In this paper, the k-trigonometric functions over the Galois Field GF(q) are introduced and their main properties derived. This leads to the definition of the cask(.) function over GF(q), which in turn leads to a finite field Hartley Transform . The main properties of this new discrete transform are presented and areas for possible applications are mentioned.

The propagator is calculated on a noncommutative version of the flat plane and the Lobachevsky plane with and without an extra (euclidean) time parameter. In agreement with the general idea of noncommutative geometry it is found that the limit when the two ‘points’ coincide is finite and diverges only when the geometry becomes commutative. The flat 4-dimensional case is also considered. This is...

Abstract. The target of this paper is to present a new approach to the electromagnetic field based on the systematic use of the global (i.e. integral) quantities. The equations of electomagnetism are obtained in a finite form directly starting from experimental facts without passing throught the differential formulation. This finite formulation is the natural extension of the network theory to ...

Abstract: In this project we will explore the properties of stochastic matrices in both the real and the finite fields. We first explore what properties 2  2 stochastic matrices in the real field have and then exam if they hold in the finite fields. We will prove how, given the conditions of a finite field, properties hold or fail to hold. We will extend our scope to 3  3 stochastic matrices ...

with minimum m such that a(y) =0; 7 is said to belong to a(x). In particular if a(x) =xp" — x, Ore calls 7 a primitive root. It is easy to see that the two varieties of primitive roots are not identical; for example in the GF{21) defind by 04+0+l, 0 is a primitive root in the original sense but not in Ore's sense (since it belongs tox*-\-xi-\-x2-\-x). On the other hand it can be verified that 8...

Dickson bases have recently been introduced in [1] for finite field arithmetic. Such a basis exists for any extension field and under certain conditions it represents a permutation of type II optimal normal bases. In this paper Dickson bases are developed using simpler mathematical terms and their properties are discussed. An algorithm/architecture based on the model presented in [1] is develop...

There are numerous directions from which one can approach the subject of the fast Fourier Transform (FFT). It can be explained via numerous connections to convolution, signal processing, and various other properties and applications of the algorithm. We (along with Geddes/Czapor/Labahn) take a rather simple view from the algebraic manipulation standpoint. As will be apparent shortly, we relate ...

We extend the band theory of linear orbital magnetoelectric coupling to treat crystals under finite electric fields. Previous work established that the orbital magnetoelectric response of a generic insulator at zero field comprises three contributions that were denoted as local circulation, itinerant circulation, and Chern-Simons. We find that the expression for each of them is modified by the ...

We review different aspects of field theory at zero and finite temperature, related to the theory of phase transitions. We discuss different renormalization conditions for the effective potential at zero temperature, emphasizing in particular the MS renormalization scheme. Finite temperature field theory is discussed in the real and imaginary time formalisms, showing their equivalence in simple...

where g is a multiplicative generator of the nonzero elements of F [pfn; i is a fixed integer in the set 0, 1, . . ., c 1; j is a fixed integer in the set 0, 1, .m. ., 1; pf _ 1 = cm; s isin the range 0, 1, . . ., m -1; t is in the range 0, 1, ..., c 1. Let the number of sets of solutions s, t of the above type be (i, j),m. Then (noting relation (2) of the present paper) the maximum value for (...