Attracting graphs of skew products with non-contracting fiber maps

We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we prove the existence of an attracting invariant graph and study its topological properties. We prove the existence of globally attracting measures and we show that (in some specific cases) the rate of convergence to these measures is exponential.

     

Piecewise linear processes with Poisson‐modulated exponential switching times

We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.     

Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity

We consider a two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity. In both the focusing and defocusing case we prove local well-posedness, i.e., existence and uniqueness of the solution for short times, as well as energy and mass conservation. In addition, we prove that this implies global existence in the defocusing case, irrespective of the power of the nonlinearity, while in the focusing case blowing-up solutions may arise.     

Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence. The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima (MHM for short) model, which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima (CHM for short) model for both plasma and geophysical flows. The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state. Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model, while stabilizing damping effect is shown with a zonal flow base state. Together with the selective decay effect from the dissipation, the secondary instability offers a complete characterization of the convergence process to the purely zonal structure. Direct numerical simulations with and without dissipation are carried out to confirm the instability theory. It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration. In comparison, the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.     

Partition regularity of polynomial systems near zero

Semigroup Forum - Recently, S. Kanti Patra and Md. Moid Shaikh proved the existence of monochromatic solutions to systems of polynomial equations near zero for particular dense...     

基于降低失效停放区比率的共享单车系统稳定性研究

共享单车失效停放区使得用户无法取车或还车,影响共享单车系统运营稳定性。本文基于排队论与马尔科夫链构建了共享单车系统稳定状态平均场方程组并求解稳态解,发现停放区交互作用使得失效停放区对相邻停放区产生需求溢出效应,增加系统失效停放区比率,影响系统运营稳定性。本文以降低系统失效停放区比率目标,引入(M,S)交互策略,调节失效停放区对相邻停放区的交互作用程度。进一步,以算例分析比较相同类型与不同类型停放区交互作用、(M,S)交互策略下共享单车系统的失效停放区比率。结果表明(M,S)交互策略能够有效降低失效停放区比率,提高系统运营稳定性。本研究为共享单车企业运营稳定性决策提供了有价值的参考。     

向后迭代区间选择算法及其在近红外光谱模型转移中的应用

近红外光谱（NIR）具有快速、无损、操作方便的特点,故广泛用于食品分析。作为一种间接的分析技术,NIR需要建立光谱与待测浓度之间的统计模型来实现检测。故模型的维护有助于保证NIR的预测准确性。在外界条件发生变化的情况下,诸如样品性状的改变、仪器对理化指标函数关系的变化、湿度和温度等环境因素的改变,会导致相同样品的光谱信号发生偏移,进而使得原有模型的预测精度下降。此时,如果重新建模,虽然可以解决光谱偏移对建模的影响,但是重新建模将耗费大量的人力物力。对此,模型转移可以在避免重新建模的情况下,校正光谱的偏移,进而提高模型预测精度。通常模型转移算法多用全光谱进行模型转移,这种方法计算量较大,且不能找到合适的有化学意义的波段。故提出一种基于模型转移中的变量选择方法：向后迭代区间选择法（IIBS）,通过计算主光谱（用于建模的那组光谱）和从光谱（发生偏移,需要通过模型转移算法将其校正的光谱）中,变量区间的重要性信息（回归系数（β）、残差向量（Res）以及变量重要性投影（VIP））。进而通过计算该区间变量重要性信息的几何平均数,并以此作为该区间的区间重要性指标。接着根据区间的重要性,删除重要性信息较小的变量区间。然后对主光谱和从光谱重复迭代上述过程：计算变量的重要性信息,计算区间的重要性信息,删除重要性信息较小的区间。最后,比较不同的主光谱和从光谱区间组合的验证均方根误差（RMSEV）,选择RMSEV最小的主光谱和从光谱区间作为最优区间。玉米、小麦两套NIR数据测试了该算法。结果显示,与全波段相比,β,Res以及VIP均可以从主光谱和从光谱中选择较少的,有化学意义的区间,提高模型转移的精度。在比较不同变量重要性向量方面,基于β的变量选择算法,模型转移的计算误差较小。     

