Using the ∂-problem and dual ∂-problem , we derive bilinear relations which allows us to construct integrable hierarchies in different parametrizations, their Darboux-Bäcklund transformations and to analyze constraints for them in a very simple way. Scalar KP, BKP and CKP hierarchies are considered as examples. There are different methods to construct integrable equations and to analyze their p...

Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

A new doubling algorithm—the alternating-directional doubling algorithm (ADDA)— is developed for computing the unique minimal nonnegative solution of an M -matrix algebraic Riccati equation (MARE). It is argued by both theoretical analysis and numerical experiments that ADDA is always faster than two existing doubling algorithms: SDA of Guo, Lin, and Xu (Numer. Math., 103 (2006), pp. 393–412) a...

A new technique for performing the bilinear transformation of polynomials is presented. The technique is both simple to understand as well as efficient in its computer implementation. The key to the method is the way in which the successive derivatives of a particular polynomial are computed. A simple recursion formula is used which can be done either by hand, if desired, or by computer. The or...

The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce circular distribution based on an existing linear model. By the genesis of ISP method, many important models have been provided by researchers. In this study, we propose new symmetric unimodal/bimodal rotated considering hyperbolic secant as baseline distribution. Rotation means that fix...

The simple direct method is adopted to find Non-Auto-Backlund transformation for variable coefficient non-linear systems. The (2+1)-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients is used as an example to elucidate the solution procedure, and its symmetry transformation and exact solutions are obtained.

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

comparison of linear and nonlinear (bilinear) time series models in reference crop evapotranspiration prediction in urmia synoptic stationreference crop evapotranspiration (eto) prediction is one of the important elements in optimizing agricultural water consumption. in this regard, one of the prediction approaches is to use the stochastic time series methods. in this research, ar (p) and arma(...