Generally, stronger reproductive isolation is expected between sympatric than between allopatric sibling species. Such reproductive character displacement should predominantly affect premating reproductive isolation and can be due to several mechanisms, including population extinction, fusion of insufficiently isolated incipient species and reinforcement of reproductive isolation in response to...

In this paper, we prove a few facts and some cardinal properties of the space permutation degree introduced in [6]. More precisely, that if productXn is Lindel?f (resp. locally Lindel?f) space, then SPnX also Lindel?f). We product Xn weakly Moreover, investigate preservation network weight, ?-character local density topological spaces by functor G-permutation degree. It proved preserves infinit...

One appealing vision is that a user should be able to design a motion trajectory by setting a small number of keyframes and constraints—and that the resulting motion should remain optimal in some way. Variations of this problem have appeared in computer graphics, biomechanics, and robotics (e.g., [9] [6] [8] [7] [4]) Despite great interest and research progress, however, optimization is still v...

In applications of Weyl character formula for AN Lie algebras, it can be shown that the followings are valid by the use of some properly chosen system of weights which we call fundamental weights. Characters can be attributed conveniently to Weyl orbits rather than representations. The classsical Schur function SN (x1, x2, .., xN ) of degree N can be defined to be character of the representatio...

This is to certify that I have examined this copy of a doctoral dissertation by Steve Capell and have found that it is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made. Date: In presenting this dissertation in partial fulfillment of the requirements for the Doctoral degree at the University of Washington, I agree ...

Let H denote a semisimple Hopf algebra over an algebraically closed field k of characteristic 0. We show that the degree of any irreducible representation of H whose character belongs to the center of H∗ must be a divisor of dimk H .

Supposem and n are integers such that 1 ≤ m ≤ n, andH is a subgroup of the symmetric group Sm of degree m. Define the generalized matrix function associated with the principal character of the group H on an m×m matrix B = (bij) by

In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a degree three 3 Deligne cocycle. We also establish the general Riemann-Roch theorem in twisted K-theory and find some applications in the study of twisted K-theory of compact simple Lie groups.