The electronic structures of HCP and FCP: A comparison of the results of SCF calculations with several different basis sets,and the inclusion of electron correlation

Ab initio calculations using a variety of basis sets and including electron correlation via the MP3 method are reported for HCP and FCP and their positive ions. Comparisons are made with the available experimental data.N.F.C.R Postgraduate Student.     

On the fuzzy team decision in a changing environment

This paper formulates a fuzzy team decision problem in a changing environment. The concept of a fuzzy set is introduced to formulate the team decision processes in a dynamic environment which contains fuzzy states, fuzzy information functions, fuzzy information signals, fuzzy decision functions and fuzzy actions.     

Two fuzzier implication operators in the theory of fuzzy power sets

The theory of fuzzy power sets requires the use of an implication operator acting within the set of values taken by the membership functions of the fuzzy sets. Two such operators and resulting relationships between fuzzy sets are studied here, and the results compared with previous ones obtained with other implication operators.     

极大非独立集可削去的因子临界图

如果对一个简单图G的每一个与G的顶点数同奇偶的独立集I，都有G-I有完美匹配，则称G是独立集可削去的因子临界图．如果图G不是独立集可削去的因子临界图，而对任意两个小相邻的顶点x与y，G xy足独立集可削去的因子临界图，则称G足极大非独立集可削去的因子临界图，本刻画了极大非独立集可削去的因子临界图。     

Fuzzy processes

In this paper, contributions to fuzzy probability and to differential equations with fuzzy parameters are made.After an introductory section, a review of fuzzy sets and fuzzy algebra is given in Section 2. The main new results of the investigation are contained in Section 3.In Section 3, Zadeh's definition of the probability of a ‘fuzzy event’ the average value of a fuzzy function are extended into the time domain. It is then shown that not only grades of membership, but also probabilistic processes with notions of fuzziness contained, can be defined which obey ordinary, matric, or integro-differential equations. Applications are also given in Section 3.     

Asymptotic independence of distributions of normalized order statistics of the underlying probability measure

Let n denote the sample size, and let r_i ∈ {1,…,n} fulfill the conditions r_i ? r_i?1 ≥ 5 for i = 1,…,k. It is proved that the joint normalized distribution of the order statistics Z_ri:n, i = 1,…,k, is independent of the underlying probability measure up to a remainder term of order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. A counterexample shows that, as far as central order statistics are concerned, this remainder term is not of the order $\text{O((}\text{k}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ if r_i ? r_i?1 = 1 for i = 2,…,k.     

Fuzzy sets and type 2 under algebraic product and algebraic sum

The concept of fuzzy sets of type 2 has been proposed by L.A. Zadeh as an extension of ordinary fuzzy sets. A fuzzy set of type 2 can be defined by a fuzzy membership function, the grade (or fuzzy grade) of which is taken to be a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1].This paper investigates the algebraic properties of fuzzy grades (that is, fuzzy sets of type 2) under the operations of algebraic product and algebraic sum which can be defined by using the concept of the extension principle and shows that fuzzy grades under these operations do not form such algebraic structures as a lattice and a semiring. Moreover, the properties of fuzzy grades are also discussed in the case where algebraic product and algebraic sum are combined with the well-known operations of join and meet for fuzzy grades and it is shown that normal convex fuzzy grades form a lattice ordered semigroup under join, meet and algebraic product.     

Generalization of domination structures and nondominated solutions in multicriteria decision making

The concepts of domination structures and nondominated solutions are important in tackling multicriteria decision problems. We relax Yu's requirement that the domination structure at each point of the criteria space be a convex cone (Ref. 1) and give results concerning the set of nondominated solutions for the case where the domination structure at each point is a convex set. A practical necessity for such a generalization is discussed. We also present conditions under which a locally nondominated solution is also a globally nondominated solution.     

On the closure of sets of attainability in ℝ2

We display a class of control systems in the plane for which it is generically true that the set attainable from any point in the plane is a closed Whitney prestratified set. That is, even if the attainable set of some given system is not closed, we can approximate the system as closely as we wish by another system whose attainable sets are closed.