Related papers: n-trivial extensions and multi Hasse-Schmidt deriv…

This paper presents a $q$-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type $A$ of infinite degree. Namely this…

Recent results have generalized Gowers' Theorem (to Lupini's Theorem) and the Furstenberg-Katznelson theorem, both infinite dimensional Ramsey Theorems. The framework of arXiv:1611.06600 provides a machine which accepts (almost…

We provide upper bounds on the density of a symmetric generalized arithmetic progression lacking nonzero elements of the form h(n) for natural numbers n, or h(p) with p prime, for appropriate polynomials h with integer coefficients. The…

We prove that any multi-variate Hasse-Schmidt derivation can be decomposed in terms of substitution maps and uni-variate Hasse-Schmidt derivations. As a consequence we prove that the bracket of two $m$-integrable derivations is also…

The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which are Nielsen transformations augmented by arbitrary…

The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel…

Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussian. The possibility for R to be B{\'e}zout is also studied,…

In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…

We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.

We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a…

We compare Fornasiero and Terzo's framework of generic derivations on algebraically bounded structures with Le\'on S\'anchez and Tressl's differentially large fields. We show in the case of a single derivation that genericity and…

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…

The method of double extension, introduced by A.~Medina and Ph.~Revoy, is a procedure which decomposes a Lie algebra with an invariant symmetric form into elementary pieces. Such decompositions were developed for other algebras, for…

We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…

We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always…

In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…

In this paper, we show that for a Koszul $n$-homogeneous algebra $\Lambda$, the quadratic dual of certain twisted trivial extension is the $(n+1)$-preprojective algebra of its quadratic dual, that is, $ (\Delta_{\nu}\Lambda)^{!,op}…

In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be decomposed into the sum of a derivation and a center valued map. We extend some known results on the…

We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…

Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…