A note on acyclic domination number in graphs of diameter two

A subset S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γ_a(G), is called the acyclic domination number of G. Hedetniemi et al. [Acyclic domination, Discrete Math. 222 (2000) 151-165] introduced the concept of acyclic domination and posed the following open problem: if δ(G) is the minimum degree of G, is γ_a(G)?δ(G) for any graph whose diameter is two? In this paper, we provide a negative answer to this question by showing that for any positive k, there is a graph G with diameter two such that γ_a(G)-δ(G)?k.     

Order Embeddings with Irrational Codomain: Debreu Properties of Real Subsets

The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-valued strictly isotone function (semicontinuous or not) also admits a representation by means of a lower (respectively, upper) semicontinuous strictly isotone function that takes values in the set of irrational numbers. These results are obtained by means of a direct construction. Moreover, they can be related to Cantor’s characterization of the real line to obtain much more general results on the semicontinuous Debreu properties of a wide family of subsets of the real line.      

Structural and electrical properties of core–shell structured GaP nanowires with outer Ga2O3 oxide layers

This paper presents a review of our current experimental research on GaP nanowires grown by a vapor deposition method. Their structural, electrical, opto-electric transport, and gas-adsorption properties are reviewed. Our structural studies showed that a GaP nanowire consisted of a core–shell structure with a single-crystalline GaP core and an outer Ga₂O₃ layer. The individual GaP nanowires exhibited n-type field effects. Their electron mobilities were in the range of about 6 to 22 cm²/V s at room temperature. When the nanowires were illuminated with an ultraviolet light source, an abrupt increase of conductance occurred resulting from carrier generation in the nanowire and de-adsorption of adsorbed OH^- or O₂ ^- ions on the Ga₂O₃ surface shell. Using an intrinsic Ga₂O₃ shell layer as a gate dielectric, top-gated GaP nanowire field-effect transistors were fabricated and characterized. Like other metal oxide nanowires, the carrier concentration and mobility of GaP nanowires were significantly affected by the surface molecular adsorption of OH or O₂. The GaP nanowire devices were fabricated as sensors for NO₂, NH₃, and H₂ gases by using a simple metal decoration technique. PACS 73.63.-b; 72.80.Ey; 85.35.-p     

Neutron interferometry in gravitational field with torsion

We consider the possibility of finding experimental evidence of the fifth force with the measurement of a phase shift of neutron beams via an interferometric apparatus and also a possible rotation of the polarization plane of polarized neutron beams when torsion is introduced in a gravitational field.     

Extremal positive and self-adjoint extensions of suboperators

This work is supported in part by the fund OTKA (No. 5-134).