Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations

This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.

Classification of discrete equations linearizable by point transformation on a square lattice

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a MSbious transformation.

Painlevé Integrability of Nonlinear Schrdinger Equations with both Space-and Time-Dependent Coefficients

We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger （NLS） equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal＇s simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.

Image detection and verification of visual navigation route during cotton field management period

In order to meet the actual operation demand of visual navigation during cotton field management period,image detection algorithm of visual navigation route during this period was investigated in this research.Firstly,for the operation images under natural environment,the approach of color component difference,which is applicable for cotton field management,was adopted to extract the target characteristics of different regions inside and outside cotton field.Secondly,the median filtering method was employed to eliminate noise in the images and realize smoothing process of the images.Then,according to the regional vertical cumulative distribution graph of the images,the boundary characteristic of the cotton seedling region was obtained and the central position of the cotton seedling row was determined.Finally,the detection of the candidate points cluster was realized,and the navigation route was extracted by Hough transformation passing the known point.The testing results showed that the algorithms could rapidly and accurately detect the navigation route during cotton field management period.And the average processing time periods for each frame image at the emergence,strong seedling,budding and blooming stages were 41.43 ms,67.83 ms,68.80 ms and 74.05 ms,respectively.The detection has the advantage of high accuracy,strong robustness and fast speed,and is simultaneously less vulnerable to interference from external environment,which satisfies the practical operation requirements of cotton field management machinery.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step,fully adaptive in space,hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions.The method is based on the hybrid level set/front-tracking approach proposed in[H.D.Ceniceros and A.M.Roma,J.Comput.Phys.,205,391-400,2005].Geometric,interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance(level set)function,which is evaluated fast and to machine precision,is used as a fluid indicator.The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in[S.Shin,S.I.Abdel-Khalik,V.Daru and D.Juric,J.Comput.Phys.,203,493-516,2005]whose success for greatly reducing parasitic currents has been demonstrated.The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude.To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic,adaptive mesh refinements.This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step,linearly implicit time integration scheme.We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications:the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability,an example of bubble ascending dynamics,and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

A Property of Continuous Mapping from a Sphere to the Euclidean Space and Its Applications

In this paper, we study the property of continuous mappings from a sphere to the Euclidean space. By using the theory of the periodic transformation in algebraic topology, we obtain a generalized Borsuk-Ulam theorem and then give some applications of the theorem.