A theorem which establishes the solutions of a given optimization problem as stable points in the state space of single-layer relaxation-type recurrent neural networks is proposed. This theorem establishes the necessary conditions for the neural network to converge to a solution by proposing certain values for the constraint weight parameters of the network. Convergence performance of the discr...

In this paper wewill consider SL(2,R)-valued cocycles over aminimal homeomorphism f : K → K of a compact set K. Such a cocycle can be defined as a pair ( f ,A) where A : K → SL(2,R) is continuous. The cocycle acts on K ×R2 by (x, y) 7→ ( f (x),A(x) · y). The iterates of the cocycle are denoted ( f ,A) = ( f ,An). We say that ( f ,A) is uniformly hyperbolic if there exists ε > 0 and N > 0 such t...

The ability to detect and identify effluent gases is, and will continue to be, of great importance. This would not only aid in the regulation of pollutants but also in treaty enforcement and monitoring the production of weapons. Considering these applications, finding a way to remotely investigate a gaseous emission is highly desirable. This research utilizes hyperspectral imagery in the infrar...

Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schroedinger evolution of states, independent of the assumptions of string theory and quantum theory. The usual properties of dimensionful fields imply an infinite, projective tower of conformal weights associated with the tangent...

Low weight and high load capacity are remarkable advantages of sandwich panels with corrugated core, which make them more considerable by engineering structure designers. It’s important to consider the limitations such as yielding and buckling as design constraints for optimal design of these panels. In this paper, multi-objective optimization of sandwich panels with corrugated core is carried ...

In this paper we develop a bilinearisation-reduction approach to derive solutions the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from second order Ablowitz-Kaup-Newell-Segur coupled as an unreduced system. With pair of $(q_0,r_0)$ bilinearize system obtain in terms quasi double Wronskians. Then implement reductions by introducing constrai...

in this paper, an algorithm is presented for the formation of optimal null basis vectors corresponding to sparse flexibility matrices. for controlling the independence of the vectors, a generator is selected in each corresponding self-equilibrating systems, and the sequence of generators is modeled as decision variables. since the equilibrium conditions and uniqueness of generators consists a u...

Property (T) for groups means a dichotomy: a representation either has an invariant vector or all vectors are far from being invariant. We show that, under a stronger condition of Żuk, a similar dichotomy holds for almost representations as well.