A Lax Equation for the Non-Linear Sigma Model

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like dispersionless systems. We show that the system has two Hamiltonian structures which are compatible so that it is truly a bi-Hamiltonian system. However, the two Hamiltonian structures act on the two distinct sets of charges to give the dynamical equations, which is quite distinct from the behavior in conventional integrable systems. We construct two recursion operators which connect the conserved charges within a given set as well as between the two sets. We show explicitly that the conserved charges are in involution with respect to either of the Hamiltonian structures thereby proving complete integrability of the system. Various other interesting features are also discussed.Comment: Latex, 13 page

HiTrust: building cross-organizational trust relationship based on a hybrid negotiation tree

Small-world phenomena have been observed in existing peer-to-peer (P2P) networks which has proved useful in the design of P2P file-sharing systems. Most studies of constructing small world behaviours on P2P are based on the concept of clustering peer nodes into groups, communities, or clusters. However, managing additional multilayer topology increases maintenance overhead, especially in highly dynamic environments. In this paper, we present Social-like P2P systems (Social-P2Ps) for object discovery by self-managing P2P topology with human tactics in social networks. In Social-P2Ps, queries are routed intelligently even with limited cached knowledge and node connections. Unlike community-based P2P file-sharing systems, we do not intend to create and maintain peer groups or communities consciously. In contrast, each node connects to other peer nodes with the same interests spontaneously by the result of daily searches

Collection of Master-Slave Synchronized Chaotic Systems

In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we were looking for the simplest coupling between master and slave system. The interval of parameters were synchronization is achieved are obtained analytically using Routh-Hurwitz conditions. Detailed calculations and numerical simulation are given for the system I from the Sprott's collection. Working in the same manner for non-linear systems based on ordinary differential equations the method can be adopted for the teaching of the topic

Collection of master–slave synchronized chaotic systems

Abstract In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the systems that contains one nonlinear term and that term contains one variable then the coupling consists of one term. The numerical intervals of parameters where the synchronization is achieved are obtained analytically by applying Routh-Hurwitz conditions. Detailed calculations and numerical results are given for the system I from the Sprott's collection. Working in the same manner for many systems this method can be adopted for the teaching of the topic

Advanced treatment solutions intended for the reuse of livestock wastewater in agricultural applications

Abstract One of the main concerns of the developing world is the mitigation of pollution of environmental components together with the recovery and reuse of valuable substances from waste resulting during diverse anthropic activities. Wastewater generated by agro-zootechnic activities is a source of nutrients (nitrogen and phosphorus compounds) and traditionally it is reused for crops irrigation. However adverse effects on the environment may be caused should a proper treatment not be performed, considering the spread of additives/drugs altering the natural metabolism in modern livestock industries and subsequently their presence in waste. In this context, research was conducted on laboratory scale setups of some advanced treatment processes for wastewater resulting from cattle farms. UV disinfection and oxidation using ozone were investigated in order to emphasize the antimicrobial effect and their contribution to the improvement of water quality. The permissible irrigation water quality which varied based on the crop type was the decisive factor in adjusting the experimental setup and effluent quality. The results have revealed the inactivation of bacteriological indicators up to 99% and even 100% in the case of faecal coliforms and faecal streptococci. Moreover, ozonation allows also the removal of organic matter, with an efficiency of over 80%. This research offers solutions suitable for areas where the water demand exceeds availability and in the regions affected by drought.</jats:p