arXiv subjects

Ya-Hui Wang

Publications and source records attributed to Ya-Hui Wang.

3 recordsLinked to original sources

arXiv2019

Propagating Terrace and Asymptotic Profile to Time-Periodic Reaction-Diffusion Equations

This paper is concerned with the asymptotic behavior of solutions of time periodic reaction-diffusion equation \begin{equation*}\label{aaa} \begin{cases} u_{t}(x,t)=u_{xx}(x,t)+f(t,u(x,t)),\quad \,\,\forall x\in\mathbb{R},\,t>0,\\ u(x,0)=u_{0}(x), \quad \quad\quad\quad\quad\quad\quad\quad\quad \forall x\in\mathbb{R}, \end{cases} \end{equation*} where $u_{0}(x)$ is the Heaviside type initial function and $f(t,u)$ satisfies $f(T+t,u)=f(t,u)$. Under certain conditions, we prove that there exists a minimal propagating terrace (a family of pulsating traveling fronts) in some specific sense and the solution of the above equation converges to the minimal propagating terrace.

math.AP↗

arXiv2017

The density theorem of a class of dilation-and-modulation systems on the half real line

In the practice, time variable cannot be negative. The space $L^2(\Bbb R_+)$ of square integrable functions defined on the right half real line $\Bbb R_+$ models causal signal space. This paper focuses on a class of dilation-and-modulation systems in $L^2(\Bbb R_+)$. The density theorem for Gabor systems in $L^2(\Bbb R)$ states a necessary and sufficient condition for the existence of complete Gabor systems or Gabor frames in $L^2(\Bbb R)$ in terms of the index set alone-independently of window functions. The space $L^2(\Bbb R_+)$ admits no nontrivial Gabor system since $\Bbb R_+$ is not a group according to the usual addition. In this paper, we introduce a class of dilation-and-modulation systems in $L^2(\Bbb R_+)$ and the notion of $Θ$-transform matrix. Using $Θ$-transform matrix method we obtain the density theorem of the dilation-and-modulation systems in $L^2(\Bbb R_+)$ under the condition that $\log_ba$ is a positive rational number, where $a$ and $b$ are the dilation and modulation parameters respectively. Precisely, we prove that a necessary and sufficient condition for the existence of such a complete dilation-and-modulation system or dilation-and-modulation system frame in $L^2(\Bbb R_+)$ is that $\log_ba \leq 1$. Simultaneously, we obtain a $Θ$-transform matrix-based expression of all complete dilation-and-modulation systems and all dilation-and-modulation system frames in $L^2(\Bbb R_+)$.

math.FA↗

arXiv2017

Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry

We study the physical properties of the persistent charged current in a metal ring on a noncommutative phase space, and temperature dependence of the noncommutative corrections are also analyzed. We find that the coordinate noncommutativity only affects the total magnitude of the current, and it is difficult to observe it. In contrast, the momentum noncommutativity can violate symmetry property of the current, and this violation of symmetry holds at a finite temperature. Based on this violation effect, we introduce an asymmetry observable to measure the momentum noncommutativity.

hep-th↗