On the Injective Tensor Product of Distinguished Frechet Spaces

An example of two distinguished Fréchet spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E?F is not distinguished. On the other hand, it is proved that for arbitrary reflexive Fréchet space E and arbitrary compact set K the space of E - valued continuous functions C(K, E) is distinguished and its strong dual is naturally isomorphic to ? where L¹(μ) = C(K)¹.     

关于Scott开滤子拓扑的core紧性

本文讨论了那样一些ＤＣＰＯ（即定向完备偏序集）的刻划问题,它们在赋以Ｓｃｏｔｔ开滤子拓扑后,其拓扑空间的开集格是连续格。该问题也是由ＬａｗｓｏｎＪＤ。与ＭｉｓｌｏｖｅＭ．提出的一系列公开问题中的一个［１］。     

Ideals of Priestley powers of semilattices

Let X be a poset and Y an ordered space; X ^Y denotes the poset of continuous order-preserving maps from Y to X with the discrete (respectively, Scott, Lawson) topology. If S is a -semilattice, its ideal semilattice, and T a bounded distributive lattice with Priestley dual space P(T), it is shown that the following isomorphisms hold: Moreover, and sufficient conditions and necessary conditions for the isomorphism to hold are obtained (both necessary and sufficient if S is a distributive -semilattice). Received September 27, 1995; accepted in final form April 6, 1998.     

Continuous Selections as Uniform Limits of δ-Continuous ε-Selections

We prove a selection theorem which unifies the nonconvex-valued and the zero-dimensional selection theorems. Our proof is based on a new method which unifies the methods of outside and inside approximations of a given lower semicontinuous multivalued mapping. As an application, we obtain a unified selection theorem ('modulo" a countable subset of the domain) and a theorem on density of selections.     

Z-Continuous Posets and Their Topological Manifestation

A subset selection Z assigns to each partially ordered set P a certain collection Z P of subsets. The theory of topological and of algebraic (i.e. finitary) closure spaces extends to the general Z-level, by replacing finite or directed sets, respectively, with arbitrary Z-sets. This leads to a theory of Z-union completeness, Z-arity, Z-soberness etc. Order-theoretical notions such as complete distributivity and continuity of lattices or posets extend to the general Z-setting as well. For example, we characterize Z-distributive posets and Z-continuous posets by certain homomorphism properties and adjunctions. It turns out that for arbitrary subset selections Z, a poset P is strongly Z-continuous iff its Z-join ideal completion Z P is Z-ary and completely distributive. Using that characterization, we show that the category of strongly Z-continuous posets (with interpolation) is concretely isomorphic to the category of Z-ary Z-complete core spaces. For suitable subset selections Y and Z, these are precisely the Y-sober core spaces.     

Lp-Computability

In this paper we investigate conditions for L^p-computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p ≥ 1 and a compact computable rectangle I ? ?^q, we show that an L^p function f ∈ L^p(I) is L^P-computable if and only if (i) f is sequentially computable as a linear functional and (ii) the L^p-modulus function of f is effectively continuous at the origin of ?^q.     

具连续变量的非线性时滞差分方程的振动性

本文研究了一类具有连续变量的非线性时滞差分方程的振动性,给出了该类方程振动的几个充分条件。     

Chebyshev-Fourier级数部分和逼近单调型连续函数的误差估计

研究了用Chebyshev级数部分和逼近单调型连续函数,得到了逼近的误差估计,并提出了3个问题,这3个问题的核心就是估计式中的因子“logn”能否去掉。     

(Mini)emulsion Polymerization: Effect of the Segregation Degree on Polymer Architecture

A continuous loop reactor was used for the production of 2‐ethylhexyl acrylate (2‐EHA), methyl methacrylate (MMA) and acrylic acid (AA) pressure sensitive adhesive by both emulsion and miniemulsion polymerization. Similar high monomer conversions were achieved in both processes, but striking differences in polymer architecture were found. A mathematical model was used to analyze these differences concluding that because the costabilizer suppressed monomer diffusion from miniemulsion droplets, the average polymer concentration in the polymerization loci was lower in the miniemulsion process. This resulted in less chain transfer to polymer, and hence in lower sol molecular weight and gel content.

     

Continuous clavulanic acid adsorption process

Adsorption kinetics and equilibrium data of clavulanic acid, a β-lactam antibiotic, on ion-exchange resin Amberlite IRA 400 were utilized to carry out the modeling and simulation of a continuous adsorption process. These simulations allowed the estimation of yield, concentration, and purification factors of the process utilizing the product final concentration. Experimental runs of this process were carried out using the conditions pointed out by simulation studies. Comparison of the experimental results and those calculated by the proposed model showed that the model could describe very well the main features of the continuous process.