Implementation in Direct Digital Synthesizers (DDS) Based on CORDIC Algorithm

The universality of computerized signal handling (DSP) has made expanding request to create territory effective and precise structures in completing numerous nonlinear math tasks. One such design is CORDIC unit which has numerous applications in the field of DSP including actualizing changes dependent on Fourier premise. This paper offers structure of CORDIC, inserted with a pipelined unit that has exclusively negligible scope of adders and shifters. It tends to be applied in pivot mode as appropriately as vectoring mode. The reason for the arrangement is to get a pipelined CORDIC unit keeping up the format of valid calculation. Preparing and discussion structures work CORDIC in round organize contraption and in both of pivot or vectoring modes.

Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

We investigate the relation between pluri-Lagrangian hierarchies of 2-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in Petrera and Suris (Nonlinear Math. Phys. 24(suppl. 1):121–145, 2017) for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural $$(1\,{+}\,1)$$ ( 1 + 1 ) -dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. The corresponding multi-time Euler–Lagrange equations coincide with the original system supplied with commuting evolutionary flows induced by the variational symmetries.

Semi-Analytic Probability Density Function for System Uncertainty

In general, the behavior of science and engineering is predicted based on nonlinear math models. Imprecise knowledge of the model parameters alters the system response from the assumed nominal model data. One proposes an algorithm for generating insights into the range of variability that can be expected due to model uncertainty. An automatic differentiation tool builds the exact partial derivative models required to develop a state transition tensor series (STTS)-based solution for nonlinearly mapping initial uncertainty models into instantaneous uncertainty models. The fully nonlinear statistical system properties are recovered via series approximations. The governing nonlinear probability distribution function is approximated by developing an inverse mapping algorithm for the forward series model. Numerical examples are presented, which demonstrate the effectiveness of the proposed methodology.

SCHRÖDINGER–LICHNEROWICZ LIKE FORMULA ON KÄHLER–NORDEN MANIFOLDS

A new kind of spinors and Dirac operator are introduced on Kähler–Norden manifolds in [Spinors on Kähler–Norden manifolds, J. Nonlinear Math. Phys.17(1) (2010) 27–34]. In this work the square D2 of the Dirac operator D is computed and a kind of Schrödinger–Lichnerowicz formula is obtained.

CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS

We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

Model and Control for Hydraulic Excavator’s Arm

To control excavator’s arm and realize autonomous excavation, firstly, full kinematic and dynamic models of the excavator arm, regarded as a planar manipulator with three degrees of freedom, were derived. Secondly, experiment excavator was retrofitted with electrohydraulic proportional valves, associated sensors, and a computer control system; then, the full nonlinear math model of electrohydraulic proportional system was achieved. Thirdly, this paper presents a discontinuous projection based on an adaptive robust controller to approximate the nonlinear gain coefficient of the valve and the nonlinear of the whole system, the error is deal with robust feedback and an adaptive robust controller was designed. Finally, the experiment of the boom motion control is presented to illustrate the feasibility. These efforts had resulted in new control design methodologies that were applicable to several hydraulic proportional systems.