The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...

Known structures and self-sustaining mechanisms of wall turbulence are reviewed and explored in the context of the scale interactions implied by the nonlinear advective term in the Navier–Stokes equations. The viewpoint is shaped by the systems approach provided by the resolvent framework for wall turbulence proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in which the...

This paper deals with the introduction of a fuzzy over-relaxed proximal point iterative scheme based on H(·, ·)-cocoercivity framework for solving a generalized variational inclusion problem with fuzzy mappings. The resolvent operator technique is used to approximate the solution of generalized variational inclusion problem with fuzzy mappings and convergence of the iterative sequences generate...

Fast control cost for heat-like semigroups: Lebeau-Robbiano strategy and Hautus test Luc Miller (joint work with Thomas Duykaerts) Since the seminal work of Russell and Weiss in [7], resolvent conditions for various notions of admissibility, observability and controllability, and for various notions of linear evolution equations have been studied intensively, sometimes under the name of infinit...

The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials V(M)=M(2p). Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit...

A new class of generalized nonlinear variational inclusions involving (A,η)-monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since (A,η)monotonicity generalizes A-monotonicity and H-monotonic...

In this paper, we introduce a generalized system of nonlinear relaxed cocoercive variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, we consider the approximation solvability of solutions. Since (A, η)-monotonicity generalizes A-monotonicity and H-monotonicity, ou...

Finite-rank expansions of the two-body resolvent operator are explored as a tool for calculating the full three-dimensional two-body T -matrix without invoking the partial-wave decomposition. The separable expansions of the full resolvent that follow from finite-rank approximations of the free resolvent are employed in the Low equation to calculate the T-matrix elements. The finite-rank expansi...

We discuss the application of the resolvent technique to prove stability of plane Couette flow. Using this technique, we derive a threshold amplitude for perturbations that can lead to turbulence in terms of the Reynolds number. Our main objective is to show exactly how much control one should have over the perturbation to assure stability via this technique. 2000 Mathematics Subject Classifica...