Let y"=f(x,y,y') be a 2nd order ODE. By Cartan equivalence method, we will study the local equivalence problem under the transformations group of time-Fixed coordinates. We are going to solve this problem by an applicable method which has been recognized by R. Gardner, and classify them.

Chlorinated phenols in many industrial effluents are usually difficult to be removed by conventional biological treatment processes. Performance of the aerobic sequencing batch reactor treating 4- chlorophenol containing wastewater at different loadings rates from 0.0075 to 1.2 g4CP/L.d was evaluated. The sequencing batch reactor was operated with fill, react, settle and decant phases in the order of 10:370:90:10 min, respectively, for a cycle time of 8 h at 10 days solid retention time and 16 h hydraulic retention time in the stable period. The effects of 4-chlorophenol loadings on the 4- chlorophenol and chemical oxygen demand removal percents, yield coefficient (Y), biomass variation and sludge volume index were investigated. High chemical oxygen demand removal efficiencies (95±3.5%) and approximately complete 4-chlorophenol removal (>99%) were observed even in the absence of growth substrate. The degradation of 4-chlorophenol led to formation of 5-chloro-2-hydroxymuconic semialdehyde, which was more oxidized, indicating complete disappearance of 4-chlorophenol via metacleavage pathway. A compact sludge with excellent settleability (sludge volume index=47±6.1 mL/g) developed during entire acclimation period. High removal efficiencies with sequencing batch reactor may be due to enforced short term unsteady state conditions coupled with periodic exposure of the microorganisms to defined process conditions which facilitate the required metabolic pathways for treating xenobiotics containing wastewater.

Planning the flight path for a fleet of Fixed-wing unmanned aerial vehicles during search and rescue operations poses a significant challenge as it requires minimizing search time and optimizing the formation of the unmanned aerial vehicles. This paper proposes a novel integration of a leaderfollower formation flight technique for multiple Fixed-wing unmanned aerial vehicles with a minimumtime search path planning algorithm. In the first step, the proposed algorithm, based on continuous ant colony optimization, plans a sequence of safe and feasible waypoints for the leader while determining appropriate azimuth angles for the followers. In the next step, the algorithm utilizes a nonlinear threedegree-of-freedom model, developed based on a leader-follower formation flight technique, to plan the followers’ flight paths. Applying Dubins curves based on kinematic constraints of the unmanned aerial vehicles not only reduces computational time but also ensures the feasibility of the best search paths between planned waypoints. Furthermore, in the presence of static obstacles, a developed function in the planning process addresses collision and obstacle avoidance constraints. The effectiveness and performance of the suggested method in detecting targets in minimum-time search missions and the ability of the planner to reconfigure the formation of unmanned aerial vehicles in cluttered environments are demonstrated through comprehensive simulation studies and Monte Carlo analysis.