Related papers: The Search for the Primitive
In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain…
A survey paper on some recent results on additive problems with prime powers.
We address a primary question of computational as well as biological research on evolution: How can an exploration strategy adapt in such a way as to exploit the information gained about the problem at hand? We first introduce an integrated…
The demands for accurate and representative generative AI systems means there is an increased demand on participatory evaluation structures. While these participatory structures are paramount to to ensure non-dominant values, knowledge and…
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.
We give an impression of the type of results that have been obtained with numerical lattice simulations of field theory in the early universe.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
Primitive prime divisors play an important role in group theory and number theory. We study a certain number theoretic quantity, called $\Phi^*_n(q)$, which is closely related to the cyclotomic polynomial $\Phi_n(x)$ and to primitive prime…
We generalize Jacobson's notion of primitive ring to the setting of quantales. We show that every primitive ring gives rise to a primitive quantale of ideals. We then prove a density theorem for strongly primitive quantales. Furthermore, we…
In this paper the discussion of the effect of trigonometric series on the theory of integration is continued from an earlier paper by Gluchoff, Trigonometric series and theories of integration, Math.Mag., 67 (1994), 3--20.
This article provides a reminder of some properties of primitive words and the morphisms that preserve them. Their proofs, which I have more or less revised, are included. This makes the article almost self-contained. I also contribute by…
In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…
This is a quick survey of theoretical and experimental efforts to understand and identify the Odderon.
In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an…
We introduce a novel framework for studying small-scale primordial perturbations and their cosmological implications. The framework uses a deep reinforcement learning to generate scalar power spectrum profiles that are consistent with…
The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.
This study is motivated by two different, yet, connected, motivations. The first one follows the observation that the classical definition of derivatives involves prospective (or forward) difference quotients, not known whenever the time is…