We develop a theory of sets with distributive products (called shelves and multi-shelves) and of their homology. We relate the shelf homology to the rack and quandle homology. 1. Binary distributive operations Let X be a set. Binary operations ? : X ×X → X with composition x ?1 ?2y = (x ?1 y) ?2 y and the identity x ? y = x form a monoid, M(X). A collection of operations ?i, i ∈ I is called mut...

In this paper the authors have studied the Glivenko congruence R in a 0-distributive nearlattice S defined by " () R b a ≡ if and only if 0 = ∧ x a is equivalent to 0 = ∧ x b for each S x ∈ ". They have shown that the quotient nearlattice R S is weakly complemented. Moreover, R S is distributive if and only if S is 0-distributive. They also proved that every Sectionally complemented nearlattice...

It is generally recognised that the potential positive and negative impacts of geoengineering will be distributed unevenly both geographically and temporally. The question of distributive justice in geoengineering thus is one of the major ethical issues associated with geoengineering. Currently, the question of distributive justice in geoengineering is framed in terms of who gets what (potentia...

In the late 1930's Garrett Birkhoff [3] pioneered the theory of distributive lattices. An important component in this theory is the concept of exponentiation of lattices [4]: for a lattice L and a partially ordered set P let L denote the set of all order-preserving maps of P to L partially ordered b y / ^ g if and only if/(;c) ^ g(x) for each x e P (see Figure 1). Indeed, If is a lattice. This ...

Clark and Lauderdale develop a novel approach for orienting Supreme Court opinions in unidimensional policy space. They argue that the most important portion of a Court’s opinion is not its judgment in favor of one party or another, but its reasoning, for it is this reasoning that becomes binding law and shapes the path of American legal development. The authors thus measure the policy orientat...

A large body of empirical evidence demonstrates that judicial review of agency action is highly politicized, in the sense that Republican appointees are significantly more likely to invalidate liberal agency decisions than conservative ones, while Democratic appointees are significantly more likely to invalidate conservative agency decisions than liberal ones. These results hold for both (a) ju...

As the opening quip of Pam Karlan’s article suggests,1 it is difficult to make sensible predictions about the future of the Roberts Court’s election law jurisprudence based upon the two cases decided during its first year. Even law professors are cautious about drawing inferences from two data points. And given the many opinions rendered in Randall v. Sorrell2 and League of United Latin America...

Generalised Distributive laws in Computer Science are rules governing the transformation of one programming structure into another. In programming, they are programs satisfying certain formal conditions. Their importance has been to date documented in several isolated cases by diverse formal approaches. These applications have always meant leaps in understanding the nature of the subject. Howev...