Following the last talk on graph homomorphisms, we continue to discuss some examples of graph homomorphisms. But this time we will focus on some models, that is, the homomorphism G → H for the graph H with fixed weights. The main reference is Section 1 in [2].

We show that if a graph H is k-colorable, then (k−1)-branching walks on H exhibit long range action, in the sense that the position of a token at time 0 constrains the configuration of its descendents arbitrarily far into the future. This long range action property is one of several investigated herein; all are similar in some respects to chromatic number but based on viewing H as the range, in...

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...

We provide a correspondence between the subjects of duality and density in classes of finite relational structures. The purpose of duality is to characterise the structures C that do not admit a homomorphism into a given target B by the existence of a homomorphism from a structure A into C. Density is the order-theoretic property of containing no covers (or ‘gaps’). We show that the covers in t...

Let X be a Riemann surface equipped with a projective structure (i.e., a covering by coordinate charts such that the transition functions are of the form z 7−→ (az + b)/(cz + d)). Let L be a line bundle on X such that L = TX . Let J (L) −→ X denote the jet bundle of order m for the line bundle L. For i ≥ j, there is a natural restriction homomorphism from J (L) onto J (L). We prove that for any...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

Based on hyperbolic geometric considerations, Roger and Yang introduced an extension of the Kauffman bracket skein algebra that includes arcs. In particular, their is a deformation quantization certain commutative curve algebra, there Poisson homomorphism between smooth functions decorated Teichmu?ller space. this paper, we consider surfaces with punctures which are not 3-holed sphere have idea...