Almost Automorphic Dynamics of Generalized Li\'enard Equation

In this study, we focus on the solutions of the Li\''enard equation being bounded in the future and characterize the almost automorphic, asymptotically almost automorphic, and weighted pseudo almost automorphic dynamics. An example is presented to illustrate the main findings.     

Circular regular dessins

Journal of Algebraic Combinatorics - A dessin is called circular if the boundary of each face is a circuit (a simple cycle). In this paper, we address the problem of characterizing edge-transitive...     

The Even Part of Finite-Dimensional Modular Lie Superalgebra Г

Let F be the underlying base field of characteristic p ＞ 3 and denote by Γō the even part of the finite-dimensional Lie superalgebra Γ.We give the generator sets of the Lie algebra Γō.Using certain properties of the canonical tori of Γō,we describe explicitly the derivation algebra of Γō.     

Approximation of the Fractional Schrödinger Propagator on Compact Manifolds

Let L be a second order positive, elliptic differential operator that is self-adjoint with respect to some C~∞ density dx on a compact connected manifold M. We proved that if 0 α 1,α/2 s α and f ∈ H~s(M) then the fractional Schr?dinger propagator e~(it Lα/2) on M satisfies e~(it Lα/2) f(x)-f(x) = o(t~(s/α-ε)) almost everywhere as t → 0~+, for any ε 0.     

p-Adic函数空间上Hardy型算子的多线性交换子估计

在p-adic域上研究分数次Hardy型算子与CMO(Qnp)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.     

An Improved Upper Bound on the Linear 2-arboricity of 1-planar Graphs

The linear 2-arboricity la_2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests,whose component trees are paths of length at most 2.In this paper,we prove that if G is a 1-planar graph with maximum degree Δ,then la_2(G)≤[(Δ+1)/2]+7.This improves a known result of Liu et al.(2019) that every 1-planar graph G has la_2(G)≤[(Δ+1)/2]+14.We also observe that there exists a 7-regular 1-planar graph G such that la_2(G)=6=[(Δ+1)/2]+2,which implies that our solution is within 6 from optimal.     

Broadband energy harvesting via magnetic coupling between two movable magnets

Harvesting energy from ambient mechanical vibrations by the piezoelectric effect has been proposed for powering microelectromechanical systems and replacing batteries that have a finite life span. A conventional piezoelectric energy harvester （PEH） is usually designed as a linear resonator, and suffers from a narrow operating bandwidth. To achieve broadband energy harvesting, in this paper we introduce a concept and describe the realization of a novel nonlinear PEH. The proposed PEH consists of a primary piezoelectric cantilever beam coupled to an auxiliary piezoelectric cantilever beam through two movable magnets. For predicting the nonlinear response from the proposed PEH, lumped parameter models are established for the two beams. Both simulation and experiment reveal that for the primary beam, the introduction of magnetic coupling can expand the operating bandwidth as well as improve the output voltage. For the auxiliary beam, the magnitude of the output voltage is slightly reduced, but additional output is observed at off-resonance frequencies. Therefore, broadband energy harvesting can be obtained from both the primary beam and the auxiliary beam.     

Photonic Aharonov-Bohm effect based on dynamic modulation

We show that when the refractive index of a photonic system is harmonically modulated, the phase of the modulation introduces an effective gauge potential for photons. This effective gauge potential can be used to create a photonic Aharonov-Bohm effect. We show that the photonic Aharonov-Bohm effect provides the optimal mechanism for achieving complete on-chip nonmagnetic optical isolation.     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20