arXiv subjects

Guangyu Xu

Publications and source records attributed to Guangyu Xu.

11 recordsLinked to original sources

arXiv2024

Supplementary Private Tutoring and Mathematical Achievements in Higher Education: An Empirical Study on Linear Algebra

The present article is an empirical study that investigates the learning situation of linear algebra. Research was performed among 60 science and engineering students from different universities in Zhejiang, Jiangsu, Hubei, and Shandong who were taught by three mathematics teachers in the course of a 3-day short-term training consisting of 24 classes; following this, the effectiveness of short-term training for mathematics curriculum learning in higher education was evaluated based on the IRT measurement model. The results indicate that regardless of the difficulty of the test, short-term training significantly enhances students' mastery of linear algebra knowledge points, and students can accurately perceive their mathematical achievements; the effect observed is not consistent with that of private tutoring (PT) in primary and secondary schools.

math.HO↗

arXiv2024

Improvement of conditions for finite time blow-up in a fourth-order nonlocal parabolic equation

This paper is devoted to the study of blow-up phenomenon for a fouth-order nonlocal parabolic equation with Neumann boundary condition, \begin{equation*} \left\{\begin{array}{ll}\ds u_{t}+u_{xxxx}=|u|^{p-1}u-\frac{1}{a}\int_{0}^a|u|^{p-1}u\ dx, & u_x(0)=u_x(a)=u_{xxx}(0)=u_{xxx}(a)=0, & u(x,0)=u_0(x)\in H^2(0, a),\ \ \int_0^au_0(x)\ dx=0, &\end{array}\right. \end{equation*} where $a$ is a positive constant and $p>1$. The existing results on the problem suggest that the weak solution will blow up in finite time if $I(u_0)<0$ and the initial energy satisfies some appropriate assumptions, here $I(u_0)$ is the initial Nehari functional. In this paper, we extend the previous blow-up conditions with proving that those assumptions on the energy functional are superfluous and only $I(u_0)<0$ is sufficient to ensure the weak solution blowing up in finite time. Our conclusion depicts the significant influence of mass conservation on the dynamic behavior of solution.

math.AP↗

arXiv2023

The Twisted Index and Topological Saddles

The twisted index of 3d $\mathcal{N}=2$ gauge theories on $S^1 \times Σ$ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the supersymmetric quantum mechanics from topological saddle points in supersymmetric localisation of abelian gauge theories. Topological saddles are configurations where the matter fields vanish and the gauge symmetry is unbroken, which exist for non-vanishing effective Chern-Simons levels. We compute the contributions to the twisted index from both topological and vortex-like saddles points and show that their combination recovers the Jeffrey-Kirwan residue prescription for the twisted index and its wall-crossing.

hep-th↗

arXiv2023

Higher regularity and finite time blow-up to nonlocal pseudo-parabolic equation with conical degeneration

This paper deals with the initial-boundary value problem to a nonlocal semilinear pseudo-parabolic equation with conical degeneration, which has been studied in [Global well-posedness for a nonlocal semilinear pseudo-parabolic equation with conical degeneration, J. Differential Equations, 2020, 269(5): 4566--4597]. We first improve the regularity of the weak solution, and then study finite time blow-up phenomenon for the problem. Our initial condition for blow-up only depends on Nehari functional and the conservative integral, which suggests that the assumption of initial energy functional in the original paper can be removed.

math.AP↗

arXiv2022

An Algebro-Geometric Approach to Twisted Indices of Supersymmetric Gauge Theories

This thesis studies the algebro-geometric aspects of supersymmetric abelian gauge theories in three dimensions. The supersymmetric vacua are demonstrated to exhibit a window phenomenon in Chern-Simons levels, which is analogous to the window phenomenon in quantum K-theory with level structures. This correspondence between three-dimensional gauge theories and quantum K-theory is investigated from the perspectives of semi-classical vacua, twisted chiral rings, and twisted indices. In particular, the twisted index admits an algebro-geometric interpretation as the supersymmetric index of an effective quantum mechanics. Via supersymmetric localisation, the contributions from both topological and vortex saddle points are shown to agree with the Jeffrey-Kirwan contour integral formula. The algebro-geometric construction of Chern-Simons contributions to the twisted index from determinant line bundles provides a natural connection with quantum K-theory.

hep-th↗

arXiv2022

Emergence of lager densities in chemotaxis system with indirect signal production and non-radial symmetry case

This paper deals with the classical solution of the following chemotaxis system with generalized logistic growth and indirect signal production \begin{eqnarray} \left\{ \begin{array}{llll} & u_t=εΔu-\nabla\cdot(u\nabla v)+ru-μu^θ,\\ & 0=d_1Δv-βv+αw,\\ & 0=d_2Δw-δw+γu \end{array} \right. \qquad(0.1)\end{eqnarray} and the so-called strong $W^{1, q}(Ω)$-solution of hyperbolic-elliptic-elliptic model \begin{eqnarray} \left\{ \begin{array}{llll} & u_t=-\nabla\cdot(u\nabla v)+ru-μu^θ,\\ & 0=d_1Δv-βv+αw,\\ & 0=d_2Δw-δw+γu, \end{array} \right.\ \qquad(0.2)\end{eqnarray} in arbitrary bounded domain $Ω\subset\mathbb{R}^n$, $n\geq1$, where $r, μ, d_1, d_2, α, β, γ, δ>0$ and $θ>1$. Via applying the viscosity vanishing method, we first prove that the classical solution of (0.1) will converge to the strong $W^{1, q}(Ω)$-solution of (0.2) as $ε\rightarrow0$. After structuring the local well-pose of (0.2), we find that the strong $W^{1, q}(Ω)$-solution will blow up in finite time with non-radial symmetry setting if $Ω$ is a bounded convex domain, $θ\in(1, 2]$, and the initial data is suitable large. Moreover, for any positive constant $M$ and the classical solution of (0.1), if we add another hypothesis that there exists positive constant $ε_0(M)$ with $ε\in(0,\ ε_0(M))$, then the classical solution of (0.1) can exceed arbitrarily large finite value in the sense: one can find some points $\left(\tilde{x}, \tilde{t}\right)$ such that $u(\tilde{x}, \tilde{t})>M$.

