Regular prism tilings in {{\widetilde{\bf SL_{2}R}}} space

\({{\widetilde{\bf SL_{2}R}}}\) geometry is one of the eight 3-dimensional Thurston geometries, it can be derived from the 3-dimensional Lie group of all 2 × 2 real matrices with determinant one. Our aim is to describe and visualize the regular infinite or bounded p-gonal prism tilings in \({{\widetilde{\bf SL_{2}R}}}\) . For this purpose we introduce the notion of infinite and bounded prisms, prove that there exist infinitely many regular infinite p-gonal face-to-face prism tilings \({\mathcal{T}^i_p(q)}\) and infinitely many regular bounded p-gonal non-face-to-face \({{\widetilde{\bf SL_{2}R}}}\) prism tilings \({\mathcal{T}_p(q)}\) for integer parameters \({p,q; 3 \leq p, \frac{2p}{p-2} < q}\) . Moreover, we describe the symmetry group of \({\mathcal{T}_p(q)}\) via its index 2 rotational subgroup, denoted by pq2 ₁ . Surprisingly this group already occurred in our former work (Molnár et al., J Geometry, 95:91–133, 2009) in another context. We also develop a method to determine the data of the space filling regular infinite and bounded prism tilings. We apply the above procedure to \({\mathcal{T}^i_3(q)}\) and \({\mathcal{T}_3(q)}\) where 6 < q and visualize them and the corresponding tilings. E. Molnár showed, that homogeneous 3-spaces have a unified interpretation in the projective 3-sphere \({\mathcal{PS}^3}\) and 3-space \({\mathcal{P}^3({\bf V}^4,{\bf V}_4, {\bf R})}\) . In our work we will use this projective model of \({{\widetilde{\bf SL_{2}R}}}\) and in this manner the prisms and prism tilings can be visualized on the Euclidean screen of a computer.     

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.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.     

Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.     

An improved method for assay of vitamin C in fish feed and tissues

Summary A method was devised to assay four forms of vitamin C: L-ascorbic acid (AA), dehydroascorbic acid (DHA), ascorbate-2-mono- and polyphosphate (AMP, APP), as well as ascorbate-2-monosulphate (AMS), in sample series of different fish tissues and feed. Direct and indirect detection were combined. Sample extractions were carried out with 0.2 mol L⁻¹ sodium acetate buffer (pH 4.8) and extracts were deproteinized after different chemical or enzymatic reactions, with perchloric acid. The DHA was reduced to AA with dithioerythritol (DTE). Ascorbate oxidase enzyme was used for the detection of background and an acidic phosphatase enzyme for the hydrolysis of different phosphate esters. Ascorbate-2-sulphate was detected directly with help of coinjection of the compound. Chromatographic analysis was carried out with a single column isocratic reverse phase method. The mobile phase was an aqueous buffer of 0.04 M sodium-acetate, 0.05 mM EDTA, 0.5 mM tetrabutylammonium dihydrogen phosphate (TBA) adjusted to pH 3.76 with 85% H₃PO₄ and with 24 mL methanol added to 1000 mL. C-18 columns were used with 0.6 mL min⁻¹ flow rate at 23°C. The vitamin C forms were detected by UV absorption at 250 nm. The determination limit was 1.0–5.0 μg g⁻¹ in AA equivalent. The standard deviations were between 1–6% and depended on the concentrations of vitamin C forms and tissues. Recoveries were between 90–96% in samples. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997     

Small dissymmetry,yet large effects on the transport propertiesof electrolytes based on imide salts: Consequences on performancein Li-ion batteries

To gain better insight into the influence of the anion size and symmetry on the transport properties and thermal stability of an electrolyte based on lithium(fluorosulfonyl)(trifluoromethanesulfonyl)-imide(FTFSI)salt,we performed the physical and electrochemical characterization of an electrolyte based on FTFSI incorporated in standard binary(3 EC/7 EMC)and ternary(EC/PC/3 DMC)alkylcarbonate mixtures.By applying the Jones-Dole-Kaminsky(JDK),Eyring and Arrhenius empirical models to the electrolyte viscosity we show that the activation enthalpy and entropy energy barriers(ΔH≠,ΔS≠)for viscous flow are between 12 and 15 kJ·mol^-1.They are strongly dependent on the solvent nature and are significantly lower than their symmetric anions LiFSI and LiTFSI(19-20 kJ·mol^-1)in the binary mixture.Furthermore,the hydrodynamic radius,rs,calculated by JDK,and the ionicity behavior illustrated by the Walden role,showed that the FTFSI anion is outside the solvation sphere(rs>0.6 nm)which is smaller in the case of an EC/EMC solvent base.In the 3 EC/7 EMC solvent mixture,LiFTFSI is less conductive than in the ternary mixture i.e.,σ_max=8.9 mS cm^-1 at C_max=1.1 mol L^-1 for 3 EC/7 EMC and,σ_max=10.5 mS cm^-1 at max=0.7 mol L^-1 for EC/PC/3 DMC,due to a strong solvation and a greater association of FTFSI ions in the binary solvent mixture.The thermal stability of FTFSI based electrolytes was determined by the shift of the evaporation temperature of the volatile solvents(DMC,EMC)in the presence of salt,towards the higher temperatures.This feature is visible on the thermograms obtained by DSC both with the liquid electrolyte and with charged LMO cathodes in presence of electrolytes.The consequences of these properties on the electrochemical behavior of a graphite(Gr)half-cell,a lithium metal(Li)anode and a manganese lithium oxide(LMO)cathode demonstrated on the one hand the formation of a thick solid electrolyte interphase(SEI)on graphite that consumed a significant amount of lithium i.e.,18%of total capacity of the first charge.Furthermore,LiFTFSI delivered 95%of the initial capacity C=360 mAh g^-1 at C/10 with EC/PC/3 DMC versus 91%when it was combined with 3 EC/7 EMC C=348 mAh g^-1,while the capacities obtained for LiTFSI in EC/PC/3 DMC were the lowest(C=275 mAh g^-1)compared to those of the other salts.After 10 cycles,the capacity loss at C/20 is<2%for LiFSI and LiFTFSI with the two solvent mixtures.On the other hand,manganese dissolution from LMO as well as current collector corrosion were confirmed by post-mortem examination of opened coin cells.The incompatibility of the LMO cathode with an electrolyte based on FTFSI was confirmed by the position of the decomposition peak of charged LMO in contact with this electrolyte observed by DSC These results demonstrate that the nature of the anion as well as the composition of the solvent considerably influence the performance of imide-based lithium salts both on the anode,but especially on the high voltage cathode.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Catalytic transfer hydrogenation of 2-butanone over oxide catalysts

Catalytic transfer hydrogenation of 2-butanone with 2-propanol was studied in gas phase over a series of oxides of different acid-base properties. Although the basic oxides (MgO, La₂O₃) gave high initial conversions, these oxides underwent deactivation during the reaction. This deactivation could be partially prevented by a previous treatment with chloroform of the oxide. The amphoteric oxides (TiO₂, ZrO₂, Al₂O₃) were also active in this reaction. Increasing the acidic character of the catalyst (Nb₂O₅, WO₃) led to a pronounced dehydration of 2-propanol. The results obtained over a series of rare earth oxides (La₂O₃, Sm₂O₃, Gd₂O₃, Dy₂O₃, Er₂O₃) revealed that beside the role of basic and acid sites a correlation seems to exist between the number of unpaired electrons of the metal ion and the catalytic activity, indicating the role of one electron donor sites.     

Theoretical study of the reaction of H atoms with vibrationally highly excited HF molecules

Vibrationally highly excited molecules react extremely fast with atoms and probably with radicals. The phenomenon can be utilized for selectively enhancing the rate of reactions of specific bonds. On the basis of quasiclassical trajectory calculations, the paper analyzes mechanistic details of a prototype reaction, H + HF(v). At vibrational quantum numbers v above 2, the reaction exhibits capture-type behavior, that is, the reactive cross section diverges as the relative translational energy of the partners decreases, both for the abstraction and for the exchange channel. The mechanism of the reaction for both channels is different at low and at high translational energy. At low vibrational energy, the reaction is activated, which is switched to capture-type at high excitation. The reason is an attractive potential that acts on the attacking H atom when the HF molecule is stretched. In contrast to the 6-SEC potential surface of Mielke et al., the switch cannot be observed on the Stark-Werner potential surface, due to a small artificial barrier at high H-HF separation, preventing the reactants from obeying the attractive potential and also proving the importance of the latter. The exchange reaction can be observed even when the total energy available for the partners is below the exchange barrier, because at low translational energies the product F atom of a successful abstraction step can re-abstract that H atom from the intermediate product H2 molecule that was originally the attacker.