Asymptotic Stability of Differential Equations on Convex Sets

We show a sufficient condition for the asymptotic stability of solutions of an abstract evolutionary equation with the right-hand side defined on a convex set. This condition is applied to a generalized version of the Tjon-Wu equation and to the Boltzmann-Kac equation.     

Remarks on the structure of the multiplicative monoid of integers modulom

This note presents some results concerningH-classes, Schützenberger groups, and regular elements in the multiplicative monoid ℤ _m of integers modulom. It also shows that in ℤ _m , the product of twoH-classes is anH-class.     

An unusual reaction of triphenylmethylsulfenyl chloride with norbornenf and norbornadiene

Triphenylmethylsulfenyl chloride reacts with norbornene and norbornadiene to yield chlorodisulfides instead of the expected products - chlorosulfides.     

Time-series analysis of traffic updates in loss systems

The paper deals with time-series analysis of one-line traffic measurements in loss systems. Discrete-time stochastic models are derived for finite-capacity trunk groups with non-exponential distributions of interarrival and service times. The modelling accuracy is characterized by a prediction error. Simulation results are used to assert situations when the application of the proposed modelling technique is practical. Finally the adaptive Kalman filter is used to deal with cases when the statistics of observed processes are not known a priori.     

Carbon-13 magnetic resonance spectra of quaternary ammonium salts derived from enamino ketones

¹³C magnetic resonance spectra of nine quaternary ammonium salts of the general formula R¹C¹(O)C²H?C³HNR₃⁴Cl (where R¹, R⁴ = alkyl) were obtained and compared with those of the parent amino compounds. The chemical shift differences between these two classes of compounds are qualitatively accounted for by π-electron density changes. Steric effects and hyperconjugation of the alkyl substituents are also discussed.     

Negative emotions boost user activity at BBC forum

We present an empirical study of user activity in online BBC discussion forums, measured by the number of posts written by individual debaters and the average sentiment of these posts. Nearly 2.5 million posts from over 18 thousand users were investigated. Scale-free distributions were observed for activity in individual discussion threads as well as for overall activity. The number of unique users in a thread normalized by the thread length decays with thread length, suggesting that thread life is sustained by mutual discussions rather than by independent comments. Automatic sentiment analysis shows that most posts contain negative emotions and the most active users in individual threads express predominantly negative sentiments. It follows that the average emotion of longer threads is more negative and that threads can be sustained by negative comments. An agent-based computer simulation model has been used to reproduce several essential characteristics of the analyzed system. The model stresses the role of discussions between users, especially emotionally laden quarrels between supporters of opposite opinions, and represents many observed statistics of the forum.