math.AP↗

arXiv2020

Boundedness and asymptotically stability to chemotaxis system with competitive kinetics and nonlocal terms

This paper deals with the solution of following chemotaxis system with competitive kinetics and nonlocal terms \begin{eqnarray*} \left\{ \begin{array}{llll} u_t=d_1Δu-χ_1\nabla\cdot(u\nabla w)+u\left(a_0-a_1u-a_{2}v-a_3\int_Ωu-a_4\int_Ωv\right), &x\in Ω, t>0,\\ v_t=d_2Δv-χ_2\nabla\cdot(v\nabla w)+v\left(b_0-b_1u-b_{2}v-b_3\int_Ωu-b_4\int_Ωv\right), &x\in Ω, t>0,\\ w_t=d_3Δw-λw+k u+l v, &x\inΩ, t>0, \end{array} \right. \end{eqnarray*} in a smoothly bounded domain $Ω\subset \mathbb{R}^N, N\geq1$, where $a_0, a_1, a_2, b_0, b_1, b_2>0$ and $a_3, a_4, b_3, b_4\in\mathbb{R}$. The purpose of this paper is to investigate the impact on nonlocal terms of the system, and to find clear conditions on parameters such that the system possesses a unique global bounded solution. Our conclusion quantitatively suggests that the nonlocal competitions can contribute to global and uniformly bounded solutions, while the global cooperations are adverse to boundedness of system. That is: o If $a_3, a_4, b_3, b_4>0$, i.e., there are nonlocal intraspecific and interspecific competitions, when $N\leq2$, then for any positive parameters the solution of system is globally bounded; when $N\geq3$, suitable large $a_1, b_2$ (local intraspecific competitions) ensure there is no blowup. o If $a_3, a_4, b_3, b_4<0$, i.e., there are globally intraspecific and interspecific cooperations, then for any $N\geq1$, a clear and largeness condition on $a_1, b_2$ is obtained which makes the system admits a boundedness solution. Furthermore, we consider the globally asymptotically stability of spatially homogeneous equilibrium with weak and strongly asymmetric competition cases, respectively.

math.AP↗

arXiv2013

Variability Effects in Graphene: Challenges and Opportunities for Device Engineering and Applications

Variability effects in graphene can result from the surrounding environment and the graphene material itself, which form a critical issue in examining the feasibility of graphene devices for large-scale production. From the reliability and yield perspective, these variabilities cause fluctuations in the device performance, which should be minimized via device engineering. From the metrology perspective, however, the variability effects can function as novel probing mechanisms, in which the 'signal fluctuations' can be useful for potential sensing applications. This paper presents an overview of the variability effects in graphene, with emphasis on their challenges and opportunities for device engineering and applications. The discussion can extend to other thin-film, nanowire and nanotube devices with similar variability issues, forming general interest in evaluating the promise of emerging technologies.

cond-mat.mes-hall↗

arXiv2011

Edge effect on resistance scaling rules in graphene nanostructures

We report an experimental investigation of the edge effect on the room-temperature transport in graphene nanoribbon and graphene sheet (both single-layer and bilayer). By measuring the resistance scaling behaviors at both low and high carrier densities, we show that the transport of single-layer nanoribbons lies in a strong localization regime, which can be attributed to an edge effect. We find that this edge effect can be weakened by enlarging the width, decreasing the carrier densities or adding an extra layer. From graphene nanoribbon to graphene sheet, the data show a dimensional crossover of the transport regimes possibly due to the drastic change of the edge effect.

cond-mat.mes-hall↗

arXiv2010

Enhanced Conductance Fluctuation by Quantum Confinement Effect in Graphene Nanoribbons

Conductance fluctuation is usually unavoidable in graphene nanoribbons (GNR) due to the presence of disorder along its edges. By measuring the low-frequency noise in GNR devices, we find that the conductance fluctuation is strongly correlated with the density-of-states of GNR. In single-layer GNR, the gate-dependence of noise shows peaks whose positions quantitatively match the subband positions in the band structures of GNR. This correlation provides a robust mechanism to electrically probe the band structure of GNR, especially when the subband structures are smeared out in conductance measurement.

cond-mat.mes-hall↗

arXiv2010

Effect of Spatial Charge Inhomogeneity on 1/f Noise Behavior in Graphene

Scattering mechanisms in graphene are critical to understanding the limits of signal-to-noise-ratios of unsuspended graphene devices. Here we present the four-probe low frequency noise (1/f) characteristics in back-gated single layer graphene (SLG) and bilayer graphene (BLG) samples. Contrary to the expected noise increase with the resistance, the noise for SLG decreases near the Dirac point, possibly due to the effects of the spatial charge inhomogeneity. For BLG, a similar noise reduction near the Dirac point is observed, but with a different gate dependence of its noise behavior. Some possible reasons for the different noise behavior between SLG and BLG are discussed.

cond-mat.mes-hall↗