The Evans function is a Wronskian type determinant used to detect point spectrum of differential operators obtained by linearizing PDEs about special solutions such as traveling waves, etc. This work is a sequel to the paper “Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves”, published by F. Gesztesy, K. Zumbrun and the second author in J. Math. Pure...

In the current contribution, integral representations of solutions homogeneous and nonhomogeneous delay differential equation a fractional Hilfer derivative are established in terms delayed Mittag-Leffler-type matrix function two parameters. By using method variation constants, solution represented. Finite-time stability is examined with provision appropriate sufficient conditions. Finally, an ...

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

A semi-empirical model of the ensemble-averaged differential Mueller matrix for microwave backscattering from bare soil surfaces is presented. Based on existing scattering models and data sets measured by polarimetric scatterometers and the JPL AirSAR, the parameters of the co-polarized phase-difference probability density function, namely the degree of correlation and the co-polarized phase-di...

In this work we consider a target tracking scenario where a moving observer with a bearings-only sensor is tracking a target. The tracking performance is highly dependent on the trajectory of the sensor platform, and the problem is to determine how it should maneuver for optimal tracking performance. The problem is considered as a stochastic optimal control problem and two sub-optimal control s...

A new approach using optimization technique for constructing low-dimensional dynamical systems of nonlinear partial differential equations (PDEs) is presented. After the spatial basis functions of the nonlinear PDEs are chosen, spatial basis functions expansions combined with weighted residual methods are used for time/space separation and truncation to obtain a high-dimensional dynamical syste...

the computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. in this approach, a truncated hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. two illustrative examples are included todemon...

Abstract. Let T : Ω → C be a matrix-valued function that is analytic on some simplyconnected domain Ω ⊂ C. A point λ ∈ Ω is an eigenvalue if the matrix T (λ) is singular. In this paper, we describe new localization results for nonlinear eigenvalue problems that generalize Gershgorin’s theorem, pseudospectral inclusion theorems, and the Bauer-Fike theorem. We use our results to analyze three non...