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Yanjun Liu

Publications and source records attributed to Yanjun Liu.

31 records · Page 2Linked to original sources
arXiv2022

Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects

Groups with various types of operators, in particular the recently introduced Rota-Baxter groups, have generated renowned interest with close connections to numerical integrals, Yang-Baxter equation, integrable systems and post-Hopf algebras. This paper gives the general notion of operated groups and provides explicit constructions of free operated groups, free differential groups and free Rota-Baxter groups.

math.GR↗
arXiv2022

Strong Neel ordering and luminescence correlation in a two-dimensional antiferromagnet

Magneto-optical effect has been widely used in light modulation, optical sensing and information storage. Recently discovered two-dimensional (2D) van der Waals layered magnets are considered as promising platforms for investigating novel magneto-optical phenomena and devices, due to the long-range magnetic ordering down to atomically-thin thickness, rich species and tunable properties. However, majority 2D antiferromagnets suffer from low luminescence efficiency which hinders their magneto-optical investigations and applications. Here, we uncover strong light-magnetic ordering interactions in 2D antiferromagnetic MnPS3 utilizing a newly-emerged near-infrared photoluminescence (PL) mode far below its intrinsic bandgap. This ingap PL mode shows strong correlation with the Neel ordering and persists down to monolayer thickness. Combining the DFT, STEM and XPS, we illustrate the origin of the PL mode and its correlation with Neel ordering, which can be attributed to the oxygen ion-mediated states. Moreover, the PL strength can be further tuned and enhanced using ultraviolet-ozone treatment. Our studies offer an effective approach to investigate light-magnetic ordering interactions in 2D antiferromagnetic semiconductors.

physics.optics↗
arXiv2022

Fringe visibility and correlation in Mach-Zehnder interferometer with an asymmetric beam splitter

We study the wave-particle duality in a general Mach-Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory. The correlations(including the classical correlation and the quantum correlation) between the particle and the which-path detector are derived when they are in pure state or mixed state at the output of Mach-Zehnder interferometer. It is found that the fringe visibility and the correlations are effected by the asymmetric beam splitter and the input state of the particle. The complementary relations between the fringe visibility and the correlations are also presented.

quant-ph↗
arXiv2020

Distributed Formation Control of Multi-Robot Systems: A Fixed-Time Behavioral Approach

This paper investigates a distributed formation control problem for networked robots, with the global objective of achieving predefined time-varying formations in an environment with obstacles. A novel fixed-time behavioral approach is proposed to tackle the problem, where a global formation task is divided into two local prioritized subtasks, and each of them leads to a desired velocity that can achieve the individual task in a fixed time. Then, two desired velocities are combined via the framework of the null-space-based behavioral projection, leading to a desired merged velocity that guarantees the fixed-time convergence of task errors. Finally, the effectiveness of the proposed control method is demonstrated by simulation results.

math.OC↗
arXiv2020

An improved Trudinger-Moser inequality involving N-Finsler-Laplacian and L^p norm

Suppose $F: \mathbb{R}^{N} \rightarrow [0, +\infty)$ be a convex function of class $C^{2}(\mathbb{R}^{N} \backslash \{0\})$ which is even and positively homogeneous of degree 1. We denote $γ_1=\inf\limits_{u\in W^{1, N}_{0}(Ω)\backslash \{0\}}\frac{\int_ΩF^{N}(\nabla u)dx}{\| u\|_p^N},$ and define the norm $\|u\|_{N,F,γ, p}=\bigg(\int_ΩF^{N}(\nabla u)dx-γ\| u\|_p^N\bigg)^{\frac{1}{N}}.$ Let $Ω\subset \mathbb{R}^{N}(N\geq 2)$ be a smooth bounded domain. Then for $p> 1$ and $0\leq γ<γ_1$, we have $$ \sup_{u\in W^{1, N}_{0}(Ω), \|u\|_{N,F,γ, p}\leq 1}\int_Ωe^{λ|u|^{\frac{N}{N-1}}}dx<+\infty, $$ where $0<λ\leq λ_{N}=N^{\frac{N}{N-1}} κ_{N}^{\frac{1}{N-1}}$ and $κ_{N}$ is the volume of a unit Wulff ball. Moreover, by using blow-up analysis and capacity technique, we prove that the supremum can be attained for any $0 \leqγ<γ_1$.

math.AP↗
arXiv2020

Concentration-compactness principle of singular Trudinger-Moser inequality involving $N$-Finsler-Laplacian operator

In this paper, suppose $F: \mathbb{R}^{N} \rightarrow [0, +\infty)$ be a convex function of class $C^{2}(\mathbb{R}^{N} \backslash \{0\})$ which is even and positively homogeneous of degree 1. We establish the Lions type concentration-compactness principle of singular Trudinger-Moser Inequalities involving $N$-Finsler--Laplacian operator. Let $Ω\subset \mathbb{R}^{N}(N\geq 2)$ be a smooth bounded domain. $\{u_n\}\subset W_0^{1, N}(Ω)$ be a sequence such that anisotropic Dirichlet norm$\int_ΩF^N (\nabla u_n)dx=1$, $u_n \rightharpoonup u \not \equiv 0$ weakly in $W_0^{1, N}(Ω)$. Then for any $0 < p < p_N(u):=(1-\int_ΩF^N (\nabla u)dx)^{-\frac{1}{N-1}},$ we have $$ \int_Ω\frac{e^{λ_{N}(1-\fracβ{N})p |u_n|^{\frac{N}{N-1}}}}{F^{o}(x)^β}dx<+\infty, $$ where $0\leqβ<N$, $λ_{N}=N^{\frac{N}{N-1}} κ_{N}^{\frac{1}{N-1}}$ and $κ_{N}$ is the volume of a unit Wulff ball. This conclusion fails if $p \geq p_N(u)$. Furthermore, we also obtain the corresponding concentration-compactness principle in the entire Euclidean space $\mathbb{R}^{N}$.

