The members of every community can be thought of as linked by a network of one-to-one ties between people who are related to one another as friends, neighbors, relatives, or coworkers. The distance between any two people is the minimum number of steps through ties in the network needed to go from one to the other. A common and unusual characteristic of communities is that these distances are no...

The term ‘emergence’ often causes confusion in science and philosophy, as it is used to express at least two quite different concepts. We can label these concepts strong emergence and weak emergence. Both of these concepts are important, but it is vital to keep them separate. We can say that a high-level phenomenon is strongly emergent with respect to a low-level domain when the high-level phen...

Sustainable development requires economic development without endangering biodiversity, without exploiting natural resources too fast and without excessive pollution. The question is if these aims can be realized at the same time and what are the options for substitution between different types of capital. The difference between the notions of weak and strong sustainability revolves around the ...

To verify fixed-time constraints in Grid workflow systems, consistency and inconsistency conditions have been defined in conventional verification work. However, with a view of the run-time uncertainty of activity completion duration, we argue that, although the conventional consistency condition is feasible, the conventional inconsistency condition is too restrictive and covers several differe...

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...

This paper considers strong consistency of heteroscedasticity and autocorrelation consistent covariance matrix estimators. Sometimes such estimators in the literature are referred to as Newey-West estimators. Weak consistency proofs for these estimators can be found in White (1984), Newey and West (1987), Gallant and White (1988), Andrews (1991), Hansen (1992a), and De Jong and Davidson (1997)....

In this paper, we propose an alternative notion, called weak forgetting, of forgetting a set of predicates in a first-order theory. One important feature of this new notion is that the result of weak forgetting is always first-order expressible. In contrast, this is not the case for the traditional notion of forgetting, called strong forgetting, introduced by Lin and Reiter. As a consequence, t...

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...