in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

Abstract. We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relie...

Introduction: Brain visual evoked potential (VEP) signals are commonly known to be accompanied by high levels of background noise typically from the spontaneous background brain activity of electroencephalography (EEG) signals. Material and Methods: A model based on dyadic filter bank, discrete wavelet transform (DWT), and singular value decomposition (SVD) was developed to analyze the raw data...

Consider the scattering of a time-harmonic plane wave by rigid obstacle embedded in homogeneous and isotropic elastic medium two dimensions. In this paper, novel boundary integral formulation is proposed its highly accurate numerical method developed for problem. More specifically, based on Helmholtz decomposition, model problem reduced to coupled equation with singular kernels. A regularized s...

This study examines a discrete-time enzyme model with Caputo fractional order. We look into the existence and uniqueness of fixed points in discrete dynamic discover parametric criteria for their local asymptotic stability. Additionally, it is demonstrated using bifurcation theory that system experiences Period-Doubling Neimark-Sacker constrained area around singular positive point an invariant...

We propose a differential difference equation in R × Z and study it by Hirota’s bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B...

This paper discusses balanced realization and model order reduction for both continuoustime and discrete-time general nonlinear systems based on singular value analysis of the corresponding Hankel operators. Singular value analysis clarifies the gain structure of a given nonlinear operator. Here it is proved that singular value analysis of smooth Hankel operators defined on Hilbert spaces can b...

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We recast a network generating partial differential equation system into singular limit of dissipative gradient flow model, which not only identifies the consistent physical boundary conditions but also generates networks. then develop set structure-preserving numerical algorithms for model. Using energy quadratization (EQ) method, we reformulate an equivalent one with quadratic density by intr...