This series of two papers is devoted to the study principal spectral theory nonlocal dispersal operators with almost periodic dependence and asymptotic dynamics nonlinear equations dependence. In this first part series, we investigate from aspects: top Lyapunov exponents generalized eigenvalues. Among others, provide various characterizations eigenvalues, establish relations between them, effec...

In this article, the existence of spectrum (the eigenvalues) for nonlinear continuous operators acting in Banach spaces is investigated. For study question it used a different approach that allows studying all eigenvalues operator relative to another operator. Here we show case necessary seek given satisfying certain conditions. The examples, which can be found, are provided. Moreover, problems...

PT-Symmetry is one of the interesting topics in quantum mechanics and optics. One of the demonstration of PT-Symmetric effects in optics is appeared in the nonlinear directional coupler (NLDC). In the paper we numerically investigate the stability of temporal bright solitons propagate in a PT-Symmetric NLDC by considering gain in bar and loss in cross. By using the analytical solutions of pertu...

In this paper we study two degree of freedom Hamiltonian systems and applications to nonlinear wave equations. Near the origin, we assume that near the linearized system has purely imaginary eigenvalues: i! 1 and i! 2 , with 0 < ! 2 =! 1 1 or ! 2 =! 1 1, which is interpreted as a perturbation of a problem with double zero eigenvalues. Using the averaging method, we compute the normal form and s...

Turbo-expanders are used in industries for cooling, liquefaction and also power generation. An important part of these turbines is the variable angle nozzle causing a nonlinear behavior that is not well recognized among the prime movers of the dispersed generators. In this paper, at first, the turbo expander system is evaluated in details and its nonlinear behavior is investigated. Then, the sy...

3. Introduction In this paper, we investigate the design optimization of structures to maximize the lowest eigenvalue of free vibration, which has been studied extensively [20, 22]. In designing civil, mechanical and aerospace structures, the eigenvalues of free vibration, as well as the linear buckling load factor, have been used widely for decades as a performance measure of structures. It wa...

We review somemore and less recent results concerning bounds on nonlinear eigenvalues NLEV for gradient operators. In particular, we discuss the asymptotic behaviour of NLEV as the norm of the eigenvector tends to zero in bifurcation problems from the line of trivial solutions, considering perturbations of linear self-adjoint operators in a Hilbert space. The proofs are based on the Lusternik-S...

By solving a set of recursion relations for the matrix elements of the Uh(sl(2)) generators, the finite dimensional highest weight representations of the algebra were obtained as factor representations. Taking a nonlinear combination of the generators of the two copies of the Uh(sl(2)) algebra, we obtained Uh(so(4)) algebra. The latter, on contraction, yields Uh(e(3)) algebra. A nonlinear map o...

This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel. Relative to numerically inverting the so-called QuEST function, the main advantages of direct kernel estim...

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schrödinger equation with a two-dimensional complex potential. This symmetry breaking is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, it is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base bra...