Free Products of digroups
We construct the free products of arbitrary digroups, and thus we solve an open problem of Zhuchok.
math.GR↗
arXiv subjects
Guangliang Zhang
Publications and source records attributed to Guangliang Zhang.
Gröbner--Shirshov bases for commutative dialgebras
We establish Gröbner--Shirshov bases theory for commutative dialgebras. We show that for any ideal $I$ of $Di[X]$, $I$ has a unique reduced Gröbner--Shirshov basis, where $Di[X]$ is the free commutative dialgebra generated by a set $X$, in particular, $I$ has a finite Gröbner--Shirshov basis if $X$ is finite. As applications, we give normal forms of elements of an arbitrary commutative disemigroup, prove that the word problem for finitely presented commutative dialgebras (disemigroups) is solvable, and show that if $X$ is finite, then the problem whether two ideals of $Di[X]$ are identical is solvable. We construct a Gröbner--Shirshov basis in associative dialgebra $Di\langle X\rangle$ by lifting a Gröbner--Shirshov basis in $Di[X]$.
math.RA↗
A construction of free digroup
We give a construction of a free digroup $F(X)$ on a set $X$ and formulate the halo and the group parts of $F(X)$. We prove that $F(X)$ is isomorphic to $F(Y)$ if and only if $card(X)=card(Y)$.
math.GR↗
A new Composition-Diamond lemma for associative conformal algebras
Let $C(B,N)$ be the free associative conformal algebra generated by a set $B$ with a bounded locality $N$. Let $S$ be a subset of $C(B,N)$. A Composition-Diamond lemma for associative conformal algebras is firstly established by Bokut, Fong, and Ke in 2004 \cite{BFK04} which claims that if (i) $S$ is a Gröbner-Shirshov basis in $C(B,N)$, then (ii) the set of $S$-irreducible words is a linear basis of the quotient conformal algebra $C(B,N|S)$, but not conversely. In this paper, by introducing some new definitions of normal $S$-words, compositions and compositions to be trivial, we give a new Composition-Diamond lemma for associative conformal algebras which makes the conditions (i) and (ii) equivalent. We show that for each ideal $I$ of $C(B,N)$, $I$ has a unique reduced Gröbner-Shirshov basis. As applications, we show that Loop Virasoro Lie conformal algebra and Loop Heisenberg-Virasoro Lie conformal algebra are embeddable into their universal enveloping associative conformal algebras.
math.RA↗
Ground-based verification and data processing of Yutu rover Active Particle-induced X-ray Spectrometer
The Active Particle-induced X-ray Spectrometer (APXS) is one of the payloads on board the Yutu rover of Chang'E-3 mission. In order to assess the instrumental performance of APXS, a ground verification test was done for two unknown samples (basaltic rock, mixed powder sample). In this paper, the details of the experiment configurations and data analysis method are presented. The results show that the elemental abundance of major elements can be well determined by the APXS with relative deviations < 15 wt. % (detection distance = 30 mm, acquisition time = 30 min). The derived detection limit of each major element is inversely proportional to acquisition time and directly proportional to detection distance, suggesting that the appropriate distance should be < 50mm.
astro-ph.IM↗
Composition-Diamond lemma for associative $n$-conformal algebras
In this paper, we study the concept of associative $n$-conformal algebra over a field of characteristic 0 and establish Composition-Diamond lemma for a free associative $n$-conformal algebra. As an application, we construct Gröbner-Shirshov bases for Lie $n$-conformal algebras presented by generators and defining relations.
math.RA↗