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.     

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.     

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.     

Continuous Restricted Radial Motion of a Gas under the Action of a Piston

The possibility of continuous conjugation of the straightline radial motion of a gas sphere toward the center and away from the center with the motion where the gas in the entire sphere stops simultaneously is shown. The motion is described by an invariant submodel of rank 1. Time reflections allow one to construct a solution that describes a periodic continuous restricted motion of the gas sphere under the action of a piston.     

Inheritance of surjectivity for partial differential operators on spaces of real analytic functions

For an open set let A(Ω) be the space of real analytic functions on Ω. Improving our previous results, we prove a new quantitative characterization of the linear partial differential operators P(D) which are surjective on A(Ω). This implies that P(D) is surjective on if P(D) is surjective on A(Ω) for some Ω≠∅. Further inheritance properties for the surjectivity of P(D) on A(Ω) are also obtained.     

Generalized elementary functions

We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions.