Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

We introduce and study the properties of a periodic model interpolating between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: the sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as {\em sn-Gordon} model, is performed with potentials written in terms of Jacobi functions. The critical properties of the sn-Gordon theory are discussed by a renormalization-group approach. The critical points, except the sinh-Gordon one, are found to be of BKT type. Explicit expressions for the critical coupling as a function of the elliptic modulus are given.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.

Disjoint Paired-Dominating sets in Cubic Graphs

A paired-dominating set of a graph G is a dominating set D with the additional requirement that the induced subgraph G[D] contains a perfect matching. We prove that the vertex set of every claw-free cubic graph can be partitioned into two paired-dominating sets

Hitting all Maximal Independent Sets of a Bipartite Graph

We prove that given a bipartite graph G with vertex set V and an integer k, deciding whether there exists a subset of V of size k hitting all maximal independent sets of G is complete for the class Sigma_2^P.Comment: v3: minor chang

List coloring in the absence of a linear forest.

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H

Perceived Correspondence of Health Effects as a New Determinant Influencing Purchase Intention for Functional Food

This study has revealed the role of a new factor, perceived correspondence of health effects, in consumer acceptance of functional foods. Using a web survey of 1016 people, we hypothesized and verified the following: when an ingredient does not occur naturally in the carrier but the consumer assigns the same health effect to it as to the carrier, the product’s acceptance will be more positive than it would be if an identical health effect was not associated with the carrier and the functional ingredient. Factors influencing consumer acceptance were examined via binary logistic regression models. According to the results, if a functional food developer fortifies the carrier with an ingredient that does not occur naturally in the carrier, the product can expect higher acceptance if the health effects perceived by consumers are properly matched. In general, it has been found that expected taste and awareness of the product were decisive in all demographic and income groups, whereas perceived correspondence of health effects had a lesser, but still positive influence on acceptance

A new characterization of P6-free graphs.

We study P 6-free graphs, i.e., graphs that do not contain an induced path on six vertices. Our main result is a new characterization of this graph class: a graph G is P 6-free if and only if each connected induced subgraph of G on more than one vertex contains a dominating induced cycle on six vertices or a dominating (not necessarily induced) complete bipartite subgraph. This characterization is minimal in the sense that there exists an infinite family of P 6-free graphs for which a smallest connected dominating subgraph is a (not induced) complete bipartite graph. Our characterization of P 6-free graphs strengthens results of Liu and Zhou, and of Liu, Peng and Zhao. Our proof has the extra advantage of being constructive: we present an algorithm that finds such a dominating subgraph of a connected P 6-free graph in polynomial time. This enables us to solve the Hypergraph 2-Colorability problem in polynomial time for the class of hypergraphs with P 6-free incidence graphs

Examinations of 600-year-old seeds by means of archaeobotanical and genetical methods

About 600-year-old plant seeds were discovered in a well of a mediaeval cellar in the course of an excavation in Budapest. After the archaeobotanic purification seed of 16 species were found in large quantities. Seeds preserved in the best state were selected from each group. The existence of endosperm was analysed in these subfossils, which turned to be successful mainly in the case of grapes (Vitis vinifera) and cornels (Cornus mas). Seeds of these two species contained the most endosperm and remains of the embryo. DNA was extracted with the help of DNEasy Plant Mini Kit and analysed by RAPD-PCR method. The amplification of DNA extracted from cornel seeds resulted in detecting a 1500 by fragment, which makes the comparison of these samples with present-day cornels possible