This paper gives new bounds for restricted isometry constant(RIC)in compressed sensing.LetΦbe an m×n real matrix and k be a positive integer with k≤n.The main results of this paper show that if the restricted isometry constant ofΦsat-isfiesδ8ak<1 andδk+ak<3/2−1+√(4a+3)^(2)−8/8aforα>3/8,then k-sparse solution can be recovered exactly via l1 minimization in the noiseless case.In particular,whenα=1,1.5,2 and3,we haveδ2k<0.5746 andδ8k<1,orδ2.5k<0.7046 andδ12k<1,orδ3k<0.7731 andδ16k<1 orδ4k<0.8445 andδ24k<1.
In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.
