代数$\Omega$-范畴的等价范畴

本文基于$\Omega$-范畴研究了(连续) $\mathcal{I}$-余万备$\Omega$-范畴的一些性质. 我们给出了双完备$\Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$\mathcal{I}$-余万备$\Omega$-范畴都是双完备$\Omega$-范畴. 得到了代数$\Omega$-范畴范畴等价于双完备$\Omega$-范畴.     

A summation‐integral type modification of Szász–Mirakjan operators

In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Construction of a new family of Bernstein‐Kantorovich operators

In the present paper, we construct a new sequence of Bernstein‐Kantorovich operators depending on a parameter α. The uniform convergence of the operators and rate of convergence in local and global sense in terms of first‐ and second‐order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of Bernstein‐Kantorovich operators and their approximation behaviors.     

Red Blood Cell Stiffness and Adhesion Are Species-Specific Properties Strongly Affected by Temperature and Medium Changes in Single Cell Force Spectroscopy

Besides human red blood cells (RBC), a standard model used in AFM-single cell force spectroscopy (SCFS), little is known about apparent Young’s modulus (Ea) or adhesion of animal RBCs displaying distinct cellular features. To close this knowledge gap, we probed chicken, horse, camel, and human fetal RBCs and compared data with human adults serving as a repository for future studies. Additionally, we assessed how measurements are affected under physiological conditions (species-specific temperature in autologous plasma vs. 25 °C in aqueous NaCl solution). In all RBC types, Ea decreased with increasing temperature irrespective of the suspension medium. In mammalian RBCs, adhesion increased with elevated temperatures and scaled with reported membrane sialic acid concentrations. In chicken only adhesion decreased with higher temperature, which we attribute to the lower AE-1 concentration allowing more membrane undulations. Ea decreased further in plasma at every test temperature, and adhesion was completely abolished, pointing to functional cell enlargement by adsorption of plasma components. This halo elevated RBC size by several hundreds of nanometers, blunted the thermal input, and will affect the coupling of RBCs with the flowing plasma. The study evidences the presence of a RBC surface layer and discusses the tremendous effects when RBCs are probed at physiological conditions.     

New polymer electrolyte membrane for medium-temperature fuel cell applications based on cross-linked polyimide Matrimid and hydrophobic protic ionic liquid

New hydrophobic protic ionic liquid, 2-butylaminoimidazolinium bis(trifluoromethylsulfonyl)imide (BAIM-TFSI), has been synthesized. The ionic liquid showed good thermal stability to at least 350 °C. The conductivity of BAIM-TFSI determined by electrochemical impedance method was found to be 5.6 × 10^?2 S/cm at 140 °C. Homogeneous composite films based on commercial polyimide (PI) Matrimid and BAIM-TFSI containing 30–60 wt% of ionic liquid were prepared by casting from methylene chloride solutions. Thermogravimetric analysis data indicated an excellent thermal stability of PI/BAIM-TFSI composites and thermal degradation points in the temperature range 377 °C–397 °C. The addition of ionic liquid up to 50 wt% in PI films does not lead to any significant deterioration of the tensile strength of the polymer. The dynamic mechanical analysis results indicated both an increase of storage modulus E′ of PI/BAIM-TFSI composites at room temperature and a significant E′ decrease with temperature compared with the neat polymer. The cross-linking of the PI with polyetheramine Jeffamine D-400 allowed to prepare PI/Jeffamine/BAIM-TFSI (50%) membrane with E′ value of 300 MPa at 130 °C. The ionic conductivity of this cross-linked composite membrane reached the level of 10^?2 S/cm at 130 °C, suggesting, therefore, its potential use in medium-temperature fuel cells operating in water-free conditions.     

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.     

Experiment investigation on effects of elastic modulus on cavitation erosion of silicone rubber

Research into cavitation phenomena in various fields shows that the elastic modulus of a boundary has a potential impact on cavitation erosion. To obtain the direct relationship between the elastic modulus of the boundary and cavitiation erosion, single-layer samples with different chemical composition and moduli, and double-layer samples with different elastic moduli and the same surface layer material, were prepared with silicone rubber. The results of cavitation experiments on single-layer samples, show that the coating chemical composition and mechanical properties together affect the cavitation morphology of the coating, and dominant factors vary with erosion stage. Through the cavitation test of double-layer samples, it was found that there is a positive correlation between the elastic modulus of the coating and the degree of cavitation. This study helps us to understand the relationship between coating elastic modulus and cavitation more directly, and provides theoretical and technical guidance for the application of anti-cavitation for elastic coating in engineering.     

多胞材料的力学行为

多胞材料具有独特的力学性质,其工程应用日益增加.人造多胞材料可以分为蜂窝材料和泡沫材料两类.本文介绍了这两类材料在不同载荷条件下力学行为的研究概况.对于某些天然材料(木材和松质骨)的多胞结构及其模型也作了简要介绍.     

HT—7U超导托克马克纵场线圈等效模量的数值分析

HT－7U托克马克装置的纵场线圈是由多种材料组成的具有周期性分布的大型复杂结构，线圈可视为由超导线、支撑结构和绝缘材料组成的复合材料，结构极其复杂。整个线圈工作在液氦温区。在设计阶段对其宏观等效力学性能进行数值分析计算是十分必要的，但要对整个线圈直接进行有限元分析或实验是极其困难的，主要利用均匀化方法对其进行等效处理，从而分析计算其宏观等效模量，为线圈的设计和评估提供参考依据。另外本文对均匀化方法的边界条件进行了一些改进，提出了更加合理的三维边界条件。