Positive definite solution of the matrix equation boldsymbol {X=Q+A^{H}(Iotimes X-C)^{delta}A}

Consider the nonlinear matrix equation X?=?Q?+?A ^H (I???X???C) ^?? A ( ???=???1 or 0?<?|??|?<?1), where Q is an n×n positive definite matrix, C is an mn ×mn positive semidefinite matrix, I is an m×m identity matrix, and A is an arbitrary mn×n matrix. This equation is connected with a certain interpolation problem when ???=???1. Using the properties of the Kronecker product and the theory for the monotonic operator defined in a normal cone, we prove the existence and uniqueness of the positive definite solution which is contained in the set {X|I???X?>?C} under the condition that I???Q?>?C. The iterative methods to compute the unique solution is proposed. Numerical examples show that the methods are feasible and effective.     

转子叶尖引射式射流的数值研究

转子叶尖射流能够有效地提高压气机的稳定工作裕度, 但是现有的各种射流器结构复杂, 并使发动机的重量增加. 研究目的在于探索一种新型的射流方式, 以方便在压气机中的实现,并且不增加发动机的重量. 采用对转子叶尖前缘位置机匣进行局部修型的方法, 提高了转子叶尖前缘附近流场的轴向速度, 从而产生类似转子叶尖射流的效果. 在Rotor37上的数值分析发现, 该方法能够提高转子的失速裕度约6.7%, 并能使转子的效率与压比有较小的提升. 对比不同机匣修型方案发现, 修型位置对压气机裕度的影响最为明显. 对转子叶尖流场的分析表明, 该方法能够提高转子叶尖前缘的轴向速度, 并将叶尖泄露涡向下游推移, 减小了转子叶尖的流动堵塞, 从而拓宽了转子的失速裕度.      

含一个无外力圆柱面带转动的三维杂交应力元简

根据一种修正的余能原理,建立了一类具有一个无外力圆柱表面及结点含转动自由度的8 结点新型三维杂交应力元. 单元边界位移场选择二次位移插值函数,且与相邻元协调;单元内假定应力场满足以柱坐标表示的平衡方程及圆柱面上无外力边界条件. 数值算例表明,这种特殊杂交应力元在相当粗的网格下即能十分准确地分析圆弧形槽口附近及曲梁的三维（及二维）的孔边应力分布.     

Fabrication of a Hierarchical Ni(OH)2@Ni3S2/Ni Foam Electrode from a Prussian Blue Analogue-Based Composite with Enhanced Electrochemical Capacitive and Electrocatalytic Properties

Developing high-efficiency, cost-effective, and durable electrodes is significant for electrochemical capacitors and electrocatalysis. Herein, a 3D bifunctional electrode consisting of nickel hydroxide nanosheets@nickel sulfide nanocubes arrays on Ni foam (Ni(OH)₂@Ni₃S₂/NF) obtained from a Prussian blue analogue-based precursor is reported. The 3D higher-order porous structure and synergistic effect of different compositions endow the electrode with large specific surface area, facile ion/electron transport path, and improved conductivity. As a result, the Ni(OH)₂@Ni₃S₂/NF electrode exhibits a high specific capacity of 211 mA h g⁻¹ at a current density of 1 A g⁻¹ and 73 % capacity retention after 5000 cycles at 5 A g⁻¹. Moreover, the Ni(OH)₂@Ni₃S₂/NF electrode has superior electrocatalytic activity for the hydrogen evolution reaction with low overpotentials of 140 and 210 mV at current densities of 10 and 100 mA cm⁻², respectively. The synthetic strategy for the unique higher-order porous structure can be extended to fabricate other composite materials for energy storage and conversion.     

Chitosan-coated hemoglobin microcapsules for use in an electrochemical sensor and as a carrier for oxygen

The article describes the preparation of chitosan-coated hemoglobin (Hb-CS) microcapsules by (a) preparing a CaCO₃ precipitate containing Hb, (b) crosslinking Hb with glutaraldehye, (c) coating the particles with chitosan, and (d) preparing Hb-CS microcapsules by removing the CaCO₃ template with a solution of disodium EDTA. The morphology and electrochemical properties of the Hb-CS microcapsules were investigated by scanning electron microscopy, cyclic voltammetry and electrochemical impedance spectroscopy. An oxygen sensor was obtained by immobilizing the Hb-CS microcapsules on the surface of a glassy carbon electrode (GCE) first modified with gold nanoparticles. The application of Hb-CS microcapsules facilitates electron transfer on the surface of GCE and warrants the integrity and biological activity of Hb. The oxygen sensor, operated best at a working voltage of ?0.335  V (vs. SCE), displays a low limit of detection (30 nM). The Hb-CS microcapsules also are shown to release loaded oxygen to an anaerobic aqueous environment within 300 min.

