With this chapter we provide a compact yet complete survey of two most remarkable “representation theorems”: every arguesian projective geometry is represented by an essentially unique vector space, and every arguesian Hilbert geometry is represented by an essentially unique generalized Hilbert space. C. Piron’s original representation theorem for propositional systems is then a corollary: it s...

This study examined Three Wishes (a projective technique commonly used with children) in boys with Duchenne muscular dystrophy (DMD), a fatal, progressive illness (n = 74). A reliable and parsimonious scoring system was developed to code wish type. Probands' responses were compared with unaffected siblings (n = 32) and a male comparison group (n = 43). Contrary to what was expected, the DMD gro...

One hundred and fifty-eight clinical psychologists practising in Britain completed a questionnaire concerning their use of and views about psychological assessment. The respondents reported spending on average slightly more than 50% of their working day on face-to-face clinical work and 13% of their time with clients on individual assessment. The results were compared to those of a similar surv...

This study examines whether coding open answers in a picture-based test, as to the extent they reflect the fear of being laughed at (i.e., gelotophobia), demonstrates sufficient validity to construct a semi-projective test for the assessment of gelotophobia. Previous findings indicate that cartoon stimuli depicting laughter situations (i.e., in the pilot version of the Picture-Geloph; Ruch et a...

(1) find colim-acyclic objects in Ab. Here, Ab denote the category of abelian groups and Ab denote the (abelian) functor category for the small category C. The functor colim : Ab → Ab is the direct limit functor and F ∈ Ab is colim-acyclic if colimi F = 0 for i ≥ 1 (see [16] and [5], and the classical books of Cartan and Eilenberg [2] and of MacLane [13]). It is clear that if F is projective th...

each. The one after 5 iterations and the other after 100 iterations. The two sets of polygons are projective transformations of each other. Figure 13: Two projective transformed initial polygons evolve identically, at 5 and 100 iterations. 6 Concluding Remarks We have attempted to outline a rather comprehensive theory of iterative invariant smoothings for planar curves and polygons, generalizin...

Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...

A family F of sets has property B(s) if there exists a set S whose intersection with each set in F is non-empty but contains fewer than s elements . P . Erdős has asked whether there exists an absolute constant c such that every projective plane has property B(c) . In this paper, the authors, as a partial answer to this question, obtain the result that for n sufficiently large, every projective...

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...