For the sake of clarity and in order to avoid convoluted arguments and text citations, below, we address the points raised in the Markel and Sarychev Comment (MSC) in a more general fashion. Clearly, we did not mean to imply that there are errors in the paper by MS but to expose a novel wave phenomenon that has not been discussed so far. The dispute can be distilled to three main points: (i) Mi...

due to the changes which may occur in their parameters, systems are usually demonstrated by some subsystems for different conditions. this paper employs modified petri nets (mpn) to model theses subsystems and makes it simple to analyze them. in this method, first, the continuous transfer function is converted to a discrete transfer function and then, by mpn, system is modeled and analyzed. all...

this paper offers an approach that could be useful for diverse types of layout problems or even area allocation problems. by this approach there is no need to large number of discrete variables and only by few continues variables large-scale layout problems could be solved in polynomial time. this is resulted from dividing area into discrete and continuous dimensions. also defining decision var...

Inspired by the linear Schrödinger operator, we consider a generalized p-Laplacian operator on discrete graphs and present new results that characterize several spectral properties of this with particular attention to nodal domain count its eigenfunctions. Just like one-dimensional continuous p-Laplacian, prove variational spectrum forests is entire spectrum. Moreover, show how transfer Weyl's ...

Abstract We study mean equicontinuous actions of locally compact σ-compact amenable groups on metric spaces. In this setting, we establish the equivalence equicontinuity and topo-isomorphy to maximal factor provide a characterization an action via properties its product. This enables us show weaker notion Besicovitch-mean in fairly high generality, including abelian as well minimal general grou...

Many physical and information processes in various fields possess an identical mathematical structure, that can be described in a common operator form. Also, the operator approach is frequently used as an analysis tool to solve a wide variety of theoretical problems. An operator-based approach for solving initial-boundary-value problems with homogeneous boundary conditions has recently been int...

We examine consequences of image-forming inhomogeneity in the form of a point-spread function that changes with position on the image plane. The familiar self-replicating sinusoids, which a homogeneous system simply multiplies by its spatial modulation-transfer function, generalize to eigenfunctions, which the system multiplies by eigenvalues. We give a way to calculate the eigenfunctions and e...

By using a spectral approach, we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. The quadrature is obtained from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite polynomials. These eigenvectors are discrete approximations of the Hermite functions, which are eigenfunctions of the fractional Fourier transform oper...

ior of small cuspidal eigenpairs of ΔS. In Theorem 1.7, we describe limiting behavior of these eigenpairs on surfaces Sm ∈Mg,n when (Sm) converges to a point in M̄g,n. Then, we consider the ith cuspidal eigenvalue, λc i (S), of S∈Mg,n. Since noncuspidal eigenfunctions (residual eigenfunctions or generalized eigenfunctions) may converge to cuspidal eigenfunctions, it is not known if λc i (S) is a...