We prove that several Feigin–Odesskii Poisson brackets associated with normal elliptic curves in $${{\mathbb {P}}}^n$$ are compatible if and only they contained a scroll or Veronese surface {P}}}^5$$ (with an exception of one case when $$n=3$$ ). In the we determine quartic corresponding to Schouten bracket two (non-compatible) $$E_1$$ $$E_2$$ .

The objective of this paper is to obtain two results in probabilistic 2-metric space by employing the concepts (E.A)-property, conditionally compatible, semi-compatible and sub-sequentially continuous mappings. These findings improve theorem proved [5]. Further, these are substantiated supporting examples.

Traditional sketching/drawing tools oncomputers lacked the freedom of real pens. They also ignore human perception. In order to avoid such limitation, we developed new techniques such as interactive beaut$ication with extended pie-menu (PieSlider), sketch with perceptual recognition (PerSketch), the function of layout according to human perception (PerLayout), and new data structure for PerSket...

In the paper we consider a new class (called NoLoess) of nonparametric estimators of regression function r(x) = E(Y jX = x): The new estimators link nonparametric and parametric methods. NoLoess extends the class of Macauley, Cleveland, and Stone estimators and replaces their locally linear models (Loess) given by (1.3) with a general locally parametric nonlinear model g(x;). The parameter is e...

Noncommutative algebras, defined by the generators and relations, are considered. The definition and main results connected with the Gröbner basis, Hilbert series and Anick’s resolution are formulated. Most attention is paid to universal enveloping algebras. Four main examples illustrate the main concepts and ideas. Algorithmic problems arising in the calculation of the Hilbert series are inves...

This paper presents a novel approach to stabilize the output of video camera installed on a moving vehicle in a rugged environment. A 2.5-D interframe motion model is proposed so that the stabilization system can perform in situations where significant depth changes are present and the camera has both rotation and translation. Inertial motion filtering is proposed in order to eliminate the vibr...