We study embeddings of P mathvariant="normal">S mathvariant="normal...

Theories of fundamental measurement begin with purported qualitative laws about observable relations among certain entities, and using these laws a numerical representation is constructed which reflects their formal structure. The best known example, extensive measurement, arose from an analysis of such familiar physical measures as mass and length. In measuring mass, the classical theory suppo...

and Applied Analysis 3 Definition 2.2 see 22 . Let E,D;Γ be an abstract convex space. If a mapping G : D → 2 satisfies

Hexapod characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. If all error values are known or can be calculated then they can be included in a model which will eliminate their defective effect. In practice there a...

We introduce a partial order on the set of all normal polytopes in Rd . This poset NPol(d) is a natural discrete counterpart of the continuum of convex compact sets in Rd , ordered by inclusion, and exhibits a remarkably rich combinatorial structure. We derive various arithmetic bounds on elementary relations in NPol(d), called quantum jumps. The existence of extremal objects inNPol(d) is a cha...

In this paper, we first establish collective fixed points theorems for a family of multivalued maps with or without assuming that the product of these multivalued maps is Φ-condensing. As an application of our collective fixed points theorem, we derive the coincidence theorem for two families of multivalued maps defined on product spaces. Then we give some existence results for maximal elements...

We describe an O(log(n)) time with O(n) processors optimal algorithm for finding the maximal elements of a set. The model of parallel computation we consider is the CREW-PRAM, i.e. it is the synchronous shared memory model where concurrent reads are allowed but no two processors can simultaneously attempt to write in the same memory location (even if they are trying to write the same thing).

– [root property] The minimum element, referred to as the root, of T is f(X1, . . . , Xn), where X1, . . . , Xn are distinct variables. – [leaves property] The maximal elements, referred to as the leaves, of T are all and only (variants of) the left hand sides of the rules defining f . Non-maximal elements of T are referred to as branches. – [parent property] If π is a pattern of T different fr...

Dehne presented an optimal algorithm to compute the contour of the maximal elements of n planar points on a pn pn mesh. We have calculated that Dehne’s algorithm requires 23pn steps and we have been able to reduce the required steps to 19pn through pre-sorting and using an efficient strategy in dividing the mesh into halves. It has also been established that any implementation of Dehne’s algori...