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     

Spectroscopy of infrared transitions of Pr ions in Ga-Ge-Sb-Se glasses

Electronic transitions of Pr³⁺ ions in Ga-Ge-Sb-Se glasses corresponding to emissions in the infrared region were studied by means of absorption and emission spectroscopies and fluorescence lifetimes measurements. Transition probabilities, radiative lifetimes, branching ratios, and quantum efficiencies of most of the emission transitions including the infrared ones occurring around 1.3, 1.7, and 2.4 μm were estimated based on a standard Judd-Ofelt analysis.     

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.     

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.     

In vitro inhibitory activity of essential oil vapors against Ascosphaera apis

This work evaluates the in vitro inhibitory activity of 70 essential oils (EOs) in the vapor phase for the control of Chalkbrood disease caused by Ascosphaera apis Maassen ex Claussen (Olive et Spiltoir). Two wild strains isolated from infected honey bee colonies together with one standard collection strain were tested by the microatmosphere method. From 70 EOs, 39 exhibited an antifungal effect against A. apis standard and wild strains. The greatest antifungal action was observed for EO vapors from Armoracia rusticana, followed by Thymus vulgaris, Cymbopogon flexosus, Origanum vulgare and Allium sativum. An investigation of chemical composition by GC-MS revealed, that the most active EOs contained allyl isothiocyanate, citral, carvacrol and diallyl sulfides as the main constituents. The chemical composition plays a key role, as activities of different EOs from the same botanical species were different according to their composition.     

Thermal-stress induced phenomena in two-component material:Part Ⅱ

The paper deals with analytical models of the elastic energy gradient Wsq representing an energy barrier. The energy barrier is a surface integral of the elastic energy density Wq. The elastic energy density is induced by thermal stresses acting in an isotropic spherical particle （q = p） with the radius R and in a cubic cell of an isotropic matrix （q = m）. The spherical particle and the matrix are components of a multi-particle-matrix system representing a model system applicable to a real two-component material of a precipitation-matrix type. The multi-particle-matrix system thus consists of periodically distributed isotropic spherical particles and an isotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with a central spherical particle in each of the cubic cells. The dimension d of the cubic cell then corresponds to an inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent micro- structural characteristics of a real two-component material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural charac- teristics. The thermal stresses originate during a cooling pro- cess as a consequence of the difference am - ap in thermal expansion coefficients between the matrix and the particle, am and ap, respectively. The energy barrier Wsq is used for the determination of the thermal-stress induced strengthening aq. The strengthening represents resistance against com- pressive or tensile mechanical loading for am - ap 〉 0 or am - ap 〈 0. respectively.