K3 surfaces,Picard numbers and Siegel disks

If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues.     

表面等离子共振现象的新应用——微弱磁场的测量

提出了一种新的表面等离子体共振传感器, 它包含三层结构: 棱镜、金属薄膜及二能级介质. 通过理论分析发现, 与通常表面等离子体共振系统不同, 这一物理系统中同时存在两种共振效应 (表面等离子体共振和能级间量子跃迁的共振效应), 它们共同作用的结果导致一系列新的物理现象, 其中一个令人感兴趣的现象是入射光的反射率对外场导致的微小能级移动十分敏感 (这一现象是通常的表面等离子体共振系统所不具有的). 由于能级移动依赖于外场, 所以最终入射光的反射率对外场具有灵敏的响应. 本文以外磁场导致能级移动的情况进行了理论计算, 结果表明, 这种表面等离子体共振系统的入射光的反射率对外加磁场极其敏感. 这一特性可以用来测量物质表面附近的微弱磁场, 有可能发展成为一种新型检测技术.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Multivariate optimization and comparison between conventional extraction (CE) and ultrasonic-assisted extraction (UAE) of carotenoid extraction from cashew apple

Carotenoids are an essential component of cashew and can be used in pharmaceuticals, cosmetics, natural pigment, food additives, among other applications. The present work focuses on optimizing and comparing conventional and ultrasound-assisted extraction methods. Every optimization step took place with a 1:1 (w:w) mixture of yellow and red cashew apples lyophilized and ground in a cryogenic mill. A Simplex-centroid design was applied for both methods, and the solvents acetone, methanol, ethanol, and petroleum ether were evaluated. After choosing the extractor solvent, a central composite design was applied to optimize the sample mass (59–201 mg) and extraction time (6–34 min). The optimum conditions for the extractor solvent were 38% acetone, 30% ethanol, and 32% petroleum ether for CE and a mixture of 44% acetone and 56% methanol for UAE. The best experimental conditions for UAE were a sonication time of 19 min and a sample mass of 153 mg, while the CE was 23 min and 136 mg. Comparing red and yellow cashews, red cashews showed a higher carotenoid content in both methodologies. The UAE methodology was ca. 21% faster, presented a more straightforward composition of extracting solution, showed an average yield of superior carotenoid content in all samples compared to CE. Therefore, UAE has demonstrated a simple, efficient, fast, low-cost adjustment methodology and a reliable alternative for other applications involving these bioactive compounds in the studied or similar matrix.     

Composition and antioxidant activity of anthocyanins from Aronia melanocarpa extracted using an ultrasonic-microwave-assisted natural deep eutectic solvent extraction method

A time-saving, efficient, and environmentally friendly ultrasonic-microwave-assisted natural deep eutectic solvent (UMAE-NADES) extraction method was developed for the extraction of anthocyanins from Aronia melanocarpa. Eight different natural eutectic solvents were screened initially, and choline chloride-glycerol was selected as the extraction solvent. The extraction conditions were optimized using the response surface methodology, and the extraction rate of anthocyanins was higher than those achieved using the traditional ethanol method, natural deep eutectic solvent extraction method, and ultrasonic-microwave-assisted ethanol method. Six anthocyanins, including cyanidin-3-O-galactoside, cyanidin-3-O-glucoside, cyanidin-3-O-arabinoside, cyanidin-3-O-xyloside, cyanidin-3,5-O-dihexoside, and the dimer of cyanidin-hexoside were identified and extracted at a purity of 448.873 mg/g using high performance liquid chromatography-mass spectrometry (HPLC-MS). The compounds extracted using UMAE-NADES had higher antioxidant capacities than those extracted by the other three methods. The UMAE-NADES demonstrated significant efficiency toward the extraction of bioactive substances and has potential utility in the food and pharmaceutical industries.     

Intelligent radio resource management in reconfigurable IRS-enabled NOMA networks

Intelligent reflecting surfaces (IRSs) are anticipated to provide reconfigurable propagation environment for next generation communication systems. In this paper, we investigate a downlink IRS-aided multi-carrier (MC) non-orthogonal multiple access (NOMA) system, where the IRS is deployed to especially assist the blocked users to establish communication with the base station (BS). To maximize the system sum rate under network quality-of-service (QoS), rate fairness and successive interference cancellation (SIC) constraints, we formulate a problem for joint optimization of IRS elements, sub-channel assignment and power allocation. The formulated problem is mixed non-convex. Therefore, a novel three stage algorithm is proposed for the optimization of IRS elements, sub-channel assignment and power allocation. First, the IRS elements are optimized using the bisection method based iterative algorithm. Then, the sub-channel assignment problem is solved using one-to-one stable matching algorithm. Finally, the power allocation problem is solved under the given sub-channel and optimal number of IRS elements using Lagrangian dual-decomposition method based on Lagrangian multipliers. Moreover, in an effort to demonstrate the low-complexity of the proposed resource allocation scheme, we provide the complexity analysis of the proposed algorithms. The simulated results illustrate the various factors that impact the optimal number of IRS elements and the superiority of the proposed resource allocation approach in terms of network sum rate and user fairness. Furthermore, we analyze the proposed approach against a new performance metric called computational efficiency (CE).     

