Gas transport through homogeneous and asymmetric polyethersulfone membranes

Both homogeneous and asymmetric polyethersulfone (PES) membranes were prepared by solvent casting. The sorption and permeation behavior of CO₂, O₂, and N₂ using these two kinds of cast PES membranes and commercially available homogeneous PES film was investigated to extract the pressure dependence of gas permeability and the permselectivity for CO₂ relative to N₂, and to confirm the validity of the working assumption that a skin layer in an asymmetric membrane can be essentially replaced by a thick homogeneous dense membrane. The pressure dependence of the mean permeability coefficient to CO₂ in homogeneous membranes obeys the dual-mode mobility model. The ideal separation factor for CO₂ relative to N₂ at an upstream pressure of 0.5 MPa attains ca. 40, while the permeability to CO₂ is about 2.7 Barrer at the same upstream pressure. The same separation factor in asymmetric membranes amounts to 35. The diffusion behavior for the skin layer in an asymmetric membrane with a thin skin layer can be simulated approximately by that in a homogeneous dense membrane. © 1993 John Wiley & Sons, Inc.     

单A直和子空间

引入单直和子空间的概念,证明了线性空间可唯一分解为单直和子空间的直和,并且给出了计算方法.     

A New Entropy Function to Analyze Isentropic Processes of Ideal Gases with Variable Specific Heats

A new entropy function s⁺ is defined in terms of the existing entropy function s° and temperature as s⁺ = s° − R lnT to facilitate the analysis of isentropic processes of ideal gases with variable specific heats. The function s⁺ also makes it possible to calculate the entropy changes of ideal gases during processes when volume information is available instead of pressure information and the variation of specific heats with temperature is to be accounted for. The introduction of the function s⁺ eliminates the need to use the dimensionless isentropic functions relative pressure P_r and relative specific volume v_r of ideal gases and to tabulate their values. The P_r and v_r data are often confused with pressure and specific volume, with an adverse effect on the study of the second law of thermodynamics. The new s⁺ function nicely complements the existing s° function in entropy change calculations: the former is conveniently used when volume information is given while the latter is used when pressure information is available. Therefore, the introduction of the new entropy function s⁺ is expected to make a significant contribution to the thermodynamics education and research by streamlining entropy analysis of ideal gases.     

Three-Way Decision Models Based on Ideal Relations in Multi-Attribute Decision-Making

In recent years, research on applications of three-way decision (e.g., TWD) has attracted the attention of many scholars. In this paper, we combine TWD with multi-attribute decision-making (MADM). First, we utilize the essential idea of TOPSIS in MADM theory to propose a pair of new ideal relation models based on TWD, namely, the three-way ideal superiority model and the three-way ideal inferiority model. Second, in order to reduce errors caused by the subjectivity of decision-makers, we develop two new methods to calculate the state sets for the two proposed ideal relation models. Third, we employ aggregate relative loss functions to calculate the thresholds of each object, divide all objects into three different territories and sort all objects. Then, we use a concrete example of building appearance selection to verify the rationality and feasibility of our proposed models. Furthermore, we apply comparative analysis, Spearman’s rank correlation analysis and experiment analysis to illustrate the consistency and superiority of our methods.     

Ideals and Subalgebras in BCI-Algebras

We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal.AMS Subject Classification (1991): 06F35, 03G25.The second author was supported by the LG Yonam Foundation (1995).     

Divisorial Linear Algebra of Normal Semigroup Rings

We investigate the minimal number of generators and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely many divisorial ideals I such that (I)C. It follows that there exist only finitely many Cohen–Macaulay divisor classes. Moreover, we determine the minimal depth of all divisorial ideals and the behaviour of and depth in arithmetic progressions in the divisor class group.The results are generalized to more general systems of linear inequalities whose homogeneous versions define the semigroup in a not necessarily irredundant way. The ideals arising this way can also be considered as defined by the nonnegative solutions of an inhomogeneous system of linear diophantine equations.We also give a more ring-theoretic approach to the theorem on minimal number of generators of divisorial ideals: it turns out to be a special instance of a theorem on the growth of multigraded Hilbert functions.     

Prime Rings with Involution Equipped with Some New Product

Let R be a ring with involution *. We consider R as a ring equipped with a new product r s = rs + sr^*. The relationship between (ordinary) ideals of R and right ideals of R with respect to the product is studied.AMS Subject Classification (2000): 16W10, 16D25     

The Lattice of Deductive Systems on Hilbert Algebras

The concept of deductive system on a Hilbert algebra was introduced by A. Diego. We show that the set Ded A of all deductive systems on a Hilbert algebra A forms an algebraic lattice which is distributive.AMS Classification (2000): 06F35, 03G25, 08A30     

On a Problem of Karpilovsky

Let G be a finite elementary group. Let ⁿ (G) denote the nth power of the augmentation ideal (G) of the integral group ring G. In this paper, we give an explicit basis of the quotient group Q_n(G) = ⁿ(G)/ⁿ⁺¹ (G) and compute the order of Qⁿ (G).2000 Mathematics Subject Classification: 16S34, 20C05     

On Positive and Weakly Positive Implicative BCI-Algebras

Prove that the notion of positive implicative BCI-algebras coincides with that of weakly positive implicative BCI-algebras, thus the whole results in the latter are still true in the former, in particular, one of these results answers definitely the first half of J. Meng and X.L. Xin’s open problem: Does the class of positive implicative BCI-algebras form a variety? The second half of the same problem is: What properties will the ideals of such an algebra have? Here, some further properties are obtained.