1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP (generalised discrete Painlevé equation) ...

In the process of searching for explicit solutions, quite a few systematic methods have been developed, such as inverse scattering transformation [1], Darboux transformations [2], Hirota’s bilinear method [3-5], and so on. Among them, the bilinear method first proposed by Hirota provides us with a comprehensive approach to construct exact solutions of nonlinear evolution equations (NEEs). Meanw...

We propose a new multivariate probabilistic encryption scheme with decryption errors MQQ-ENC that belongs to the family of MQQ-based public key schemes. Similarly to MQQ-SIG, the trapdoor is constructed using quasigroup string transformations with multivariate quadratic quasigroups, and a minus modifier with relatively small and fixed number of removed equations. To make the decryption possible...

A method for registering pairs of digital images of the retina is presented, using a small set of intrinsic control points whose matching is not known. Control point matching is then achieved by calculating similarity transformation (ST) coefficients for all possible combinations of control point pairs. The cluster of coefficients associated with the matched control point pairs is identified by...

Fine-grained visual recognition typically depends on modeling subtle difference from object parts. However, these parts often exhibit dramatic visual variations such as occlusions, viewpoints, and spatial transformations, making it hard to detect. In this paper, we present a novel attention-based model to automatically, selectively and accurately focus on critical object regions with higher imp...

The paper deals with the realization theory of linear and bilinear hybrid systems, i.e. hybrid systems with continuous dynamics determined by linear ( respectively bilinear ) control systems. We will formulate necessary and sufficient conditions for the existence of a linear (bilinear ) hybrid system realizing the specified input/output maps. We will also present a characterization of a minimal...

This paper studies the realizability property of bilinear input-output (i/o) models in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The complete list of 2nd and 3rd order realizable inputoutput bilinear models together with the corresponding state equations is given. In the general case some subclasses of r...

A Shallow Water Wave-like nonlinear differential equation is considered by using the generalized bilinear equation with the generalized bilinear derivatives 3,x D and 3,t D , which possesses the same bilinear form as the standard shallow water wave bilinear equation. By symbolic computation, four presented classes of rational solutions contain all rational solutions to the resulting Shallow Wat...

Bilinear systems offer a promising approach for nonlinear control because a broad class of nonlinear problems can be reformulated and approximated in bilinear form. System identification is a technique to obtain such a bilinear approximation for a nonlinear system from input-output data. Recent discrete-time bilinear model identification methods rely on Input-Output-to-State Representations (IO...

Bilinear systems offer a promising approach for nonlinear control because a broad class of nonlinear problems can be reformulated in bilinear form. In this paper system identification is shown to be a technique to obtain such a bilinear approximation of a nonlinear system. Recent discrete-time bilinear model identification methods rely on Input-Output-to-State Representations. These IOSRs are e...