arXiv subjects

Yuanyuan Ke

Publications and source records attributed to Yuanyuan Ke.

6 recordsLinked to original sources

arXiv2025

The Spectrum Zero Problem of nonlinear Dirac equation with particle-antiparticle interaction

In this study, we investigate the Spectrum Zero Problem of nonlinear Dirac equations with a focus on the behavior of zero at the boundaries of the spectral gap. We introduce a nonlinear particle-antiparticle interaction and demonstrate that the problem exhibits asymmetric behavior at the left and right boundaries of the spectrum. Specifically, when zero is at the right boundary, the problem has only trivial solutions and is identified as a bifurcation point on the left, whereas nontrivial solutions exist when zero is at the left boundary or within the spectral gap. The main idea is to employ a variational method involving a perturbation technique that places zero within the spectral gap. We use the critical point theorem of the perturbed functional to construct a Palais-Smale sequence in order to approach the critical point of the target energy functional. Additionally, we utilize the concentration-compactness principle to identify critical points of the original functional and explore the associated bifurcation phenomena. Our results reveal an asymmetric phenomenon in nonlinear quantum systems and provide insights into why strongly indefinite problems typically address zero only at the left boundary of the spectral gap.

math.AP↗

arXiv2019

Blow-up prevention by nonlinear diffusion in a 2D Keller-Segel-Navier-Stokes system with rotational flux

This paper investigates the following Keller-Segel-Navier-Stokes system with nonlinear diffusion and rotational flux $$\begin{align}\begin{cases} &n_t+u\cdot\nabla n=Δn^m-\nabla\cdot(nS(x, n, c)\nabla c),\quad &x\in Ω, t>0, \\ &c_t+u\cdot\nabla c=Δc-c+n,\quad &x\in Ω, t>0, \\ &u_t+κ(u\cdot\nabla)u+\nabla P=Δu+n\nabla ϕ,\quad &x\in Ω, t>0, \\ &\nabla\cdot u=0,\quad &x\in Ω, t>0, \end{cases}\end{align}$$ where $κ\in \mathbb{R},ϕ\in W^{2,\infty}(Ω)$ and $S$ is a given function with values in $\mathbb{R}^{2\times2}$ which fulfills $$ |S(x,n,c)| \leq C_S $$ with some $C _S > 0$. Systems of this type describe chemotaxis-fluid interaction in cases when the evolution of the chemoattractant is essentially dominated by production through cells. If $m>1$ and $Ω\subset \mathbb{R}^2$ is a {\bf bounded} domain with smooth boundary, then for all reasonably regular initial data, a corresponding initial-boundary value problem for $(KSNF)$ possesses a global and bounded (weak) solution, which significantly improves previous results of several authors. Moreover, the {\bf optimal condition} on the parameter $m$ for global existence is obtained. Our approach underlying the derivation of main result is based on an entropy-like estimate involving the functional %Our main tool is consideration of the energy functional $$\int_Ω(n_{\varepsilon} +\varepsilon)^{m}+\int_Ω|\nabla c_\varepsilon|^{2},$$ where $n_\varepsilon$ and $c_\varepsilon$ are components of the solutions to (2.1) below.

math.AP↗

arXiv2019

On split regular BiHom-Poisson superalgebras

The paper introduces the class of split regular BiHom-Poisson superalgebras, which is a natural generalization of split regular Hom-Poisson algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Poisson superalgebras $A$ is of the form $A=U+\sum_{\a}I_\a$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{\a}$, a well described ideal of $A$, satisfying $[I_\a, I_\b]+I_\a I_\b = 0$ if $[\a]\neq [\b]$. Under certain conditions, in the case of $A$ being of maximal length, the simplicity of the algebra is characterized.

math.RA↗

arXiv2017

-DMP elements in $$-semigroups and $*$-rings

In this paper, we investigate *-DMP elements in $*$-semigroups and $*$-rings. The notion of *-DMP element was introduced by Patrício in 2004. An element $a$ is *-DMP if there exists a positive integer $m$ such that $a^{m}$ is EP. We first characterize *-DMP elements in terms of the \{1,3\}-inverse, Drazin inverse and pseudo core inverse, respectively. Then, we give the pseudo core decomposition utilizing the pseudo core inverse, which extends the core-EP decomposition introduced by Wang for matrices to an arbitrary $*$-ring; and this decomposition turns to be a useful tool to characterize *-DMP elements. Further, we extend Wang's core-EP order from matrices to $*$-rings and use it to investigate *-DMP elements. Finally, we give necessary and sufficient conditions for two elements $a,~b$ in $*$-rings to have $aa^{\scriptsize\textcircled{\tiny D}}=bb^{\scriptsize\textcircled{\tiny D}}$, which contribute to investigate *-DMP elements.

math.RA↗

arXiv2016

The reverse order law of the $(b, c)$-inverse in rings

We present equivalent conditions of reverse order law for the $(b, c)$-inverse $(aw)^{(b,c)}=w^{(b,s)}a^{(t,c)}$ to hold in a ring. Also, we study various mixed-type reverse order laws for the $(b,c)$-inverse. As a consequence, we get results related to the reverse order law for the inverse along an element. More general case of reverse order law $(a_1a_2)^{(b_3, c_3)}=a_2^{(b_2, c_2)}a_1^{(b_1, c_1)}$ is considered too.

math.RA↗

arXiv2016

One-sided $(b, c)$-inverses in rings

In this paper we introduce a new generalized inverse in a ring -- one-sided $(b, c)$-inverse, derived as an extension of $(b, c)$-inverse. This inverse also generalizes one-sided inverse along an element, which was recently introduced by H. H. Zhu et al. [H. H. Zhu, J. L. Chen, P. Patrício, Further results on the inverse along an element in semigroups and rings, Linear Multilinear Algebra, 64 (3) (2016) 393-403]. Also, here we present one-sided annihilator $(b, c)$-inverse, which is an extension of the annihilator $(b, c)$-inverse. Necessary and sufficient conditions for the existence of these new generalized inverses are obtained. Furthermore, we investigate conditions for the existence of one-sided $(b, c)$-inverse of a product of three elements and we consider some properties of one-sided $(b, c)$-inverses.

math.RA↗