Twist within a somersault

The twisting somersault is a key skill in diving and gymnastics. The components of twist and somersault are defined with respect to anatomical axes, and combinations of multiples of half rotations of twist and somersault define specific twisting somersault skills. To achieve a twisting somersault skill twist must be continuous; otherwise oscillations in twist while somersaulting may be observed. The posture-dependent inertial properties of the athlete and the initial conditions determine if continuous or oscillating twist is observed. The paper derives equations for the amount of somersault required per half twist, or per twist oscillation, without making assumptions about the relative magnitudes of the moments of inertia. From these equations the skills achievable may be determined. The error associated with the common assumption that the medial and transverse principal moments of inertia are equal is explored. It is concluded that the error grows as the number of twists per somersault decreases, when the medial and transverse moments of inertia diverge, and when the longitudinal moment of inertia approaches either the medial or transverse moment of inertia. Inertial property data for an example athlete are used to illustrate the various rotational states that can occur.     

Axiomatisierung Einiger Begriffe aus Nelson Goodmans

Ohne Zusammenfassung

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Nelson algebras through Heyting ones: I

The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley ([15], [16]) for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described (Thm 2.3). The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction ([6], [25]) is also given (Thm 3.6). These results are applied to compare the equational category N of Nelson algebras and some its subcategories (and their duals) with the equational category H of Heyting algebras (and its dual). It is proved (Thm 4.1) that the category N is topological over the category H. The main results of this article are a part of theses of the author's doctoral dissertation at the Nicholas Copernicus University in 1984 (cpmp. [24]).Research partially supported by Polish Government Grant CPBP 08-15.     

A Categorical Equivalence for Tense Nelson Algebras

Studia Logica - In this paper we present a category equivalent to that of tense Nelson algebras. The objects in this new category are pairs consisting of an IKt-algebra and a Boolean IKt-congruence...     

PROFILES OF INDEPENDENT SOCLAL WORK: Julie Nelson

No abstract available for this article.