Contents 1. Introduction. 2. Heirs. 3. The invariance group of a cut. 4. Review of T-convex valuation rings. 5. The invariance valuation ring of a cut. 6. A method for producing cuts with given signature. 7. Existentially closed extensions. 8. The elementary theory of convex subgroups. 9. The elementary theory of cuts. 10. Counter examples. 1. Introduction. Let X be a totally ordered set. A (De...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

We call an undirected graph X half-transitive if the automorphism group Aut X of X acts transitively on the vertex set and edge set but not on the set of ordered pairs of adjacent vertices of X. In this paper we determine all half-transitive graphs of order p3 and degree 4, where p is an odd prime; namely, we prove that all such graphs are Cayley graphs on the non-Abelian group of order p3 and ...

For any type of abstract algebra, a variety is an equationally defined class of such algebras. Recently, attempts have been made to study varieties of lattice-ordered groups (/-groups). Martinez has shown that the set L of all /-group varieties forms a lattice under set inclusion with a compatible associative multiplication. Certain varieties Sp (p prime) have been proved by Scrimger to be mini...

1. The inhibition of pepsin-catalysed hydrolysis of N-acetyl-l-phenylalanyl-l-phenylalanylglycine by products and product analogues was studied. 2. The non-competitive nature of the inhibition by the product N-acetyl-l-phenylalanine confirms an ordered release of products, and points to a common mechanism (involving an amino-enzyme) for pepsin-catalysed transpeptidation and hydrolysis reactions...

We consider the polynomial time learnability of finite unions of ordered tree patterns with internal structured variables, in the query learning model of Angluin (1988). An ordered tree pattern with internal structured variables, called a term tree, is a rooted tree pattern which consists of tree structures with ordered children and internal structured variables. A term tree is suited for repre...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...