We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (?1)-enumeration of these lozenge tilings. In the case that a = b = c, we also provide closed formulas for certain...

Perceptual scientists have recently enjoyed success in constructing mathematical theories for specific perceptual capacities, capacities such as stereovision, auditory localization, and color perception. Analysis of these theories suggests that they all share a common mathematical structure. If this is true, the elucidation of this structure, the study of its properties, the derivation of its c...

A new nite element method is presented that features the ability to include in the nite element space knowledge about the partial diierential equation being solved. This new method can therefore be more eecient than the usual nite element methods. An additional feature of the partition-of-unity method is that nite element spaces of any desired regularity can be constructed very easily. This pap...

In previous studies we found that generalized functions can be smooth, discrete, periodic or discrete periodic and they can either be local or global and they are regular or generalized functions. We also saw that these properties were related to Poisson’s summation formula on one hand and to Heisenberg’s uncertainty principle on the other. In this paper, we interlink these studies and show tha...

When, in the primeval sea, creatures first began to crawl, "right" and "left" came into being, yielding neuronal nets to control response to the sidedness of stimuli. In the half billion years of moving and sensing, two brains have evolved, the right and the left; and human experience now shows them to be roughly equivalent, potentially independent, conscious entities. This dramatic fact is evi...