In this paper, a decentralized adaptive neural controller is proposed for a class of large-scale nonlinear systems with unknown nonlinear, non-affine subsystems and unknown nonlinear time-delay interconnections. The stability of the closed loop system is guaranteed through Lyapunov-Krasovskii stability analysis. Simulation results are provided to show the effectiveness of the proposed approache...

Background: Surgery and accurate removal of the brain tumor in the operating room and after opening the scalp is one of the major challenges for neurosurgeons due to the removal of skull pressure and displacement and deformation of the brain tissue. This displacement of the brain changes the location of the tumor relative to the MR image taken preoperatively. Methods: This study, which is done...

This paper provides a survey for the latest developments in the theory of affine q-Schur algebras and Schur–Weyl duality between affine quantum gln and affine type A Hecke algebras. More precisely, we will establish, on the one side, an isomorphism between the double Ringel–Hall algebra D△(n) of a cyclic quiver △(n) and the quantum loop algebra of gln, and establish, on the other side, explicit...

Introduction 3 1. Affine geometry 4 1.1. Affine spaces 5 1.1.1. Euclidean geometry and its isometries 5 1.1.2. Affine spaces 7 1.1.3. Affine transformations 8 1.1.4. Tangent spaces 9 1.1.5. Acceleration and geodesics 10 1.1.6. Connections 11 1.2. The hierarchy of structures 11 1.3. Affine vector fields 12 1.4. Affine subspaces 13 1.5. Volume in affine geometry 14 1.6. Centers of gravity 14 1.7....

An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle dynamics based on an affine simple root system. It is a ‘cross’ between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system. Polynomials describing the equilibrium positions of affine Toda-Sutherland systems are determined for all affine simple root systems.

We study affine Jacobi structures on an affine bundle π : A→M . We prove that there is a one-toone correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A = ⋃ p∈M Aff(Ap,R) of affine functionals. Some examples and applications, also for the linear case, are discussed. For a special type of affine Jacobi structures which are canonically exhibited ...