On time versus size for monotone dynamic monopolies in regular topologies

We consider a well-known distributed colouring game played on a simple connected graph: initially, each vertex is coloured black or white; at each round, each vertex simultaneously recolours itself by the colour of the simple (strong) majority of its neighbours. A set of vertices M is said to be a dynamo, if starting the game with only the vertices of M coloured black, the computation eventually reaches an all-black configuration.The importance of this game follows from the fact that it models the spread of faults in point-to-point systems with majority-based voting; in particular, dynamos correspond to those sets of initial failures which will lead the entire system to fail. Investigations on dynamos have been extensive but restricted to establishing tight bounds on the size (i.e., how small a dynamic monopoly might be).In this paper we start to study dynamos systematically with respect to both the size and the time (i.e., how many rounds are needed to reach all-black configuration) in various models and topologies.We derive tight tradeoffs between the size and the time for a number of regular graphs, including rings, complete d-ary trees, tori, wrapped butterflies, cube connected cycles and hypercubes. In addition, we determine optimal size bounds of irreversible dynamos for butterflies and shuffle-exchange using simple majority and for DeBruijn using strong majority rules. Finally, we make some observations concerning irreversible versus reversible monotone models and slow complete computations from minimal dynamos.     

The reduced Redlich–Kister excess molar Gibbs energy of activation of viscous flow and derived properties in 1,4-dioxane + water binary mixtures from 293.15 to 309.15 K

The excess molar volume, viscosity deviation and excess Gibbs free energy of activation of viscous flow have been investigated from the density and shear viscosity measurements of water–dioxane mixtures over the entire range of mole fractions from 293.15 to 309.15?K. The results were fitted by the Redlich–Kister equation. Partial molar volume and Gibbs energy at infinite dilution were deduced from four methods, activation parameters and partial molar Gibbs energy of activation of viscous flow against compositions were investigated. The water–dioxane interactions have principally an H-bound character and there are two principal types’ structures limited by 0.08?mole fraction in dioxane. The reduced Redlich–Kister excess properties provide an indication of the intermolecular interactions and for dioxane–water cluster formation as suggested in the literature.     

The reduced Redlich–Kister equations for correlating volumetric and viscometric properties of N,N-dimethylacetamide + dimethylformamide binary mixtures at temperatures from 298.15 to 318.15 K

Excess molar volumes and viscosity deviations in N,N-dimethylacetamide?+?dimethylformamide binary mixtures at 298.15, 308.15 and 318.15?K were calculated from experimental density and viscosity data presented in the previous work. Here these experimental values were used to test the applicability of the correlative reduced Redlich–Kister equation and the recently proposed Herráez equation. Their correlation ability at different temperatures, and the use of different number of parameters, is discussed for the case of limited experimental data. These relative functions are important to reduce the effect of temperature and, consequently, to reveal the effects of different types of interactions. Limiting excess partial molar volumes at infinite dilution were deduced from different methods, parameters of molar Gibbs energy of activation of viscous flow against compositions were investigated. The results of these observations have been interpreted in terms of structural effects of the solvents. ¹H-NMR studies of these mixtures are also reported.     

Design and synthesis of novel indoline-(thio)urea hybrids

Abstract

A series of novel indoline-(thio)urea were designed and prepared using indoline(s) as a new platform and tested as organocatalysts in the Michael and Morita–Baylis–Hillman reactions. Most of the compounds were found to be very active catalysts although they did not promote the enantioselectivity. As agents for the conversion of thiocarbonyl compounds into carbonyl compounds, potentials of PIFA and DDQ were also displayed. Furthermore, DFT calculations rationalized the experimentally observed non-enantioselectivity of the catalysts.     

Stereoelectronic structure of MCl4-benzoyl chloride (M=Si,Ge, Sn) systems resulting from ab initio calculations and NQR 35Cl

Results of quantum-chemical calculations of MCl₄–C₆H₅COCl (M=Si, Ge, Sn) systems of 1?:?1 composition using RHF/3-21?G* and MP2/3-21?G* levels as well as those of 1?:?2 composition using the RHF/3-21?G* level have been represented. MCl₄?←?C₆H₅COCl complexes of 1?:?1 composition are energetically more advantageous. They are formed in solid state provided that the M···O distance in individual systems is considerably less than the sum of van der Waals radii of M and O and their total energies are appreciably less than the sum of total energies of components. These conditions are realized only for M=Sn. In systems of 1?:?2 compositions, calculated M···O distances are practically equal to the sum of covalent radii of M and O. Nonetheless, complexes with such composition are not formed in solid state. Total energy of the system which is lower than the sum of its components’ energies is not an indispensable condition for complex formation. The ³⁵Cl nuclear quadrupole resonance (NQR) frequencies and asymmetry parameters of the electric field gradient at the ³⁵Cl nuclei have been evaluated using the results of ab initio calculations.     

Improved lower bounds on the total variation distance for the Poisson approximation

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen–Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.     

One‐Step Reaction of Friedel–Crafts Acylation and Demethylation of Aryl‐Methyl Ethers Catalyzed by Ytterbium(III) Triflate

Abstract

Catalytic amount of ytterbium(III) triflate [Yb(OTf)₃] has been used to catalyze Friedel–Crafts acylation and demethylation of aryl‐methyl ethers in one‐step reaction to produce hydroxyacylphenones with moderate yields under mild conditions.     

Etude de la restauration de l'aluminium irradié aux electrons (Etape III)

The nature of the electron bombarded aluminium electrical recovery process has been studied by combining quenches with irradiations. Measured Frenkel pair formation rates per incident electrons as well as annealing kinetics emphasize the role of impurity interstitial trapping.     

Synthesis of Naphtho[2,1-b]pyrano Pyrrolothiazole Derivatives through 1,3-Cycloaddition Reaction

Facile synthesis of a series of naphtho[2,1,b]pyrano pyrrolo thiazoles was accomplished in good yields in a one-pot reaction through intramolecular 1,3-dipolar cycloaddition of cyclic azomethine ylides with Baylis–Hillman adducts as dipolarophiles. The protocol is applicable to a wide variety of photochromic and biologically active napthopyrano products. The regio- and stereochemical outcome of the cycloaddition reaction was ascertained by x-ray crystallographic study of one of the cycloadducts.     

Auslander–Reiten Components with Sectional Bypasses

In this work, we will prove that the modules lying in a sectional bypass of an arrow in the Auslander–Reiten quiver of an artin algebra, are either all left stable or all right stable, but not τ-periodic. Moreover, if such a bypass exists, then the Auslander–Reiten quiver has an infinite left or right stable component which contains a section with a bypass.