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].

A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...

in this paper, we give a necessary condition for function in l^2with its dual to generate a dual shearlet tight frame with respect to admissibility.

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...

The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

On the basis of the tree-regular language theory, we study document transformation and schema transformation. A document is represented by a tree t, and a schema is represented by a tree-regular language L. Document transformation is de ned as a composition of a marking function mPC and a linear tree homomorphism h, where P is a pattern and C is a contextual condition. Pattern P is a tree-regul...

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...

We study the lattice finite representability of the Bochner space Lp(μ1, Lq(μ2)) in `p{`q}, 1 ≤ p, q < ∞, and then we characterize the ideal of the operators which factor through a lattice homomorphism between L∞(μ) and Lp(μ1, Lq(μ2)).