It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic subgroups. Similarly, the Bruhat order is also the conjunction of a larger number of simpler quotients obtained by projecting onto two-sided (i.e., “double”) quotients by pairs of maximal parabolic subgroups. Each one-sided quotient may be r...

In this study, a series of interaction coefficients of the Brønsted-Guggenheim-Scatchard specific interaction theory (SIT) have been estimated up to 200 degrees C and 400 bars. The interaction coefficients involving Cl- estimated include epsilon(H+, Cl-), epsilon(Na+, Cl-), epsilon(Ag+, Cl-), epsilon(Na+, AgCl2 -), epsilon(Mg2+, Cl-), epsilon(Ca2+, Cl-), epsilon(Sr2+, Cl-), epsilon(Ba2+, Cl-), ...

Leavitt path algebras are shown to be algebras of right quotients of their corresponding path algebras. Using this fact we obtain maximal algebras of right quotients from those (Leavitt) path algebras whose associated graph satisfies that every vertex connects to a line point (equivalently, the Leavitt path algebra has essential socle). We also introduce and characterize the algebraic counterpa...

We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini[11] and Tits[15]. MSC2000 : 05B25, 51E24, 20B25.

Recently, Bergman [2] provided an explicit, nonrecursive description of the partial quotients in (1), and by implication, in (2). (This description is our Theorem 3.) The purpose of this paper is to prove Bergman's result, and to provide similar results for the continued fractions given in [3] and [4]. We start off with some terminology about "strings." By a string9 we mean a (finite or infinit...

Completeness is a desirable, although uncommon, property of abstract interpretations, formalizing the intuition that, relatively to the underlying abstract domains, the abstract semantics is as precise as possible. We consider here the most general form of completeness, where concrete semantic functions can have different domains and ranges, a case particularly relevant in functional programmin...

We introduce generalized class invariants as quotients of Thetanullwerte, which realize the computation of class polynomials more efficiently than as quotients of values of the Dedekind η−function. Furthermore, we prove that these invariants are units in the corresponding class field as most of their classical counterparts. keywords: class polynomials, theta functions, complex multiplication

We announce misère-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. We also introduce several advances in the structure theory of misère quotients, including a connection between the combinatorial structure of normal and misère play.

We give a unified approach to analysing, for each positive integer s, a class of finite connected graphs that contains all the distance transitive graphs as well as the locally s-arc transitive graphs of diameter at least s. A graph is in the class if it is connected and if, for each vertex v, the subgroup of automorphisms fixing v acts transitively on the set of vertices at distance i from v, ...