For this one requires explicit character values on four kinds of

conjugacy classes of elements in [GL.

lambda]] denotes the value of [chi] on

conjugacy class [lambda].

Here, a K-loop is an A-loop with the AIP, a Bruck loop is a Bol loop with the AIP, a Burn loop is Bol loop with the

conjugacy closed property, an homogeneous loop is an A-loop with the IP and a Kikkawa loop is an A-loop with the IP and AIP.

Then, there exists a space shift X', a

conjugacy [THETA] : X' [right arrow] X and an u-right-resolving 1-block code [PHI]' such that [PHI]' [omicron] [THETA] = [PHI], that is to say, the following diagram commutes:

s] Y if, up to

conjugacy, Y [subset] X and [delta] is the restriction of [gamma] to Y.

Describing the

conjugacy classes or characters of [UT.

Since the multiplication of functions on Y corresponds to convolution of central functions on partial permutations, we see that the algebra P turns out to be very closely related to the problems of computing connection coefficients and multiplication of

conjugacy classes in the symmetric groups.

For more complicated

conjugacy classes it turns out to be more convenient to express not directly the characters [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] but rather cumulant

k] to have this complex

conjugacy in the MMT model, the nonlinear energies based on the two auxiliary variables become identical, and we may be able to investigate the energy budget in more detail.

Unfortunately, the "state-of-the-art" tool to detect eye

conjugacy is asking a patient to follow along with a physician's finger, according to Dr.

We remark that this is in general not a polynomial system because of the

conjugacy in the expression [[bar.

Classes which have few types up to

conjugacy are proved to be so-called ~~dependent~~ classes (which have also been called NIP classes).

Tanisaki, Defining ideals of the closures of

conjugacy classes and representations of the Weyl groups, Tohoku Math.

Among the topics are finite groups in which the

conjugacy class sizes form an arithmetic progression, three-dimensional loops as sections in a four-dimensional solvable Lie group, applications of Clifford's theorem to Frobenius groups of automorphisms, examples of Markov chains on spaces with multiplicities, and decomposition numbers for projective modules of finite Chevalley groups.

The announcement of the award cited her, in part, for successfully constructing "a measure-preserving

conjugacy between Thurston's earthquake flow on Teichmuller space and horocycle flow on the associated space of quadratic differentials and as an immediate and long sought-after consequence of this to prove that earthquake flow is ergodic.