Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

配位化学课程中研究型教学模式探讨

In this paper, the implementation of research-oriented teaching mode in coordination chemistry was introduced, including the strategies, main contents and evaluation.     

SYNTHESIS AND PROPERTIES OF COPOLYMERS FROM 1-[3,5-BIS(TRIMETHYLSILYL)PHENYL]-2-PHENYLACETYLENE

Copolymerization of 1-[3,5-bis(trimethylsilyl)phenyl]-2-phenylacetylene (m,m-(Me₃Si)₂DPA) with other diphenylacetylene derivatives and their copolymer properties were investigated. Homopolymerization of m,m-(Me₃Si)₂DPA by TaCl₅─n-Bu₄Sn (1:2) did not give the polymer due to steric hindrance. However, m,m-(Me₃Si)2DPA copolymerized with diphenylacetylene (DPA), 1-phenyl-2-[p-(trimethylsilyl)phenyl]acetylene (p-Me₃Si DPA), and 1-phenyl-2-[m-(trimethylsilyl)phenyl]acety-lene (m-Me₃SiDPA) in the presence of TaCl₅─n-Bu₄Sn at various feed ratios to give copolymers in moderate yields. The formed copolymers were yellow to orange solids, which were soluble in common organic solvents such as toluene and CHCl₃. The highest weight-average molecular weights (M_w) of these copolymers reached ca. 6 × 105 and tough films could be obtained by solution casting. Their onset temperatures of weight loss in air were observed around 400°C, indicating high thermal stability. The oxygen permeability coefficients at 25°C of copoly(m,m-(Me₃Si)₂ DPA/DPA) (feed ratio 1:1) and copoly(m,m-(Me₃Si)₂DPA/p-Me₃SiDPA) (feed ratio 1:2) were 21 and 100 barrers, respectively, medium in magnitude among polymers from substituted acetylenes.     

Primary Studies on Variation in Position of Trifluoromethyl Groups in Several Aromatic Group‐14 Derivatives by 19F‐NMR Spectroscopy

Variation in the position of CF₃ groups in several aromatic Group‐14 compounds was studied by ¹⁹F‐NMR spectroscopy. In these compounds R_nECl_4?n (n=1 or 2; E=Si, Ge, or Sn; R=2,4,6‐(CF₃)₃C₆H₂ (=Ar), 2,6‐(CF₃)₂C₆H₃ (=Ar′), or 2,4‐(CF₃)₂C₆H₃ (=Ar″)), Ar, Ar′, and Ar″ are all bulky, strongly electron‐withdrawing ligands. The ¹⁹F‐NMR studies of the variation in position of the CF₃ substituents in these compounds as revealed by chemical shifts could be correlated with the electronegativities of the central elements E, and with intramolecular E–F interactions derived from single‐crystal X‐ray diffraction data. These interactions are considered to play an important role in the stabilization of these compounds.     

Matrix Infrared Spectroscopy and Quantum‐Chemical Calculations for the Coinage‐Metal Fluorides: Comparisons of Ar?AuF,Ne?AuF,and Molecules MF2 and MF3

The reactions of laser‐ablated Au, Ag, and Cu atoms with F₂ in excess argon and neon gave new absorptions in the M? F stretching region of their IR spectra, which were assigned to metal‐fluoride species. For gold, a Ng? AuF bond was identified in mixed neon/argon samples. However, this bonding was much weaker with AgF and CuF. Molecules MF₂ and MF₃ (M=Au, Ag, Cu) were identified from the isotopic distribution of the Cu and Ag atoms, comparison of the frequencies for three metal fluorides, and theoretical frequency calculations. The AuF₅ molecule was characterized by its strongest stretching mode and theoretical frequency calculations. Additional evidence was observed for the formation of the Au₂F₆ molecule.     

Electronic structure and thermochemistry for monocarbides MC,MC+ and MC− (M=Zn,Cd, Hg): CCSD(T) and DFT works

In this work, the ab-initio coupled cluster CCSD(T) method and the B3LYP, BP91W and CAM-B3LYP functional of DFT method in conjunction with the aug-cc-pVTZ-PP basis have been applied to study the group 12 monocarbides MC, MC⁺ and MC^?. The potential energy curves (PECs) for the three electronic states ³Σ^?, ⁵Σ^? and ¹Δ of the MC and the two states ²∑^- and ⁴∑^- for the MC⁺ cations and MC^? anions have been investigated. In addition, Bond distance Re, transition energy Te, vibrational frequency ω_e, ionization energy IE, electron affinity EA, dipole moment μ, dissociation energy D₀ and heat formation ΔH°f₀/ΔH°f₂₉₈, were determined for each species. The analysis of the dissociation energy for ZnC, CdC and HgC shows the decrease in the stability of the monocarbides from Zn to Hg. For ΔH°f₀/ΔH°f₂₉₈ values of MC, which are not known experimentally or theoretically, we recommend the following CCSD(T) predictions of ZnC, CdC and HgC: 181.3/178.54, 180.65/178.4 and 175.35/174.71 kcal/mol respectively. Comparing the three functionals with the CCSD(T) results, the CAM-B3LYP functional shows excellent predictive agreement for the various properties of the group 12 monocarbides.     

The Surface Analysis Working Group at the Consultative Committee for Amount of Substance,Metrology in Chemistry and Biology: A successful initiative by Martin Seah

Dr Martin Seah, NPL, was the initiator, founder, and first chairman of the Surface Analysis Working Group (SAWG) at the Consultative Committee for Amount of Substance, Metrology in Chemistry and Biology (CCQM) at the Bureau International des Poids et Mesures (BIPM), the international organization established by the Metre Convention. This tribute letter summarizes his achievements during his chairmanship and his long-running impact on the successful work of the group after his retirement.     

The enormity of the zinc deficiency problem and available solutions; an overview

The societal cost of micronutrient deficiency (MND) or the “hidden hunger” is in millions of dollars/year, reducing the GDP of some countries by as much as 11%. Zn is an important micronutrient for both plants and animals. An estimated 17% of the world population, or around 1.1 billion people, are at the risk of zinc (Zn) deficiency. The deficiency has been related to adverse pregnancy outcomes, stunted growth, premature deaths, immune system dysfunctions, neuro-behavioral disorders, and recently with the failure to recover from COVID-19. These health risks associated with Zn deficiency have compelled FAO and WHO to recommend Zn fortification of diet. Correcting Zn deficiency is a challenge due to several reasons. Close to half of the agricultural soils are Zn deficient, and chemical Zn fertilizers are costly and ineffective. Developing Zn-rich crops through plant breeding and genetic engineering is challenging. Zn-dense diet is costly and cannot be implemented in the low-income region most affected by Zn deficiency. Lack of consensus among regulatory bodies on defining and diagnosing Zn deficiency in plants and Humans. Awareness and other sociocultural issues. Among the most important available solutions are zinc biofortification of the cereal crops, use of zinc biofertilizers, development of Zn-efficient crops with reduced phytate content. The use of Zn supplements, dietary modification, and diversification, especially with fish, are proposed as the most accessible and affordable solutions. Awareness programs in areas suffering the most from Zn deficiency are required. Despite the suggestions from FAO and WHO, global efforts to combat Zn deficiency matching those for combating diseases like HIV are not in place. Coordinated efforts of the international community, especially policy-makers, agricultural scientists, dieticians, physicians, and others, are required to address the issue of hidden hunger.