Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Submanifolds of dimension n-1 in [epsilon]n̳ with normals satisfying a Lipschitz condition.

"Paper written under Contract Nonr. 58304."

The English flora: or, A catalogue of trees, shrubs, plants and fruits, natives as well as exotics, cultivated, for use or ornament, in the English nurseries, greenhouses and stoves, arranged according to the Linnæan system; with the Latin trivial, and common English names, and an English index referring to the Latin names. Also, a general catalogue of seeds ...

Added t.-p. in Latin.

Trivial poems, and triolets. Written in obedience to Mrs. Tomkin's commands,

Edited from the original manuscript by Sir Walter Scott. cf. Introd.

Life's trivial round,

Mode of access: Internet.

Irreducible cyclic presentations of the trivial group

We produce families of irreducible cyclic presentations of the trivial group. These families comprehensively answer questions about such presentations asked by Dunwoody and by Edjvet, Hammond, and Thomas. Our theorems are purely theoretical, but their derivation is based on practical computations. We explain how we chose the computations and how we deduced the theorems.

The effects of ingroup-outgroup membership on minority influence when group membership is determined by a trivial categorisation

Two experiments are reported which investigate the influence of ingroup and outgroup minority influence where group membership was determined according to a trivial dimension. The results of the first experiment replicate an earlier study and show that an ingroup minority has significantly more influence than an outgroup minority. In the second study the connotations associated with membership of the ingroup and outgroup (positive/negative) were experimentally manipulated. When ingroup/outgroup membership was associated with a positive/negative image respectively, the ingroup minority had the most influence. However, when ingroup/outgroup membership was associated with a negative/positive image, as predicted, an outgroup minority had more influence than an ingroup minority. These results are interpreted as supporting an intergroup analysis of minority influence processes.

Minority influence and 'trivial' social categorization

This experiment examines ingroup and outgroup minority influence when group membership was determined by a trivial categorization. The results show that ingroup minorities had more public influence than outgroup minorities when the categorization was trivial and when subjects also believed that they were similar to their ingroup. However, no differences were found when group membership was not associated with similarity. These results are interpreted as supporting the social identification model of social influence.

Approximation of Lipschitz Mappings

2000 Mathematics Subject Classification: 46B03

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.

Trivial Jensen measures without regularity

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.