The σ<Emphasis Type="Italic">g</Emphasis>-Drazin Inverse and the Generalized Mbekhta Decomposition

In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended Mbekhta decomposition gives a characterization of circularly isolated spectral sets.     

抗核辐射条件的应变计粘贴与防护技术

本文介绍了在重水反应堆中进行应变测量的若干技术成果，主要是较好地解决了用在核辐射条件下，有水流冲刷的环境中的应用变计的粘贴与防护技术。在具有核辐射的环境中测试，通常选用聚酰亚胺胶作粘结剂。但是这种胶需在高温条件下固化，如果被测构件较大，是无法实现的。经测试筛选出具有防水防辐射性能的常温固化胶，并介绍了可用航空导线替代具有抗辐射性能的铠装电缆在堆内进行测量问题。采用有关措施后，经标定，在核辐射前后应     

足底压力统计变化规律测试与侦破技术

利用现场足迹特征,分析罪犯的性别、年龄、身高、体态、行走姿势等个人形体特点,常称为给罪犯“画像”。这一技术在侦破案件中起了一定作用。（１）研究人在常态下行走时留在地面上的平面足迹反映出压力的分布和变化规律,分析压力与年龄的相关性,从中研究出分析年龄的科学方法,提高分析年龄的准确率。（２）研究平面足迹压力与人的性别、身高、体态、行走姿势的相关性找出各自的科学分析方法。（３）从分析理论上全面加以提高,     

A heuristic approach for deriving the priority vector in AHP

This paper proposes an approach for deriving the priority vector from an inconsistent pair-wise comparison matrix through the nearest consistent matrix and experts judgments, which enables balancing the consistency and experts judgments. The developed algorithm for achieving a nearest consistent matrix is based on a logarithmic transformation of the pair-wise comparison matrix, and follows an iterative feedback process that identifies an acceptable level of consistency while complying with experts preferences. Three numerical examples are examined to illustrate applications and advantages of the developed approach.     

Preparation and characterization of alumina-zirconia composite material with different acid ratios by the sol-gel method

Alumina-zirconia composite materials were produced with different acid ratios by the sol-gel method using aluminum isopropoxide and zirconium chloride. The composites were produced by changing acid/alkoxside ratio in alumina. The composite materials were calcinated at 600°C, 900°C and 1300°C. The effects of acid concentration and calcination temperature on the surface area and pore radius were determined from the nitrogen adsorption isotherm at 77 K. The density of the composites was also measured. The minimum density of produced material was recorded as 1.35 g cm⁻³ at an acid/alkoxside ratio of 0.2. The highest specific surface area and pore diameter of the lightest material are 191.86 m² g⁻¹ and 18.4 Ǻ, respectively. Although pore diameter and specific surface area are not changed at any of the experimental temperatures which were tested by decreasing acid/alkoxside ratio, the density is slightly increased. However, it was observed that the calcination temperature significantly affects the surface area and density of the material.      

Equations ax = c and xb = d in rings and rings with involution with applications to Hilbert space operators

This paper reviews the equations ax = c and xb = d from a new perspective by studying them in the setting of associative rings with or without involution. Results for rectangular matrices and operators between different Banach and Hilbert spaces are obtained by embedding the ‘rectangles’ into rings of square matrices or rings of operators acting on the same space. Necessary and sufficient conditions using generalized inverses are given for the existence of the hermitian, skew-hermitian, reflexive, antireflexive, positive and real-positive solutions, and the general solutions are described in terms of the original elements or operators. New results are obtained, and many results existing in the literature are recovered and corrected.     

Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.     

纳米酶

纳米酶(Nanozymes)是由我国科学家首次提出的新概念,它是一类具有生物催化功能的纳米材料,能够基于特定的纳米结构催化天然酶的底物并作为酶的代替品。自2007年首次报道以来,全球已有来自于55个国家的420多个研究机构证实了纳米酶的普遍规律。纳米酶的发现第一次揭示纳米材料蕴含一种独特的纳米效应——类酶催化效应。纳米酶作为一种新材料,既有纳米材料本身的理化性质,又有类似酶的催化功能,兼具天然酶与人工酶的优势于一身。其中,纳米结构不仅赋予纳米酶高效催化功能,而且使纳米酶比天然酶稳定,易于规模化生产。另外,纳米酶独特的多酶活性将为设计廉价、稳定、各种各样全新的催化级联反应提供功能分子。纳米酶是多学科交叉融合的典范,2022年被IUPAC评为十大化学新兴技术。在全球从事化学、酶学、材料学、生物学、医学、理论计算等多领域科学家的共同推进下,如今纳米酶已经成为新的研究热点。我国科学家在这一新兴领域一直发挥着引领作用,解析了纳米酶的构-效关系,将其催化活性提高了约1万倍,实现了超越天然酶的理性设计,创造了全球首个纳米酶产品,出版了纳米酶学英文专著,发布纳米酶术语及中国/国际标准化。更可喜的是,纳...     

Positive and real-positive solutions to the equation axa*=c in C*-algebras

We obtain new representations for the general positive and real-positive solutions of the equation axa*=c in a C*-algebra using the characterization of positivity based on a matrix representation of an element and the generalized Schur complement. Applications to the equation AXA*=C for operators between Hilbert spaces and for finite matrices are given.     

A statistical approach to measure the consistency level of the pairwise comparison matrix

The consistency of the pairwise comparison matrix (PCM) has been extensively studied in the Analytic Hierarchy Process. Most of the existing approaches for the consistency test of the PCM are based on the consistency ratio threshold (0.1) introduced by Saaty (1977). To accurately measure the consistency level of the PCM, a statistical approach based on the significance level is proposed in this paper by combining the hypothesis test and the random consistency index. The proposed statistical approach is applied to an education evaluation problem in order to demonstrate the rationality and reliability of it.