systems operations with high penetrations ofrenewable energy at multiple geographic and temporal scales.However,…

A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving…