New upper bounds for the chromatic number of a graph*

We show that for any graph G, the chromatic number χ(G) ≤ Δ₂(G) + 1, where Δ₂(G) is the largest degree that a vertex ν can have subject to the condition that ν is adjacent to a vertex whose degree is at least as big as its own. Moreover, we show that the upper bound is best possible in the the following sense: If Δ₂(G) ≥ 3, then to determine whether χ(G) ≤ Δ₂(G) is an NP‐complete problem. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 117–120, 2001     

Angle-resolved photoemission of chain-like molecules: the electronic band structure of sexithiophene and sexiphenyl

Here we report the electronic π-band structure of sexithiophene obtained from 6T(010) oriented films. The angle-resolved valence band photoemission results taken parallel and perpendicular to the molecular axis are compared to those of sexiphenyl and interpreted in terms of intra- and inter-molecular band dispersion. We show that the strong photoemission intensity variations with emission angle parallel to the molecular axis are well reproduced by the Fourier transforms of the molecular orbitals of the isolated molecules. These results imply that ARUPS can yield quite detailed information about molecular geometry, both in terms of molecular orientation and internal structure.     

Fluoridhaltige Gäste in Alumosilicaten: Tetrafluoroborate in dem Sodalithen Na8Al6Si6O24(BF4)2

In the course of investigations on optical properties resulting from the interaction of fluorides with alumosilicate host materials and rare earth guests, a well defined BF₄^– ion wasfound to be incorporated within the sodalite of composition Na₈Al₆Si₆O₂₄(BF₄)₂. The resulting cubic molecular structure, which was determined by Rietveld methods (space group P4 n, a = 906.91 pm, wRp = 0.045, Rp = 0.027), contains one anion in each sodalite cage and is, contrarily to expectations, thermally stable. NMR spectroscopic investigations indicated a fast rotatory motion of the BF₄^– tetrahedra at room temperature and agreed with the tetrahedral BF₄^– ions found in IR and Raman spectra. Preliminary attempts to obtain a luminescent material by incorporation of Eu³⁺ through aqueous ion exchange only yielded low rare earth concentrations, giving rise to characteristic red emission lines at 581 nm (⁵D₀ → ⁷F₁) and 615 nm (⁵D₀ → ⁷F₂) in a 1:2 intensity ratio. The material unexpectedly exhibited a strong broad band emission at 520 nm after calcination under Ar, which is attributed to the formation of an Eu²⁺ species. Further calcination under air partially reestablished the Eu³⁺ emission.     

Synthesis,spectral, thermal and structural study of bis(2-bromobenzoato-O,O′)-bis(methyl-3-pyridylcarbamate-N)-zinc(II)

The new complex bis(2-bromobenzoato-O,O′)-bis(methyl-3-pyridylcarbamate-N)-zinc(II), [Zn(2-BrC₆H₄COO)₂mpc₂] (1), has been prepared and characterized by elemental analysis, IR spectroscopy, thermal analysis and single-crystal X-ray diffraction. The bonding between the ligands and the central atom was investigated by DFT studies. The theoretical infrared spectrum of 1 was compared with the experimental data. The complex proved to be thermally stable up to 165 °C. Volatile intermediate products of its thermal decomposition were identified by mass spectrometry. The coordination environment of the zinc atom consists of two nitrogen atoms of two methyl-3-pyridylcarbamate ligands and is chelated by four oxygen atoms of two 2-bromobenzoate ligands (ZnO₄N₂ – chromophore).     

Redox freezing temperature and Bartenev equation in a 25Na2O-15B2O3-60SiO2 glass doped with chromium and manganese

In a melt with the base mol% composition 25Na₂O-15B₂O₃-60SiO₂, doped with chromium and manganese, a redox reaction takes place during cooling the melt. This reaction was studied using high temperature UV-vis spectroscopy. Above 600 °C, the reaction is in equilibrium and shifted during cooling to the Cr³⁺ and Mn³⁺ species. At temperatures between 500 and 600 °C, the kinetics of the redox reaction is decisive and the cooling rate plays an important part. At temperatures < 500 °C, the reaction is frozen in. The smaller the cooling rate, the smaller is the Cr⁶⁺ concentration and the lower is the fictive redox temperature.The kinetics of the reaction was described by a differential equation assuming Arrhenian behaviour. The equation was numerically solved and fictive temperatures were calculated. These temperatures depended on cooling rate similar to Bartenev equation. Activation energies calculated hereof were around 38 kJ?mol⁻¹ larger than those inserted into the kinetic equation. The experimentally determined activation energy is 565 kJ?mol⁻¹, a value much larger than the activation energies of diffusion of the polyvalent elements. The rate determining step in the case of the Cr³⁺/Cr⁶⁺/Mn²⁺/Mn³⁺ system is the electron transfer reaction, because a notable structural rearrangement is necessary during the course of the electron transfer reaction (Cr³⁺ and Cr⁶⁺ occur in octahedral and tetrahedral coordination, respectively). The latter leads to a large inner reorganisation energy and to an activation energy similar to that of the viscous flow. In the case of the redox reaction between copper and arsenic, the activation energy is much smaller (210 kJ?mol⁻¹), because here the coordination numbers do not change during the course of the redox reaction.     

Polyhydroxyalkanoate (PHA) Biosynthesis from Whey Lactose

Summary: The potential of three different microbial wild type strains as polyhydroxyalkanoate (PHA) producers from whey lactose is compared. Homopolyester and co-polyester biosynthesis was investigated by the archaeon Haloferax mediterranei and the eubacterial strains Pseudomonas hydrogenovora and Hydrogenophaga pseudoflava. H. mediterranei accumulated 50 wt.-% of poly-3-(hydroxybutyrate-co-6%-hydroxyvalerate) in cell dry mass from hydrolyzed whey without addition of 3-hydroxyvalerate (3HV) precursors (specific productivity q_p: 2.9 mg/g h). Using P. hydrogenovora, the final percentage of poly-3-hydroxybutyrate (PHB) amounted to 12 wt.-% (q_p: 0.03 g/g h); co-feeding of valeric acid resulted in the production of 12 wt.-%. P-3(HB-co-21%-HV) (q_p: 0.02 g/g h). With H. pseudoflava, it was possible to reach 40 wt.-% P-3 (HB-co-5%-HV) on not-hydrolyzed whey lactose plus valeric acid as 3HV precursor (q_p: 9.1 mg/g h); on hydrolyzed whey lactose without addition of valeric acid, the strain produced 30 wt.-% of PHB (q_p: 0.16 g/g h). The characterization of the isolated biopolyesters completes the study.     

Measuring capital market efficiency: long-term memory,fractal dimension and approximate entropy

We utilize long-term memory, fractal dimension and approximate entropy as input variablesfor the Efficiency Index [L. Kristoufek, M. Vosvrda, Physica A 392, 184(2013)]. This way, we are able to comment on stock market efficiency after controlling fordifferent types of inefficiencies. Applying the methodology on 38 stock market indicesacross the world, we find that the most efficient markets are situated in the Eurozone(the Netherlands, France and Germany) and the least efficient ones in the Latin America(Venezuela and Chile).     

Voltage enhancement in dye-sensitized solar cell using (001)-oriented anatase TiO2 nanosheets

A nanocrystalline TiO₂ (anatase) nanosheet exposing mainly the (001) crystal faces was tested as photoanode material in dye-sensitized solar cells. The nanosheets were prepared by hydrothermal growth in HF medium. Good-quality thin films were deposited on F-doped SnO₂ support from the TiO₂ suspension in ethanolic or aqueous media. The anatase (001) face adsorbs a smaller amount of the used dye sensitizer (C101) per unit area than the (101) face which was tested as a reference. The corresponding solar cell with sensitized (001)-nanosheet photoanode exhibits a larger open-circuit voltage than the reference cell with (101)-terminated anatase nanocrystals. The voltage enhancement is attributed to the negative shift of flatband potential for the (001) face. This conclusion rationalizes earlier works on similar systems, and it indicates that careful control of experimental conditions is needed to extract the effect of band energetic on the current/voltage characteristics of dye-sensitized solar cell.     

How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlation detection — classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short-term memory and long-term memory. To do so, we analyze the behavior of the estimators for independent, short-range dependent, and long-range dependent processes with innovations from eight different distributions. We find that apart from a combination of very high levels of kurtosis and skewness, both estimators are quite robust to distributional properties. Importantly, we show that R/S$R/S$ is biased upwards (yet not strongly) for short-range dependent processes, while M-R/S$M\text{-}R/S$ is strongly biased downwards for long-range dependent processes regardless of the distribution of innovations.