Characterization of Basil Volatile Fraction and Study of Its Agronomic Variation by ASCA

Basil is a plant known worldwide for its culinary and health attributes. It counts more than a hundred and fifty species and many more chemo-types due to its easy cross-breeds. Each species and each chemo-type have a typical aroma pattern and selecting the proper one is crucial for the food industry. Twelve basil varieties have been studied over three years (2018–2020), as have four different cuts. To characterize the aroma profile, nine typical basil flavour molecules have been selected using a gas chromatography–mass spectrometry coupled with an olfactometer (GC–MS/O). The concentrations of the nine selected molecules were measured by an ultra-fast CG e-nose and Principal Component Analysis (PCA) was applied to detect possible differences among the samples. The PCA results highlighted differences between harvesting years, mainly for 2018, whereas no observable clusters were found concerning varieties and cuts, probably due to the combined effects of the investigated factors. For this reason, the ANOVA Simultaneous Component Analysis (ASCA) methodology was applied on a balanced a posteriori designed dataset. All the considered factors and interactions were statistically significant (p < 0.05) in explaining differences between the basil aroma profiles, with more relevant effects of variety and year.     

Rotational analysis of the v 2 + v 6 ±1, v 5 ∓1 + v 6 ∓1 and v 5 ∓1 + v 6 ±1 interacting infrared bands of methyl bromide

The rotational analysis of the infrared absorption spectrum of CH₃ ⁷⁹Br and CH₃ ⁸¹Br between 2150 and 2510 cm^-1 was performed on a Fourier transform spectrum with a resolution of 0·007 cm^-1. The bands v ₂ + v ₆(E) and v ₅ + v ₆(A ₁ + A ₂ + E) occur in this region, giving rise to several perturbations as in the corresponding system of methyl chloride [3]. Forbidden transitions, observed in correspondence of the level crossing of the x-y Coriolis coupling between v ₂ + v ₆ and v ₅ + v ₆(E), enabled us to estimate the value of A″ - 225D″_K at 5·16186 cm^-1 for CH₃ ⁷⁹Br and 5·16173 cm^-1 for CH₃ ⁸¹Br. The parallel system of v ₅ + v ₆ exhibits a perpendicular structure, and an l-type resonance couples those levels of the parallel and perpendicular components of v ₅ + v ₆ involved in transitions from the K″ = 0 levels of the ground state. The ^QQ ₀ branches of the A ₂ component of v ₅ + v ₆, made active by this resonance, are observed for both isotopic species.     

Comparison of subwavelength focusing properties of diffraction and Fresnel zone plate plasmonic planar lenses

The subwavelength focusing properties of diffractive plasmonic planar lenses (DPLs) and Fresnel zone plate plasmonic planar lenses (FZPs) have been compared in this paper. To that end, we use the same lens material, incident wavelength, thickness and focal length for comparison. Both DPLs and FZPs consist of central circular slits surrounded by transparent and opaque zones and can get clear focusing performances. By using the rigorous electromagnetic numerical method, the fields in the focal region are analyzed in detail, and our results demonstrate that FZP can generate higher transmission efficiency, and higher peak field intensity at the focal plane. Focusing polarization properties of the lens illuminated by linearly polarized state, are calculated and analyzed also. The numerical results show that both the DPL and the FZP produce asymmetrical focal spot distributions with a low f-number. To the FZP, the full-width at half-maximum (FWHM) varies from 256 nm (along y-axis) to 516 nm(along x-axis) and to the DPL, the FWHM varies from 256 nm(along y-axis) to 580 nm(along x-axis), respectively. But for a high f-number, the asymmetrical performance of the focal spot will be reduced due to complicated electromagnetical field interferences and micro waveguide effect. Otherwise, the DPL can get a higher depolarization effect than the FZP does.