this article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. it is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

In this paper we introduce the celebrated Kakeya Conjecture in the original real case setting and discuss the proof of its finite field analogue. The story begins in 1917 when, with the hope of figuring out a mathematical formalization of the movement of a samurai during battle, Sochi Kakeya proposed the following problem: What is the least area in the plane required to continuously rotate a ne...

Let X c pn be an irreducible projective variety defined over the finite field F q. We will say that X satisfies the property F F N (k, q) (Finite Field Nullstellensatz of degree k over F q) if every homogeneous polynomial over F q of degree k on pn vanishing on X (F q) vanishes on X, that is, it vanishes at all points of X defined over the algebraic closure of F q . We study when FFN(k,q) holds...

We generalize Joyal’s theory of species to the case of functors from the groupoid of finite sets to the category of varieties over Fq . These have cycle index series defined by counting fixed points of twisted Frobenius maps. We give an application to configuration spaces.

A condensed introduction to the basic concepts of causal perturbation theory is given. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis by avoiding infinities from the outset. It goes back to a seminal work by Henri Epstein and Vladim...

Let X C ]p'N be a projective variety defined over the Galois field GF(q). Denote by X(q) the set of GF(q)-rational points of X. Let k be an integer. We say that the pair (X, X(q)) satisfies the Finite Field Nullstellensatz of order k, (the FFN(k), for short), if every homogeneous form of degree :::; k on r N (J<) vanishing on X (q), vanishes on X (J<). Here, we prove the Finite Field Nullstelle...

In this paper, thermal effects of laser irradiance on biological tissue is investigated using computer simulations. Earlier attempts in this field made use of finite difference and finite element techniques. Here a novel approach is adopted to improve the results. The effect of our implicit approach on the convergence procedure and accuracy of results, with different timing steps, is explor...

For q = 5, this was proved to be true by Betti; for q = 7 the corresponding result was verified by Dickson [l, p. 119]. In this note we show very simply that this result holds for all q. Since the totality of permutation polynomials evidently furnishes a representation of the symmetric group on q letters, it will suffice to show that every transposition (Oa) can be generated by means of the spe...