多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

Quantized-states-based adaptive control against unknown slippage effects of uncertain mobile robots with input and state quantization

An adaptive tracking design strategy based on quantized state feedback is developed for uncertain nonholonomic mobile robots with unknown wheel slippage effects. All state variables and control torques are assumed to be quantized by the state and input quantizers, respectively, in a network control environment. Thus, the quantized state feedback information is only available for the tracking control design. An approximation-based adaptive controller using quantized states is recursively designed to ensure the robust adaptive tracking against unknown wheel slippage effects where the quantized-states-based adaptive mechanism is derived to compensate for unknown wheel slippage effects, system nonlinearities, and quantization errors. The boundedness of the quantization errors and estimated parameters in the closed-loop system is analyzed by presenting some theoretical lemmas. Based on these lemmas, we prove the uniform ultimate boundedness of closed-loop signals and the convergence of the trajectory tracking error in the presence of wheel slippage effects. Simulations verify the effectiveness of the resulting tracking scheme.     

“Quad-band flexible magnesium zinc ferrite (MgZnFe2O4)-based double negative metamaterial for microwave applications”

This article presents vertically coupled, rectangular complementary split-ring resonator-shaped quad-band double-negative (DNG) metamaterial unit cells, that is, having both negative permittivity and permeability, which redirect negative refractive and also are not found in nature. The metamaterial is fabricated on magnesium zinc ferrite-based flexible microwave substrates, and the flexible substrates are chosen with two different concentrations of magnesium (Mg) denoted by Mg₃₀ and Mg₅₀ for 30% and 50% of Mg, which possess dielectric constants of 4.32 and 3.15 and loss tangents of 0.003 and 0.005, respectively. The proposed metamaterials are demonstrated by utilizing the CST microwave simulator, and their effective parameters are extracted according to the Nicolson-Ross-Wire method. With Mg_30, the prepared, flexible metamaterial shows measured resonances at 3.70 GHz, 7 GHz, 8.60 GHz, and 9.78 GHz, whereas with Mg₅₀ it shows the measured resonances at 4.10 GHz, 7.70 GHz, 9.33 GHz, and 10.62 GHz. Very good effective medium ratios (EMR) along with DNG properties are obtained, namely 6.5 and 5.85 for Mg₃₀ and Mg_50, respectively, with a physical dimension of 12.5 × 9.5 mm² for both of the unit cells_. Also, the electric field, magnetic field, and surface current distribution at different resonances and the polarization insensitivity at different polarization angles were observed. Thus, the designed new flexible substrate microwave materials based on DNG metamaterials are potential candidates for S-, C- and X-band applications, as well as for flexible microwave technologies.     

The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

Hybrid control strategy of delayed neural networks and its application to sampled-data systems: an impulsive-based bilateral looped-functional approach

Nonlinear Dynamics - In this work, the problem of hybrid control strategy for delayed neural networks is investigated via an impulsive-based bilateral looped-functional (IBBLF) approach. Firstly, a...     

Effect of thickness variations of lithium niobate on insulator waveguide on the frequency spectrum of spontaneous parametric down-conversion

We study the effect of waveguide thickness variations on the frequency spectrum of spontaneous parametric down-conversion in the periodically-poled lithium niobate on insulator (LNOI) waveguide. We analyze several variation models and our simulation results show that thickness variations in several nanometers can induce distinct effects on the central peak of the spectrum, such as narrowing, broadening, and splitting. We also prove that the effects of positive and negative variations can be canceled and thus lead to a variation-robust feature and an ultra-broad bandwidth. Our study may promote the development of on-chip photon sources in the LNOI platform, as well as opens up a way to engineer photon frequency state.