The concept of a k-pairable graph was introduced by Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In this talk, we introduce a special class of k-pairable graphs which are called uniquely pairable graphs. Then we give a characterization of uniquely pairable graphs in terms of the prime factor decomposi...

There exists a model in a countable language having a unique element which is not definable in Lω1,ω. We answer problem 10.12 from the updated version of Arnie Miller’s problem list, [3]. Definition For a structure M and a ∈ M, we say that a is definable over Lω1,ω if there is a formul ψ ∈ Lω1,ω such that for all b ∈ M a = b ⇔ M |= ψ(b). Theorem 0.1 There is a countable language L and a model M...

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.

Let P1, . . . ,Pn be properties of graphs. A (P1, . . . ,Pn)-partition of a graph G is a partition of the vertex set V (G) into subsets V1, . . . , Vn such that the subgraph G[Vi] induced by Vi has property Pi; i = 1, . . . , n. A graph G is said to be uniquely (P1, . . . ,Pn)-partitionable if G has exactly one (P1, . . . ,Pn)-partition. A property P is called hereditary if every subgraph of ev...

Dunn et al. (2011) attempt an exciting piece of research, investigating which word-order parameters are co-dependent or independent, and which are stable or not. Claims about “universality” have to be taken with several grains of salt, since they investigate only four families, compared to the dozens of families that have been part of samples for the last several decades. More significantly, ho...

1 Mestak O, Kullac R, Mestak J, Nosek A, Krajcova A, Sukop A. Evaluation of the long-term stability of sheath plication using absorbable sutures in 51 patients with diastasis of the recti muscles: an ultrasonographic study. Plast Reconstr Surg. 2012 Nov;130(5):714e-719e. 2 Tadiparthi S1, Shokrollahi K, Doyle GS, Fahmy FS. Rectus sheath plication in abdominoplasty: assessment of its longevity an...

In this paper two classical theorems by Levinson and Marchenko for the inverse problem of the Schrödinger equation on a compact interval are extended to finite trees. Specifically, (1) the Dirichlet eigenvalues and the Neumann data of the eigenfunctions determine the potential uniquely (a Levinson-type result) and (2) the Dirichlet eigenvalues and a set of generalized norming constants determin...

We define the family of n-gram embeddings from strings over a finite alphabet into the semimodule N . We classify all ∈ N that are valid images of strings under such embeddings, as well as all whose inverse image consists of exactly 1 string (we call such uniquely decodable). We prove that for a fixed alphabet, the set of all strings whose image is uniquely decodable is a regular language. © 20...