math.FA↗
arXiv2019

A Theoretical Study of Process Dependence for Critical Statistics in Standard Serial Models and Standard Parallel Models

Critical parts of the definitions of standard serial and standard parallel modes refer to stochastic independence. Standard serial models are defined by stochastic independence and identical distributions of their processing times. Processing times in the serial models are identical to the intercompletion time statistics. Similarly, standard parallel models assume stochastically independent and identical processing times. Their processing times are equivalent to the statistic known as total completion times. Little is known about what standard serial models can predict for the total completion time or what standard parallel models can predict for the intercompletion times. Here we demonstrate that standard serial models possess a tendency to predict a positive dependence for the total completion times with that always being true in the case of a single processing order. However, with mixtures of processing orders, standard serial models may predict negative dependence of the total completion times. Comparably, standard parallel models typically predict neither independence of the intercompletion times nor identical distributions. In fact, standard parallel models predict increasing intercompletion times as the individual channels continue to finish. Nevertheless, dramatically increasing hazard functions of the channels can defeat that tendency. And, standard parallel models can predict intercompletion time independence but only when individual channel distributions are exponential. Finally, we use these and ancillary mathematical results to conclude that standard serial and standard parallel models can never perfectly mimic one another. Therefore, our findings set the stage for explicit model testing between these classes.

q-bio.NC↗
arXiv2018

Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter

We study the fringe visibility and the distinguishability of a general Mach-Zehnder interferometer with an asymmetric beam splitter. Both the fringe visibility V and the distinguishability D are affected by the input state of the particle characterized by the Bloch vector S=(Sx,Sy,Sz) and the second asymmetric beam splitter characterized by paramter /beta. For the total system is initially in a pure state, it is found that the fringe visibility reaches the upper bound and the distinguishability reaches the lower bound when cos(/beta) = -Sx. The fringe visibility obtain the maximum only if Sx = 0 and /beta = /pi/2 when the input particle is initially in a mixed state. The complementary relationship V2 + D2 <= 1 is proved in a general Mach-Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.

quant-ph↗
arXiv2017

A Theoretical Study of Process Dependence for Standard Two-Process Serial Models and Standard Two-Process Parallel Models

In this article we differentiate and characterize the standard two-process serial models and the standard two process parallel models by investigating the behavior of (conditional) distributions of the total completion times and survivals of intercompletion times without assuming any particular forms for the distributions of processing times. We address our argument through mathematical proofs and computational methods. It is found that for the standard two-process serial models, positive dependence between the total completion times does not hold if no specific distributional forms are imposed to the processing times. By contrast, for the standard two-process parallel models the total completion times are independent. According to different nature of process dependence, one can distinguish a standard two process serial model from a standard two-process parallel model. We also find that in standard two-process parallel models the monotonicity of survival function of the intercompletion time of stage 2 conditional on the completion of stage 1 depends on the monotonicity of the hazard function of processing time. We also find that the survival of intercompletion time(s) from stage 1 to stage 2 is increasing when the ratio of hazard function meets certain criterion. Then the empirical finding that the intercompletion time is grown with the growth of the number of recalled words can be accounted by standard parallel models. We also find that if the cumulative hazard function is concave or linear, the survival from stage 1 to stage 2 is increasing.

stat.AP↗
arXiv2017

The block graph of a finite group

This paper studies intersections of principal blocks of a finite group with respect to different primes. We first define the block graph of a finite group $G$, whose vertices are the prime divisors of $|G|$ and there is an edge between two vertices $p\neq q$ if and only if the principal $p$- and $q$-blocks of $G$ have a nontrivial common complex irreducible character of $G$. Then we determine the block graphs of finite simple groups, which turn out to be complete except those of $J_1$ and $J_4$. Also, we determine exactly when the Steinberg character of a finite simple group of Lie type lies in a principal block. Based on the above investigation, we obtain a criterion for the $p$-solvability of a finite group which in particular leads to an equivalent condition for the solvability of a finite group. Thus, together with two recent results of Bessenrodt and Zhang, the nilpotency, $p$-nilpotency and solvability of a finite group can be characterized by intersections of principal blocks of some quotient groups.

math.RT↗
arXiv2017

Groups satisfying the two-prime hypothesis with a composition factor isomorphic to ${\rm PSL}_2(q)$ for $q\geq 7$

Let $G$ be a finite group, and write ${\rm cd}(G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the {\it two-prime hypothesis} if, for any distinct degrees $a, b \in {\rm cd}(G)$, the total number of (not necessarily different) primes of the greatest common divisor ${\rm gcd}(a, b)$ is at most $2$. In this paper, we prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to ${\rm PSL}_2 (q)$ for $q \geq 7$.

math.GR↗
arXiv2016

Complementarity via error-free measurement in a two-path interferometer

We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information Ipath are derived: their complementary relation V + Ipath less than or equal to 1 are found, and the condition for the equality is also presented.

quant-ph↗