SPECTRUM-PRESERVING ELEMENTARY OPERATORS ON B（X）

1.IntroductionLetXbeaninfinitedimensionalcomplexBanachspaceandB(X)theBanachalgebraofallboundedlinearoperatorsonX.ForTEB(X),a(T),asusual,willdenotethespectrumofT.Let4bealinearmapfromB(X)intoitself.4isspectrum-preservingifa(di(T))=a(T)forallTEB(X);4isspectrum-compressingifa(4(T))ga(T)forallTEB(X).Itisclearthatif4isunital(i.e.,ac(I)=I),thenacisspectrum-preserving(spectrum-compressing)ifandonlyif4preservesinvertibilityinbothdirections(preservesinvertibility),i.e.,4(T)isinvertibleifando…     

有机锗化合物中碳氢的快速测定

报道了用Co3O4 作覆盖氧化剂分析有机锗化合物中碳氢元素的方法。通过对 9个样品的十几次分析 ,碳、氢的相对误差分别小于± 1.30 % ,4 .4 0 %。方法简便 ,结果稳定可靠 ,可用于含锗有机化合物的碳氢分析。     

Infinite lexicographic products

We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define dense substructures in infinite products and show that any countable product of countable transitive homogeneous structures has a unique countable dense substructure, up to isomorphism. Furthermore, this dense substructure is transitive, homogeneous and elementarily embeds into the product. This result is then utilized to construct a rigid elementarily indivisible structure.     

Efficiency of composite vs. conically shaped chromatographic columns

The theory of composite chromatographic columns has been re-examined and general equations relating their efficiency to those of individual columns were derived. The derivations were based on elementary principles without reference to the principle of variance additivity. Derived also, were general equations for the efficiency of columns with continuously varying diameters, HETP and other properties from which formulae for special cases of practical interest were deduced. An example comparing the efficiencies of two columns, one conical and the other composite was given. The calculations show clearly that the conical column is superior in efficiency for the same total length and total retention volume.     

1，4二环己基取代六元瓜环与Na(Ⅰ)自组装实体的合成与晶体结构

A novel complex of a new 1,4-dicyclohexyl cucurbituril(DCYQ[6]) with sodium(Ⅰ) ion was synthesized, and the crystal structure was determined by X-ray diffraction technique. In this self-assembled entity both the cavity interaction of DCYQ[6] included a nitrate anion and the portal interaction of the dipole carbonyls of DCYQ[6] with sodium cations lead to form self assembled molecular capsules. The crystal structure of the entity shows a packing of the self assembled molecular capsules connected by hydrogen bonds of water molecules. CCDC: 271400.     

Molecular entity vacancy model

A novel molecular entity vacancy model was proposed to describe thermodynamic properties in a multicomponent solution system using its binary interaction parameters only. A derivation of the model for its general expression has been shown in detail. Under some special conditions, this model may be reduced to Flory–Huggins equation, Wilson equation and non-random two liquids (NRTL) equation as well as molecular interaction volume model (MIVM), respectively, and can be verified by Gibbs–Duhem equation, and can express thermodynamic properties of partially miscible systems. The predicted activities are in good agreement with experimental data of some liquid alloys. The results show that the model is of better predictability and reliability because it has a certain physical basis.     

Corrigendum to the Elementary Process Theory

To fully resolve Theseus' paradox in the framework of the Elementary Process Theory, this paper corrects its formalism and axiomatization.     

Optical microscopy to study single nanoparticles electrochemistry: From reaction to motion

Nanoparticles (NPs)-based electrochemical devices are generating a growing interest and optical microscopy has recently proven to be a powerful tool to apprehend their electrochemical behavior. Through several striking examples, this review demonstrates how label-free optical imaging coupled to an electrochemical actuation can be used to probe operando the physical and electrochemical properties of single NPs, with high resolution and sensitivity and without additional emitters. Such an approach can be particularly relevant to establish clear structure-motion/reactivity relationships required to optimize NPs exploited as electrode materials.     

Second graders articulating ideas about linear functional relationships

In this paper, we explore the ideas that second grade students articulate about functional relationships. We adopt a function-based approach to introduce elementary school children to algebraic content. We present results from a design-based research study carried out with 21 second-grade students (approximately 7 years of age). We focus on a lesson from our classroom teaching experiment in which the students were working on a problem that involved a linear functional relationship (y = 2x). From the analysis of students’ written work and classroom video, we illustrate two different approaches that students adopt to express the relationship between two quantities. Students show fluency recontextualizing the problem posed, moving between extra-mathematical and intra-mathematical contexts.