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Operation Cocoon:The forest brigand Veerappan and three of his key associates, who were killed in an encounter, were lured out of their hideout by Special Task Force personnel who had finally managed to infiltrate the gang. An STF man, who had gained their confidence, drove Veerappan and his gang straight into the trap set up at Paparapatti village in Tamil Nadu's Dharmapuri district.Tamil Nadu STF chief, Additional Director General of Police, K. Vijay Kumar, said `Operation Cocoon' was the result of 10 months of planning and three weeks of meticulous preparation. But the operation lasted only 45 minutes from the time the gang got into the ambulance, which was actually an STF vehicle. Veerappan may have been on his way to get treatment for an eye ailment (cataract).A 35-member team lay in wait at Paparapatti village. Some of the securitymen were hidden in a reinforced tanker lorry parked by the road; others had taken position atop a nearby school.Mr. Vijay Kumar said that when challenged the gang initially did not respond. A second warning to surrender was greeted with gunfire. The STF retaliated with stun grenades and gunfire. Before this the driver of the ambulance, an STF operative, made good his escape as planned.Veerappan died on the spot. His lieutenant, Sethukuzhi Govindan, Chandre Gowde, and the Tamil Nadu Liberation Army (TNLA) extremist, Sethumani, who had joined the gang during recent abduction episodes, died on way to hospital.The STF seized a non-ballistic 12 bore Remington pump action gun, which can spray bullets effectively for bush fighting, two AK-47s, a self-loading rifle (7.62) and two hand grenades. About Rs. 3.5 lakhs was also recovered.The operation was the result of intelligence inputs the STF had got over a period, Mr. Vijay Kumar said. It had managed to plant four men in the Veerappan gang. They had settled in the villages on the fringes of the forest and won the confidence of the gang. Other STF men posed as taxi drivers, bus conductors, hawkers and masons and provided information crucial to the operation.However, Mr. Vijay Kumar said it was unclear where the brigand was heading. Further investigation by the STF and the police may throw light on any accomplices, facilitators or abettors.Mr. Vijay Kumar said, "the absence of red-tapism and miscommunication" proved to be the advantage of the STF. "One aim, one goal and one mission of both the STFs led to the accomplishment of the task," Mr. Vijay Kumar said.After monitoring the movement of the brigand, the entire manpower was deployed in the area, thus "bringing the elusive fugitive into a tightly knit police net," he said.Asked whether there would be any DNA tests to confirm the identity of the bodies, Mr. Vijay Kumar said the intelligence sleuths had confirmed the identity. The gang was, unusually, not in camouflage clothing; Veerappan was in white, with the moustache trimmed to deceive the police, he said.Mr. Vijay Kumar's Karnataka counterpart, the IGP (STF), Jyoti Prakash Mirji; the IG (West Zone-Tamil Nadu), A. Subramanian and the Deputy Inspector-General of Police, Salem Range, N. Tamizh Selvan, were present at the media event.The operation was led by the ADGP himself, assisted by the Superintendents of Police, N.K. Senthamaraikannan (who masterminded the intelligence trap), K. Shanmugavelu and P. Chinnasamy.The core team consisted of the Deputy Superintendents of Police, N. Thirunavukkarasu, and Hussain. Inspectors N. Rajarajan and Mohan Nawaz led the ambush team.Mr. Vijay Kumar said that he "salutes and worships the valour and sincerity shown by the boys in accomplishing the mission." The brigand was both physically and psychologically down, facing squabbles within the four-member group, he said.Despite the presence of reinforcements, including the standby paramilitary forces from the neighbouring districts, the police had a tough time managing the crowd here.Onlookers swamped the General Hospital since morning to take a look at the bodies.UNI reports:The post-mortem examination conducted on Veerappan's body today revealed that he had suffered three bullet injuries. A confidential medical report said he had sustained bullet injuries on his forehead, chest and hip. One bullet was taken out during the post-mortem examination.

This is a decomposition into irreducible representations ("irreps"), and it's part of the branch of Group Theory (mathematics) called Representation Theory (mathematics). Irreducible representations are pieces that do not mix with each other under the group action (here it's SO(n) for rotating the basis) and can not be decomposed further.A rank 2 tensor [math]T_{ij}[/math] has three irreducible pieces:The scalar trace, [math]T=T^i{}_i[/math]. This is clearly SO(n) invariant, being a scalar. The rest of the irreps must be tracefree, because they must be irreducible (and having a trace means there is another irrep hiding inside).The antisymmetric piece [math]T^A_{ij}=\frac{1}{2}(T_{ij} - T_{ji})[/math]. This is clearly tracefree.The symmetric, tracefree (STF) piece [math]T^{STF}_{ij}=\frac{1}{2}(T_{ij}+T_{ji}) - \frac{1}{n}\delta_{ij} T[/math]. The trace piece has been removed, so it is tracefree.The decomposition is [math]T_{ij} = T^A_{ij}+T^{STF}_{ij}+\frac{1}{n}\delta_{ij}T[/math], the sum of the antisymmetric, symmetric-trace-free, and trace parts. Here is the important part: under the group action (here SO(n) for rotating the basis), the components of [math]T^A_{ij}[/math] mix among themselves, and similarly the components of [math]T^{STF}_{ij}[/math] mix among themselves. However, the components of [math]T^A[/math] do not mix with those of [math]T^{STF}[/math], and similarly for the trace. You can think of each of [math]T, T^A, T^{STF}[/math] as its own object and they don't affect each other.Also notice that each of these three parts are orthogonal in the sense that [math]T^A_{ij} T_{STF}^{ij} = 0[/math] and likewise for the other two possible contractions.Each irreducible part has a different physical meaning, too. For the stress tensor, the trace part is isotropic and corresponds to the isotropic pressure; the STF part that remains corresponds to anisotropic shear stresses. There is no antisymmetric piece.A more advanced example where this comes up is in the Raychaudhuri equation. There, the covariant derivative of the velocities of nearby particles, [math]\nabla_a v_b[/math] is decomposed into trace, STF, and antisymmetric pieces. The trace corresponds to the convergence/focusing or divergence/defocusing of nearby trajectories. The STF part corresponds to any shearing of nearby trajectories, i.e. if an initially circular bundle of trajectories becomes elliptical. Finally, the antisymmetric part corresponds to how much twisting the trajectories do about each other.This same type of decomposition holds for higher rank tensors, though it is more complicated than the rank 2 case. There is always a completely antisymmetric[1] and a symmetric-tracefree part, though. The higher rank decomposition is performed using Young symmetrizers.[1] But in a vector space of dimension d, you can only have completely antisymmetric tensors of rank [math]0\le k \le d[/math]. For ranks greater than d, the completely antisymmetric part must vanish because you can not find k linearly independent vectors with [math]k>d[/math].

Vikas Dubey has been killed in an encounter that broke out between the gangster and the Uttar Pradesh Special Task Force (STF) on Friday morning when he was being brought to Kanpur.He was killed in pre - planned encounter.#Justice is prevailed when everyone linked with it get punishment. Nowadays only politicians are safe, such criminal existed because he had connection with politicians and officers.