Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System

It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.

Symmetry Transformations and Exact Solutions of a Generalized Hyperelastic Rod Equation

In this paper,a nonlinear wave equation with variable coefficients is studied,interestingly,this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities.With the aid of Lou’s direct method1,the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained.The corresponding numerical examples of exact solutions are presented by using different coefficients.Particularly,while the variable coefficients are taken as some special constants,the nonlinear wave equation with variable coefficients reduces to the one with constant coefficients,which can be used to describe the propagation of the travelling waves in general cylindrical rods composed of generally hyperelastic materials.Using the same method to solve the nonlinear wave equation,the validity and rationality of this method are verified.

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposedto build the transverse constraints on the basic vertices in gauge theories.I show that,while the BRST symmetryin non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluonvertex which constrains the longitudinal part of the vertex,the transverse symmetry transformation associated with theBRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex,which constrainsthe transverse part of the quark-gluon vertex from the gauge symmetry of QCD.

Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The magnetohydrodynamics （MHD） convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the pres- ence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill- based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.

Eye and Iris Detection Using Projection and Radial Symmetry Transform

This paper presents an eye and iris detection algorithm for human facial images. The authors combine three features of the eye to develop the algorithm：1） the pixels surrounding the eyes are more variable than other parts of the face; 2） eye pixels are darker than their neighbors; 3） eyes often exhibit radial symmetric properties. Through the first feature,two rough regions of both eyes are detected on the face. Eye masks are then formed based on the second feature,and a fast radial symmetry transform is applied to the two rough regions of both eyes. Finally,accurate iris centers are located by searching the maximum value of the radial symmetry transform results. Using 450 human facial images from the Caltech face database,experiments show that the success rate of the proposed method is 91.7%. The effectiveness of the method was also verified through detection of video frames.

Iris Localization Algorithm Based on Improved Generalized Symmetry Transform

Accuracy and fastness of iris localization are very important in automatic iris recognition. A new fast iris localization algorithm based on improved generalized symmetry transform (GST) was proposed by utilizing (iris) symmetry. GST was improved in three aspects:1) A new distance weight function is defined. The new weight function, which is effective in iris localization, utilized the characteristic of irises that the iris is a circular object and it has one inner boundary and one outer boundary. 2) Each calculation of the symmetry measurement of a pair of symmetry points was performed by taking one point of a pair as the starting point of the transformation. This is the most important reason for fast iris localization,due to which, repetitious computation was largely excluded. 3) A new phase weight function was proposed to adjust GST to locate circle target much better because the inner part of iris is darker than the outer part. The edge map of iris image was acquired and GST was only implemented on the edge point, which decreased computation without loss of accuracy. The modification of distance weight function and phase weight function leads to the accuracy of localization, and other ideas speed up the localization. Experiments show that the average speed of new algorithm is about 7.0—8.5 times as high as traditional ones including integro-differential operator and Hough transform method.

Spatial Interpolation of Soil Texture Using Compositional Kriging and Regression Kriging with Consideration of the Characteristics of Compositional Data and Environment Variables

The spatial interpolation for soil texture does not necessarily satisfy the constant sum and nonnegativity constraints. Meanwhile, although numeric and categorical variables have been used as auxiliary variables to improve prediction accuracy of soil attributes such as soil organic matter, they （especially the categorical variables） are rarely used in spatial prediction of soil texture. The objective of our study was to comparing the performance of the methods for spatial prediction of soil texture with consideration of the characteristics of compositional data and auxiliary variables. These methods include the ordinary kriging with the symmetry logratio transform, regression kriging with the symmetry logratio transform, and compositional kriging （CK） approaches. The root mean squared error （RMSE）, the relative improvement value of RMSE and Aitchison＇s distance （DA） were all utilized to assess the accuracy of prediction and the mean squared deviation ratio was used to evaluate the goodness of fit of the theoretical estimate of error. The results showed that the prediction methods utilized in this paper could enable interpolation results of soil texture to satisfy the constant sum and nonnegativity constraints. Prediction accuracy and model fitting effect of the CK approach were better, suggesting that the CK method was more appropriate for predicting soil texture. The CK method is directly interpolated on soil texture, which ensures that it is optimal unbiased estimator. If the environment variables are appropriately selected as auxiliary variables, spatial variability of soil texture can be predicted reasonably and accordingly the predicted results will be satisfied.

In-pit coal mine personnel uniqueness detection technology based on personnel positioning and face recognition

Since the coal mine in-pit personnel positioning system neither can effectively achieve the function to detect the uniqueness of in-pit coal-mine personnel nor can identify and eliminate violations in attendance management such as multiple cards for one person, and swiping one's cards by others in China at present. Therefore, the research introduces a uniqueness detection system and method for in-pit coal-mine personnel integrated into the in-pit coal mine personnel positioning system, establishing a system mode based on face recognition + recognition of personnel positioning card + release by automatic detection. Aiming at the facts that the in-pit personnel are wearing helmets and faces are prone to be stained during the face recognition, the study proposes the ideas that pre-process face images using the 2D-wavelet-transformation-based Mallat algorithm and extracts three face features: miner light, eyes and mouths, using the generalized symmetry transformation-based algorithm. This research carried out test with 40 clean face images with no helmets and 40 lightly-stained face images, and then compared with results with the one using the face feature extraction method based on grey-scale transformation and edge detection. The results show that the method described in the paper can detect accurately face features in the above-mentioned two cases, and the accuracy to detect face features is 97.5% in the case of wearing helmets and lightly-stained faces.

Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation

Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method（GCTM）. The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor（DSCF） becomes singular when the inhomogeneity parameter of medium is close to zero.

Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems

This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.

Nonlocal Symmetry,CTE Solvability and Interaction Solutions of Whitham–Broer–Kaup Equations

Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.

Non-equidistance DGM(1,1) Model Based on the Concave Sequence and Its Application to Predict the China’s Per Capita Natural Gas Consumption

Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved, such as for the DGM(1,1) model, based on a concave sequence, the modeling error will be larger. In this paper,firstly the definition of sequence convexity is given out, and it is proved that the output sequence of DGM(1,1) model is a convex sequence. Next, the residual change law of DGM(1,1) model based on the concave sequence is discussed, and the non-equidistance DGM(1,1) model is proposed. Finally, by introducing the symmetry transformation, a concave sequence is transformed into a convex sequence, called the symmetric sequence of the concave sequence, and then construct the non-equidistance DGM(1,1)model based on the convex sequence. The example results show that the novel method is more accurate than the direct modeling for a concave sequence.

New Algebraic Approaches to Classical Boundary Layer Problems

Classical non-steady boundary layer equations are fundamental nonlinear partial differential equations in the boundary layer theory of fluid dynamics. In this paper, we introduce various schemes with multiple parameter functions to solve these equations and obtain many families of new explicit exact solutions with multiple parameter functions. Moreover, symmetry transformations are used to simplify our arguments. The technique of moving frame is applied in the three-dimensional case in order to capture the rotational properties of the fluid. In particular, we obtain a family of solutions singular on any moving surface, which may be used to study turbulence. Many other solutions are analytic related to trigonometric and hyperbolic functions, which reflect various wave characteristics of the fluid. Our solutions may also help engineers to develop more effective algorithms to find physical numeric solutions to practical models.

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States

Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.