Design and Prototype Test of key components of Segmented Ligusticum wallichii Harvester

According to the harvest demand of Ligusticum wallichii, a segmented Ligusticum wallichii harvester was designed. The crushing device was set in the front end of tractor and the vibrating harvester was mounted in the rear end of tractor. Firstly, the strength test of Ligusticum wallichii stalks was carried out, and the basic parameters of the crushing device were determined. The results showed that the minimum required speed of the crushing device was 3880r/min. Secondly, the vibration structure was modeled and analyzed by vector equation, and the vibration structure was simulated and analyzed by ADAMS, and the parameters of the vibration structure were determined. The results showed that when the crank angle was 22~100°, the Ligusticum wallichii-soil mixture was thrown backward away from the vibration steel bar, and throw away distance was 88.42mm. Finally, the field prototype test was carried out. During the test, the crushing device could crush the stems of Ligusticum wallichii normally. The rotational speed was measured at 4020r/min. The obvious rate, loss rate and damage rate of Ligusticum wallichii stem were calculated. The stems obvious rate was 95%, loss rate was 4.5% and damage rate was 0.4%, which met the harvest requirements of Ligusticum wallichii.

Theory of vector equations of electromagnetic wave diffraction on a rectilinear tubular cylinder

The vector equation for the diffraction of electromagnetic waves on the surface of a rectilinear circular cylinder without ends with respect to surface currents is considered. As a result of transformations from the original equation, one-dimensional systems of integral equations are obtained. For all four integral operators describing the systems, the main parts are highlighted. Using the remarkable properties of one-dimensional diffraction operators, the Fredholm equation of the second kind in Sobolev spaces is obtained.

Stochastic multi-step saddle point process minimax control parametric synthesis

The actual research problem of operations is development of methods of increase of a management efficiency by processes of the conflict nature. Article is devoted to development of methods of increase of a management efficiency by such processes. The purpose of article is the substantiation of the approach to parametrical synthesis of optimum control by multi-step stochastic minimax processes and procedures of the numerical analysis of likelihood dynamic characteristics of process. Formalization of process consists in definition of its type, a vector of phase coordinates and corresponding restrictions, the task of set of the actions sold by each the parties, efficiency of each action, control parameters (varied parameters of process) which task of values each of the parties influences a course of process, control restrictions, criteria of efficiency of the parties expressed through elements of a vector of phase coordinates. Discrete final stochastic process is considered. Change of phase coordinates occurs during the discrete moments of time, named steps of process. Phase coordinates depend on values of two groups of control parameters (controls of the counteracting parties). Within the limits of the modern theory of optimization of stochastic systems procedure of synthesis of optimum control is realized two-phase. At the first stage with use of analytical methods the structure of optimum control is determined. For these purposes the simplified determined model of process can to be used. At the second stage parametrical control optimization with use of algorithmic methods and computing procedures statistical linearization is carried out. Dynamics of process is described vectorial finite-difference equation. It is necessary to distinguish cases when there is saddle a point and when saddle the point is absent. Parametrical synthesis of optimum control is possible only in the first case. It is considered three basic variants of the equation: the linear equation; the nonlinear equation with optimum controls on border of a range of definition; the nonlinear equation with optimum controls inside of a range of definition. For the first variant there is an effective algorithm of parametrical synthesis of optimum control. For the second variant of synthesis of optimum control it is possible, but the algorithm is not effective. For the third variant to determine optimum managements it is not possible. Procedure statistical linearization is offered. Procedure consists in generation of set of realizations of the casual process set by the vector equation, calculation of optimum control for each concrete realization and the further statistical processing of the received results. The process described by the piecewise linear vector equation, is a special case of nonlinear process. At that it keeps property of independence of optimum control from coordinates of process. It provides expansion of a scope of effective computing procedure of synthesis of optimum control on a new class of piecewise linear processes. Property of a constancy process Hamiltonian can be used as criterion of correctness of calculation of optimum control in concrete cases. Application of the offered procedure provides use of methods of statistical modelling for the decision of tasks of the analysis of dynamics of the conflict and synthesis of optimum control in view of nonlinearity of functions of losses of the parties, dependence of efficiency of means used by them on the random factors formalized in the form of stochastic functions with various likelihood distributions, and also uncertainty concerning actions of the opponent.

On the Deformation Retractions of Frenet Curves in Minkowski 4 - Space

In this paper, the position vector equation of   the Frenet curves with constant curvatures in Minkowski 4 -space has been presented. New types for retractions and deformation retracts of Frenet curves in  are deduced. The relations between the Frenet apparatus of the Frenet curves before and after the deformation retracts are obtained.

Dynamics of viscoelastic element of flow channel

We consider the plane problem of aerohydroelasticity on small oscillations arising during bilateral flow around a viscoelastic element located on the rectilinear wall of an infinite channel. A mathematical model describing the problem in a linear formulation and corresponding to small perturbations of homogeneous subsonic flows and small deflections of a viscoelastic element is formulated. Using the methods of the theory of functions of a complex variable, the solution of the problem is reduced to the study of the integro-differential equation with partial derivatives with respect to the deflection function of the element. To solve this equation, a numerical method based on the application of the Bubnov-Galerkin method is proposed, followed by the reduction of the resulting system of integro-differential equations to the Volterra vector equation of the second kind. On the basis of the developed numerical method the computer simulation of the dynamics of the deformable element is carried out.

Detailed description of the evolution mechanism for singularities in the system of pressureless gas dynamics

The system of pressureless gas dynamics is a hydrodynamically justified generalization of the system consisting of the Burgers vector equation in the limit of vanishing viscosity and the mass conservation law. The latter system of equations was intensively used, in particular, in astrophysics to describe the large scale structure of the Universe. The solutions of the vector Burgers equation involve interesting dynamics of singularities, which can describe concentration processes. However, this dynamics does not satisfy the law of momentum conservation, which prevents us from treating it as dynamics of material objects. In this paper, momentum-conserving dynamics of singularities is investigated on the basis of the pressureless gas dynamics system. Such dynamics turns out to be more diverse and complex, but it is also possible to formulate a variational approach, for which the basic principles and relations are obtained in the work.