We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obey these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota equation). The bilinear relations were previously known for a particular class of transfer matrices corresponding to rectangular Young diagrams. We extend th...

An ID-based cryptographic scheme enables the user to public keys without exchanging public key certificates. In these schemes, users can generate their public and private keys using their identity. The positive application of bilinear pairings over elliptic curves makes the system easy and efficient in providing security. In this paper, we propose an ID-based signature scheme using bilinear pai...

The Moulton Hydragas suspension system improves small car ride quality by interconnecting the front and rear wheel on each side of the vehicle via a hydraulic fluid pipe between the front and rear dampers. A Hydragas system from a Rover Group MGF sports car was statically and dynamically tested to generate stiffness and damping coefficient matrices. The goal was to develop the simplest possible...

Introduction:  The  advent  of  dual-modality  PET/CT  scanners  has  revolutionized  clinical  oncology  by  improving lesion localization and facilitating treatment planning for radiotherapy. In addition, the use of  CT images for CT-based attenuation correction (CTAC) decreases the overall scanning time and creates  a noise-free  attenuation  map  (6map).  CTAC  methods  include  scaling,  s...

This paper considers the problem of controlling the solution of an initial boundary-value problem for a wave equation with time-dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performance measure over sound speed is subjected to the...

This paper presents a new algorithm for the closed-loop H∞ composite control of singularly perturbed bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale via singular perturbation theory, and then...

In this paper, Whitham–Broer–Kaup (WBK) equations with time-dependent coefficients are exactly solved through Hirota’s bilinear method. To be specific, the WBK equations are first reduced into a system of variable-coefficient Ablowitz–Kaup– Newell–Segur (AKNS) equations. With the help of the AKNS equations, bilinear forms of the WBK equations are then given. Based on a special case of the bilin...

In this paper, we prove several new results that give insights into bilinear systems. We show under which conditions a system is asymptotically stable. Moreover, provide global ch...