静脉血流动力学模型基本波的相互作用北大核心CSCD

静脉系统是心血管系统的重要组成部分.脉搏波在血液流动中有着突出的重要性.本文主要研究静脉血流动力学模型基本波的相互作用.血流动力学模型是2×2严格双曲型方程组,其基本波包括疏散波和激波,属于血液流动中的脉搏波.基本波相互作用后血管截面面积和血流速度发生相应的变化.     

Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation

We investigate a (2+1)-dimensional shallow water wave equation and describe its nonlinear dynamical behaviors in physics. Based on the N-soliton solutions, the higher-order fissionable and fusionable waves, fissionable or fusionable waves mixed with soliton molecular and breather waves can be obtained by various constraints of special parameters. At the same time, by the long wave limit method, the interaction waves between fissionable or fusionable waves with higher-order lumps are acquired. Combined with the dynamic figures of the waves, the properties of the solution are deeply studied to reveal the physical significance of the waves.     

多分散Au-Ag合金纳米球的光谱消光法反演

贵金属纳米颗粒具有局域表面等离子体共振特性而引起了广泛的关注,其中Au-Ag合金纳米颗粒具有良好的结构稳定性、光热性能以及潜在的抗癌功效而得到普遍研究。在众多应用中的特性与其粒径和浓度密切相关,然而目前常用的电子显微镜观察法和动态光散射法不能同时获得粒径和浓度信息,因此采取有效手段测量颗粒粒径和浓度信息至关重要。基于光谱消光法,利用非负的Tikhonov正则化方法解决反演问题,并根据Mie理论计算消光矩阵。针对噪声问题,采取两种情况研究多分散Au-Ag合金纳米球粒径分布与浓度的反演问题。未添加噪声情况下,颗粒系Ⅰ的反演相对误差小于颗粒系Ⅱ,在波长范围300～500 nm之间的反演相对误差最小,对应平均粒径、粒径标准差和颗粒数浓度的反演相对误差分别为0%,-0.03%和0%。添加随机噪声情况下,将0.5%和1.0%的随机噪声添加进颗粒系Ⅰ中的消光谱,经过数据比较发现在波长范围200～600 nm之间的反演相对误差最小。当添加0.5%的随机噪声时,粒径分布、粒径标准差和颗粒数浓度的变化范围分别为79.76～80.15 nm, 5.60～6.61 nm和0.995 8×1010～1.005 9×1010个·cm-3;当添加1.0%的随机噪声时,粒径分布、粒径标准差和颗粒数浓度的变化范围分别为78.87～80.27 nm, 5.36～9.00 nm和0.992 4×1010～1.027 7×1010个·cm-3。反演结果随着随机噪声的增大,变化范围也明显增大即反演相对误差增大,并且每次添加相同随机噪声后的反演结果不同。为了减少随机噪声导致的不稳定性,对100次反演结果进行平均得到平均粒径、粒径标准差和颗粒数浓度。当随机噪声从0.5%增大至1.0%时,其反演结果的相对误差均增大,但是反演得到的粒径分布、粒径标准差和颗粒数浓度相对误差均小于6%,这说明通过反演算法得到的反演结果具有较好的稳定性。研究表明,光谱消光法为反演多分散Au-Ag合金纳米球粒径分布与浓度提供了一种简单、快速的表征手段,也对研究非球形纳米颗粒有启示作用。     

Propagation of terahertz waves in nonuniform plasma slab under "electromagnetic window"

The application of magnetic fields, electric fields, and the increase of the electromagnetic wave frequency are up-and-coming solutions for the blackout problem. Therefore, this study considers the influence of the external magnetic field on the electron flow and the effect of the external electric field on the electron density distribution, and uses the scattering matrix method (SMM) to perform theoretical calculations and analyze the transmission behavior of terahertz waves under different electron densities, magnetic field distributions, and collision frequencies. The results show that the external magnetic field can improve the transmission of terahertz waves at the low-frequency end. Magnetizing the plasma from the direction perpendicular to the incident path can optimize the right-hand polarized wave transmission. The external electric field can increase the transmittance to some extent, and the increase of the collision frequency can suppress the right-hand polarized wave cyclotron resonance caused by the external magnetic field. By adjusting these parameters, it is expected to alleviate the blackout phenomenon to a certain extent.