# a 6 Integers 11 B ( 2011 ) Degrees of Streams

Communal Partitions of Integers

There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter. In this note, we consider the analagous question counting the number of k-tuples of nonnegative integers none of which is more than 1/(k−1) of the sum of all the integers. We give an explicit function for the generating function which counts these k-tuples in th...

On Finite Groups With Two Irreducible Character Degrees

Evil twins alternate with odious twins

An integer is called evil if the number of ones in its binary expansion is even and odious if the number of ones in the binary expansion is odd. If we look at the integers between 0 and 15 we find that 0, 3, 5, 6, 9, 10, 12, 15 are evil and that 1, 2, 4, 7, 8, 11, 13, 14 are odious. Next we say that if two consecutive integers are evil then this is a pair of evil twins and that if two consecuti...

Causes and Functional Consequences of Denitrifying Bacteria Community Structure in Streams Affected to Varying Degrees by Watershed Urbanization

CAUSES AND FUNCTIONAL CONSEQUENCES OF DENITRIFYING BACTERIA COMMUNITY STRUCTURE IN STREAMS AFFECTED TO VARYING DEGREES BY WATERSHED URBANIZATION by

On Free Partially Associative Triple Systems

A triple system is partially associative (by definition) if it satisfies the identity (abc)de + a(bcd)e + ab(cde) 0. This paper presents a computational study of the free partially associative triple system on one generator with coefficients in the ring Z of integers. In particular, the Z-module structure of the homogeneous submodules of (odd) degrees 5 11 is determined, together with explicit ...