We study the property of tame combability for groups. We show that quasi-isometries preserve this property. We prove that an amalgamation, A ∗C B, where C is finitely generated, is tame combable iff both A and B are. An analogous result is obtained for HNN extensions. And we show that all one-relator groups are tame combable.

Abstract A logic L has the ‘variable-sharing property’ (VSP) if in all L-theorems of form $A\rightarrow B$, $A$ and $B$ share at least a propositional variable. ‘Ackermann (AP) (B\rightarrow C)$, contains conditional connective ($\rightarrow $). Anderson Belnap consider VSP necessary property any relevant logic, both AP properties (relevant) entailment logic. Now, among logicians, Brady’s BN4 i...

We characterize pairs of convex sets A, Bin the k-dimensional space with the property that every probability distribution (p 1 ,. • • , P~<) has a repsesentation p, =a;· b;, a EA, bE B. Minimal pairs with this property are antiblocking pairs of convex corners. This result is closely related to a new entropy concept. The main application is an information theoretic characterization of perfect gr...

In this article we we continue the study of property Np of irrational ruled surfaces begun in [12]. Let X be a ruled surface over a curve of genus g ≥ 1 with a minimal section C0 and the numerical invariant e. When X is an elliptic ruled surface with e = −1, there is an elliptic curve E ⊂ X such that E ≡ 2C0 − f . And we prove that if L ∈ PicX is in the numerical class of aC0 + bf and satisfies...

B is the de facto standard for evaluation and development of statistical machine translation systems. We describe three real-world situations involving comparisons between different versions of the same systems where one can obtain improvements in B scores that are questionable or even absurd. These situations arise because B lacks the property of decomposability, a property which is a...

A complex diophantine quadruple with the property D (z), where z ∈ Z[√−2], is a subset of Z[√−2] of four elements such that the product of its any two distinct elements increased by z is a perfect square in Z[ √−2]. In the present paper we prove that if b is an odd integer, then there does not exist a diophantine quadruple with the property D(a + b √−2). For z = a + b√−2, where b is even, we pr...

Abstract We systematically study several versions of the disjunction and existence properties in modal arithmetic. First, we newly introduce three classes $\mathrm {B}$ , $\Delta (\mathrm {B})$ $\Sigma formulas arithmetic basic them. Then, prove implications between properties. In particular, among other things, that for any consistent recursively enumerable extension T $\mathbf {PA}(\mathbf {K...

Providing a query interface for querying " schema-less " JSON documents using SQL as declarative query language [1] is finally gaining momentum (e.g. [4], [5]). The approach proposed in [2] called JSON SQL, however, represents an alternative approach as it adheres to the following principles: • extends the SQL 92 grammar ([3]) without changing the existing grammar rules, but by strictly adding ...

We extend the Alpern and Schneider linear time characterization of safety and liveness properties to branching time, where properties are sets of trees. We define two closure operators that give rise to the following four extremal types of properties: universally safe, existentially safe, universally live, and existentially live. The distinction between universal and existential properties capt...

In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate stability results by using Hyers method in modular space for equations without Fatou property, ?b-condition both property. Moreover, with help fixed-point technique involving idea property spaces. Furthermore, suitable counter example is also demonstrated to prov...