It is proven that the intersection of convex transversals of finitely many sets in R is a convex polytope, possibly empty. Related results on support hyperplanes and complements of finite unions of convex sets are given. MSC 2000: 52A20

Objectives: This nonlinear three-dimensional finite element analysis (FEA) study evaluated the effect of number implants, distal implant inclination, and use angled abutments on stress magnitude distribution in cortical bone (CB), abutment screw (AS), prosthetic (PS) implant-supported fixed complete dentures. Methods: Nonlinear 3D FEA models mandibular dentures were created with five, four, or ...

The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from P(ω) to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokob...

Throughout this paper, we denote byN and R the sets of positive integers and real numbers, respectively. Let D be a nonempty closed subset of a real Banach space X. A mapping T : D → D is said to be nonexpansive, if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ D. Let N D and CB D denote the family of nonempty subsets and nonempty closed bounded subsets of D, respectively. The Hausdorff metric on CB D is...

This note studies the following question: If a researcher is given a finitely supported mixed strategy for each player over a continuous strategy space, does there exist a game whose unique Nash equilibrium is given by these mixed strategies? This note finds that any set of finitely supported mixed strategies on metric spaces can be represented as the unique Nash equilibrium to a separable game...

The endocannabinoid system is known to regulate neural progenitor (NP) cell proliferation and neurogenesis. In particular, CB(2) cannabinoid receptors have been shown to promote NP proliferation. As CB(2) receptors are not expressed in differentiated neurons, CB(2)-selective agonists are promising candidates to manipulate NP proliferation and indirectly neurogenesis by overcoming the undesired ...

For -continuous endofunctors of Set an ordering of a final coalgebra is exhibited which makes a CPO. Moreover, an initial algebra, considered as a canonical subobject of , has as its ideal completion. In more generality, for -continuous endofunctors of locally finitely presentable categories the analogous result holds: here the ordering is considered on the hom-sets for all finitely presentable...

Background Single-use (SU) technologies supply a number of values to any mode of bioprocessing, but can provide some specific and enabling features in continuous bioprocessing (CB) implementations [1-3]. Most every operation in a CB process train is now supported by a commercially available single-use, or at least hybrid, solution (Figure 1). First of all, many of the SU equipment and solutions...

For which groups G is it true that whenever one forms a direct limit of left G-sets, lim −→ i∈I Xi, the set of its fixed points, (lim −→I Xi) , can be obtained as the direct limit lim −→I (X i ) of the fixed point sets of the given G-sets? An easy argument shows that this holds if and only if G is finitely generated. If we replace “group G ” by “monoid M”, the answer is the less familiar condit...