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Graphical abstract The hemoglobin-chitosan microcapsule shows an excellent ability of electrocatalysis and carrying of oxygen.

     

矩阵方程A~TXA=D的双对称最小二乘解

１．引 言 本文用 Ｒｎ×ｍ表示全体 ｎ×ｍ实矩阵集合，用 ＳＲｎ×ｎ（ＳＲ０ｎ×ｎ）表示全体 ｎ× ｎ实对称（实对称半正定）矩阵集合，ＯＲｎ×ｎ表示全体 ｎ× ｎ实正交矩阵集合，ＢＳＲｎ×ｎ表示全体ｎ×ｎ双对称实矩阵集合．这里，一个实对称矩阵Ａ＝（ａｉｊ）ｎ×ｎ被称为双对称矩阵，如果对所有的 　　　　　　　 　　　　　　　　　　　　　　　用Ａ×Ｂ表示矩阵 Ａ与 Ｂ的Ｈａｄａｍａｒｄ乘积，Ｉｋ表示 ｋ× ｋ阶单位矩阵，Ｏ表示零矩阵，Ｓｋ＝（ｅｋ，…，ｅ２，ｅ１）∈ Ｒｋ×ｋ，其中ｅｉ表示Ｉｋ的第ｉ列． 矩阵方程…     

Preparation and characterization of molecularly imprinted microspheres for selective extraction of trace melamine from milk samples

We describe molecularly imprinted microspheres (MIMs) for the selective extraction of melamine from milk. The MIMs were made from melamine as the template molecule, methacrylic acid as the functional monomer, and ethylene glycol dimethacrylate as the linking agent. The MIMs were synthesized by suspension polymerization and characterized by rebinding experiments. They displayed high adsorption capacity, fast rebinding kinetics, and highly specific rebinding of melamine. The imprinting factor is 4.1. Scatchard analysis revealed a one-type rebinding behavior, the dissociation constant and maximum rebinding capacity being 37.59 g L^?1 and 30.85 μmol g^?1, respectively. The MIMs exhibited a 25% cross-reactivity towards atrazine, but less than 3.0% towards prometryn, clenbuterol and metronidazole. In addition, a MIM-based solid phase extraction (MISPE) column for melamine was prepared by packing MIMs into a common SPE cartridge. The MISPE extraction gave recoveries of 89.8 to 100.6% of melamine, with relative standard deviations of 5.9 to 7.5%. There was no significant loss of rebinding capacity after more than 60 repeated uses, thus demonstrating the high stability of the MISPE column. The MSPE column also was applied to the extraction of melamine from spiked liquid and powdered milk with satisfying accuracy and precision.

锂离子电池硼酸盐电极材料的研究进展

硼酸盐作为新一代锂离子电池电极材料,其具有摩尔质量小、资源丰富、环境友好和理论比容量高等优点.本文对LiFeBO3、LiMnBO3和LiCoBO3等硼酸盐正极材料以及Fe3BO6、FeBO3、Cr3BO6、Co2B2O5、Cu3B2O6和VBO3等硼酸盐负极材料的结构、制备方法、电化学性能的研究现状进行了综述,并对存在的主要问题提出了改进方法.     

Searching for counterfeit coins

The well-known counterfeit problem asks for the minimum number of weighings necessary to determine all fake coins in a given set ofn coins. We derive a new upper bound when we know that at mostd coins are defective, improving a previous result of L. Pyber.     

双对称非负定阵一类逆特征值问题的最小二乘解

１．引言 逆特征值问题在工程中有广泛的应用,其研究已有一些很好的结果［１－５］．最近,文［６］还研究了双对称矩阵逆特征值问题,即研究了如下两个问题： 问题Ａ．已知Ｘ∈Ｒｎｘｍ,Ａ＝ｄｉａｇ（λ１…,λｍ）,求Ａ∈ＢＳＲｎｘｎ使 ＡＸ＝ＸＡ,其中 Ｒｎｘｍ表示全体 ｎ ｘ ｍ实矩阵集合, ＢＳＲｎｘｎ表示全体 ｎ ｘ ｎ双对称阵集合． 问题Ｂ．已知Ａ＊ＥＲｎｘｎ,求Ａ∈ＳＥ使 ｜｜Ａ＊－Ａ｜｜＝ ｉｎｆ ｜｜Ａ＊－Ａ｜｜ ＡＦＳＥ其中 ＳＥ是问题 Ａ的解集合,｜｜． ｜｜表示 Ｆｒｏｂｅｎｉｕｓ范数． 在实际问题中, …