Current techniques for generating a knowledge space, such as QUERY, guarantees that the resulting structure is closed under union, but not that it satisfies wellgradedness, which is one of the defining conditions for a learning space. We give necessary and sufficient conditions on the base of a union-closed set family that ensures that the family is well-graded. We consider two cases, depending...

We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension ω0, or, equivalently, of small transfinite dimension ω0; that is, the family consists of compact metrizable spaces whose transfinite dimension is ω0, and every compact metrizable space with transfinite dimension ω0 is embeddable in a space of the ...

Abstract. We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a smoothing operator of nonzero but possibly arbitrarily small degree. This family naturally interpolates between the 2D Euler equation ...

urbanisation is still one of the social themes in developing countries. in china, the rapid process of urbanisation and economic growth bring to people not only more opportunities for creating new life and pursuing happiness, but also the challenge to face various and complex social, economical and environmental problems. among them some are outstanding, like the shrinking plowland devoured by ...

Let L be the space of line transversals to a nite family of pairwise disjoint compact convex sets in R 3. We prove that each connected component of L can itself be represented as the space of transversals to some nite family of pairwise disjoint compact convex sets.

Technology affected human life in many ways in different eras of mankind history. Today, the information and telecommunication technology has revolutionized basic structures of human life. Changes are from the whole to the parts and vice versa, which include family and society too. Family lost its former structure in the information age and differentiated from patriarchy family. Societies have ...

Salkowski [11], one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space E. In this paper, we adapt definition of such curves to time-like curves in Minkowski 3-space E31. Thereafter, we introduce an explicit parametrizati...