Two-Dimensional Spaces in Which There Exist Contiguous Points

Orders for Which There Exist Exactly Two Groups

Introduction. A long-standing problem in group theory is to determine the number of non-isomorphic groups of a given order. The inverse problem–determining the orders for which there are a given number of groups–has received considerably less attention. In this note, we will give a characterization of those positive integers n for which there exist exactly 2 distinct groups of order n (up to is...

There Exist Caps Which Block All Spaces of Fixed Codimension in G (n, 2)

Recall that a cap in PG(n, 2) is simply a set of points with no three collinear. A cap which intersected all codimension 2 subspaces would yield an interesting example of a 2-block: 2-blocks have been much studied in the literature. An interesting folklore conjecture, which received considerable attention, had it that in fact no cap is a 2-block. Although this conjecture can be shown to be true...

Institute for Mathematical Physics Does There Exist the Lebesgue Measure in the Infinite-dimensional Space? Does There Exist the Lebesgue Measure in the Infinite-dimensional Space?

We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional

Do acupuncture points exist?

We used synchrotron x-ray fluorescence analysis to probe the distribution of four chemical elements in and around acupuncture points, two located in the forearm and two in the lower leg. Three of the four acupuncture points showed significantly elevated concentrations of elements Ca, Fe, Cu and Zn in relation to levels in the surrounding tissue, with similar elevation ratios for Cu and Fe. The ...

Common Fixed Points of Two Commuting Mappings in Complete Metric Spaces