The present work shows a coupling of electrical and gravitational fields through Cauchy-Riemann conditions for quaternions present in a previous paper [1]. It is also obtained an extended version of the Laplace-like equations for quaternions, now written in terms of both electric and gravitational fields.
AMS Subject Classification: 30G99, 30E99Key Words: quaternions, Laplace's equations, quate
Initial ProvisionsThroughout this work, are considered quaternionic functions which follow the pattern f i (t, x, y, z), with i = 1, 2, 3, 4, where t is the time and the coordinates x, y and z are considered the spatial coordinates. Thus, the quaternion q is written here as follows;The next section based on a paper by Borges and Machado [2] shows a set
This paper presents an application of Laplace's equation obtained from a quaternionic function that satisfies the Cauchy-Riemann conditions determined earlier by Borges and Machado [1]. Therefore, we show that it is possible to express in a single equation gravity, electric and magnetic potential fields, and this expression can only be provided due to a function that will be called here the coupling function.
ABSTRACT. The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.
The present work has the scope to show the relationship between four three-dimensional waves. This fact will be made in the form of coupling, using for it the Cauchy-Riemann conditions for quaternionic functions [1], through certain Laplace's equation in [2]. The coupling will relate those functions that determine the wave as well as their respective propagation speeds.
Abstract:The technologies are rapidly developing, but some of them present in the computers, as for instance their processing capacity, are reaching their physical limits. It is up to quantum computation offer solutions to these limitations and issues that may arise. In the field of information security, encryption is of paramount importance, being then the development of quantum methods instead of the classics, given the computational power offered by quantum computing. In the quantum world, the physical states are interrelated, thus occurring phenomenon called entanglement. This study presents both a theoretical essay on the merits of quantum mechanics, computing, information, cryptography and quantum entropy, and some simulations, implementing in C language the effects of entropy of entanglement of photons in a data transmission, using Von Neumann entropy and Tsallis entropy.
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