In the Compressed Sensing (CS) framework, underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find sparsest solution, which is l0-norm minimization. finding an l0 norm solution out solutions NP-hard problem that becomes non-convex optimization problem. It has been a practically proven fact penalty be adequately estimated by l1 norm...

A theorem of Bôcher and Grace states that the critical points of a cubic polynomial are the foci of an ellipse tangent to the sides of the triangle joining the zeros. A more general result of Siebert and others states that the critical points of a polynomial of degree N are the algebraic foci of a curve of class N − 1 which is tangent to the lines joining pairs of zeroes. We prove the analogous...

A characteristic feature of wave propagation in cold plasma is the possibility that a hybrid resonance surface, along which the linearized equation for the scalar potential changes from elliptic to hyperbolic type, may be tangent to a flux surface. This property can be represented in two dimensions by setting the hybrid resonance curve tangent to the line x = 0 at the origin of coordinates. The...

We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical eviden...

During the actual wind power generation process, turbines are often affected by side effects such as blade vibrations, input constraints, and actuator faults. This can lead to a reduction in efficiency even result unforeseen losses. study discusses robust adaptive fault-tolerant boundary control approach address issues of input-constrained actuator-fault problems turbine vibration control. By e...

The Oseledec splitting of the tangent space into covariant subspaces for a hyperbolic dynamical system is numerically accessible by computing the full set of covariant Lyapunov vectors. In this paper, the covariant Lyapunov vectors, the orthogonal Gram-Schmidt vectors, and the corresponding local (time-dependent) Lyapunov exponents, are analyzed for a planar system of rough hard disks (RHDS). T...

To model advanced 3-D forming strategies for paper materials, the effects of environmental conditions on the mechanical behavior must be quantitatively and qualitatively understood. A tensile test method has been created, verified, and implemented to test paper at various moisture content and temperature levels. Testing results for one type of paper for moisture contents from 6.9 to 13.8 percen...