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.     

Preparation of activated carbons from cherry stones by activation with potassium hydroxide

Using cherry stones, the preparation of activated carbon has been undertaken in the present study by chemical activation with potassium hydroxide. A series of KOH-activated products was prepared by varying the carbonisation temperature in the 400-900 °C range. Such products were characterised texturally by gas adsorption (N₂, −196 °C), mercury porosimetry, and helium and mercury density measurements. FT-IR spectroscopy was also applied. The carbons prepared as a rule are microporous and macroporous solids. The degree of development of surface area and porosity increases with increasing carbonisation temperature. For the carbon heated at 900 °C the specific surface area (BET) is 1624 m² g⁻¹, the micropore volume is 0.67 cm³ g⁻¹, the mesopore volume is 0.28 cm³ g⁻¹, and the macropore volume is 1.84 cm³ g⁻¹.     

VUV-UV excited luminescent properties of LnCa4O(BO3)3:RE (Ln=Y, La, Gd; Re=Eu, Tb, Dy, Ce)

Calcium lanthanide oxyborate doped with rare-earth ions LnCa₄O(BO₃)₃:RE³⁺ (LnCOB:RE, Ln=Y, La, Gd, RE=Eu, Tb, Dy, Ce) was synthesized by the method of solid-state reaction at high temperature. Their fluorescent spectra were measured from vacuum ultraviolet (VUV) to visible region at room temperature. Their excitation spectra all have a broadband center at about 188 nm, which is ascribed to host absorption. Using Dorenbos’ and Jφrgensen's work [P. Dorenbos, J. Lumin. 91 (2000) 91, R. Resfeld, C.K. Jφrgensen, Lasers and Excite States of Rare Earth [M], Springer, Berlin, 1977, p. 45], the position of the lowest 5d levels E(Ln,A) and charge transfer band E_ct were calculated and compared with their excitation spectra.Eu³⁺ and Tb³⁺ ions doped into LnCOB show efficient luminescence under VUV and UV irradiation. In this system, Ce³⁺ ions do not show efficient luminescence and quench the luminescence of Tb³⁺ ions when Tb³⁺ and Ce³⁺ ions are co-doped into LnCOB. GdCOB doped with Dy³⁺ shows yellowish white light under irradiation of 254 nm light for the reason that Gd³⁺ ions transfer the energy from itself to Dy³⁺. Because of the existence of Gd³⁺, the samples of GdCOB:RE³⁺ show higher excitation efficiency than LaCOB:RE³⁺ and YCOB:RE³⁺, around 188 nm, which indicates that the Gd³⁺ ions have an effect on the host absorption and can transfer the excitation energy to the luminescent center such as Tb³⁺, Dy³⁺ and Eu³⁺.