Some regularity properties of algorithms and additive functions with respect to them

Summary The paper deals with the behaviour of the so-called algorithms with respect to interval filling sequences A connection is established between the uniquely representable points and the continuity points of the algorithms; also strong continuity properties on monotonic algorithms are proved. Finally the results are applied to additive functions. The theorems extend some former results by the authors, by I. Kátai and by A. Járai.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

On the maximal number of certain subgraphs inK r -free graphs

Given two graphsH andG, letH(G) denote the number of subgraphs ofG isomorphic toH. We prove that ifH is a bipartite graph with a one-factor, then for every triangle-free graphG withn verticesH(G) H(T ₂(n)), whereT ₂(n) denotes the complete bipartite graph ofn vertices whose colour classes are as equal as possible. We also prove that ifK is a completet-partite graph ofm vertices,r > t, n max(m, r – 1), then there exists a complete (r – 1)-partite graphG* withn vertices such thatK(G) K(G*) holds for everyK _r -free graphG withn vertices. In particular, in the class of allK _r -free graphs withn vertices the complete balanced (r – 1)-partite graphT _r–1(n) has the largest number of subgraphs isomorphic toK _t (t < r),C ₄,K _2,3. These generalize some theorems of Turán, Erdös and Sauer.Dedicated to Paul Turán on his 80th Birthday     

A new heuristic and an exact approach for a production planning problem

Central European Journal of Operations Research - We deal with a very complex and hard scheduling problem. Two types of products are processed by a heterogeneous resource set, where resources have...     

Partitioning 2-edge-colored graphs by monochromatic paths and cycles

We present results on partitioning the vertices of 2-edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárközy: the vertex set of every 2-edge-colored graph can be partitioned into at most 2α(G) monochromatic cycles, where α(G) denotes the independence number of G. Another direction, emerged recently from a conjecture of Schelp, is to consider colorings of graphs with given minimum degree. We prove that apart from o(|V (G)|) vertices, the vertex set of any 2-edge-colored graph G with minimum degree at least \(\tfrac{{(1 + \varepsilon )3|V(G)|}} {4}\) can be covered by the vertices of two vertex disjoint monochromatic cycles of distinct colors. Finally, under the assumption that \(\bar G\) does not contain a fixed bipartite graph H, we show that in every 2-edge-coloring of G, |V (G)| ? c(H) vertices can be covered by two vertex disjoint paths of different colors, where c(H) is a constant depending only on H. In particular, we prove that c(C ₄)=1, which is best possible.     

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.     

Debye screening of dislocations

Debye-like screening by edge dislocations of some externally given stress is studied by means of a variational approach to coarse grained field theory. Explicitly given are the force field and the induced geometrically necessary dislocation (GND) distribution, in the special case of a single glide axis in 2D, for (i) a single edge dislocation and (ii) a dislocation wall. Numerical simulation demonstrates that the correlation in relaxed dislocation configurations is in good agreement with the induced GND in case (i). Furthermore, the result (ii) well predicts the experimentally observed decay length for the GND developing close to grain boundaries.     

Biological UV dosimeters in quality control of tanning tubes

Although according to the International Radiological Protection Association-International Non-Ionizing Radiation Committee recommendation (1991) the use of sunbeds for cosmetic purposes is not recommended, tanning devices are used widely. Ten different types of commercially available sunbed tubes have been studied using a uracil biological UV dosimeter, and three of them were analyzed in detail. Dimerization effectiveness of the tubes was measured directly, whereas efficiency of erythema induction was calculated weighting the emission spectra by the Commission Internationale de l'Eclairage erythema action spectrum. The data obtained demonstrate that quality control of sunbed tubes has to include not only the determination of the UV doses administered but also the assessment of the health risk due to the UVB and UVA components of the lamp. A method of quality control using the uracil biological dosimeter was elaborated, and the estimation of the "acceptable" exposure time was checked/controlled on 15 volunteers by assessing individually the erythema induction threshold. A correct classification of the sunbed tubes is proposed by characterizing the erythema induction versus DNA-damaging effectiveness of tubes.     

Structure of aqueous solutions of tetraethylammonium chloride investigated by positron annihilation and ultrasonic methods

The structure of aqueous solutions of tetraethylammonium chloride was investigated using compressibility and density measurements and positron annihilation methods. The experimental results are different from those obtained earlier for systems where hydrophobic hydration dominates, although some evidences for formation of cage-like hydrates in liquid phase were observed. The results are interpreted, among others, in terms of competition among different hydrates of the tetraethylammonium cations, hydration of chloride anions, and formation of ionic pairs.     

Refractive index behavior of SiO2-P2O5 glass in optical fiber application

The refractive index of SiO₂-P₂O₅ glass prepared by a modified chemical vapor deposition method is measured using an interference microscope. It is found that the refractive index in bulk form increases linearly at 9.5×10^-4 (mol.%)^-1 as the P₂O₅ concentration increases. It is also found that quenching at extremely high speed reduces the refractive index over 2 mol.% P₂O₅. The wavelength dispersion of the refractive index dn/dλ is constant up to 5 mol.% P₂O₅ producing a refractive index difference of 5×10^-3 compared with fused silica. Consequently, this glass materials is thought to be suitable for wide band-width optical fiber applications.