Banach spaces that admit support sets

It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

     

An improved Menshov-Rademacher theorem

We study the a.e. convergence of orthogonal series defined over a general measure space. We give sufficient conditions which contain the Menshov-Rademacher theorem as an endpoint case. These conditions turn out to be necessary in the particular case where the measure space is the unit interval and the moduli of the coefficients form a nonincreasing sequence. We also prove a new version of the Menshov-Rademacher inequality.

     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

Spatial chaotic structure of attractors of reaction-diffusion systems

The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

     

The formation of the Ba(CuOx)1−y(CO3)y

Carbocuprate compounds are generally described as multiple perovskites with CO ₃ ² - and Cu-O alternating layers containing Ba and/or Sr; they have gained an unexpected importance in the high temperature superconductivity field, because many compounds with transition temperature above 100 K belong to this class of materials.We have started a systematic study on phase formation and stabilisation in the Ba-Cu-C-O system in the temperature range 20-600°C, by using thermal analysis techniques. Starting from a BaCO₃-BaO₂-CuO mixture (311 mol), a new phase isomorphic with BaCO₃ formed after heat treatment above 390°C in air. TG, DSC, EGA and high temperature XRD were employed to follow the complex interaction of the reactants with the atmosphere and the formation of the new phase.     

不共轴光学系统自动优化中的有关问题

描述不共轴光学系统计算机优化中坐标变换与逆变换、“入瞳”与光线坐标、像面基准与质量函数定义的一致性问题。     

计算机专用实时母系统在VAX／VMS环境下的实现

“母系统—子系统”的工作方式是计算机专用实时系统研制中的一次重要尝试,本文闸明计算机专用实时母系统在VAX/VMS环境下的工程实现。     

Primal-dual interior point approach for computingl 1-solutions andl ∞-solutions of overdetermined linear systems

This paper concerns solving an overdetermined linear systemA ^T x=b in the leastl ₁-norm orl -norm sense, whereA ^m×n ,m<n. We show that the primal-dual interior point approach for linear programming can be applied, in an effective manner, to linear programming versions of thel ₁ andl -problems. The resulting algorithms are simple to implement and can attain quadratic or superlinear convergence rate. At each iteration, the algorithms must solve a linear system with anm×m positive-definite coefficient matrix of the formADA ^T , whereD is a positive diagonal matrix. The preliminary numerical results indicate that the proposed algorithms offer considerable promise.This research was supported in part by Grants NSF DMS-91-02761 and DOE DE-FG05-91-ER25100.     

新工科视阈下石油化工类高校应用化学专业课程体系重构

Taking a typical local and industry-orientated applied chemistry major as an example with focusing on the major changes in the form and content of the petrochemical industry, the way to reform the core curriculum system and teaching contents is presented. Based on the changing tendency of refinement of the petrochemical industry, a complete curriculum system with distinctive industry characteristics is set up according to the principles of the emerging engineering education (3E) with several reasonable suggestions. A new model for the construction of a 3E major in chemistry-related majors is suggested. It is a good reference for the construction of curriculum systems for other local and industry-orientated colleges who want to make 3E reform.     

The theoretical basis of column chromatography in multicomponent separations. Part 2: Peak capacity. Column systems with good selectivity

The selectivity of a column system, S, defined by equation 28, includes a variation coefficient (β) of plate number with capacity ratio which has a large influence on the peak capacity, as shown in Fig. 18. Some typical chromatograms are given. In order to predict S for a column system from Kovat's Index, equations 40 and 41 are given to calculate the constant of the carbon number rule for squalane at different temperatures or for different stationary phases. The specific retention value of heptane on squalane at different temperatures can be calculated from equation 42. The nonpolarity index, defined by equation 43, was used to calculate the retention value of heptane on various stationary phases. In liquid chromatography, the order of elution may be reversed by changing the composition of the eluent on the same chemically bonded silica (manufactured in China). The linear relations between the log retention values of different kinds of solutes or of a single solute on the silicas of different surface areas when using the same eluent are given.