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A new method to importance identification and optimization of meta-action unit for electromechanical product is proposed herein. In the present method, the influence factors and optimization factors related to the importance identification and optimization of meta-action unit were given. The weight vectors of influence factors and optimization factors were obtained by the improved EAHP (extension analytical hierarchy process), and the importance matrix and optimization weight vector of meta-action unit were also built by fuzzy theory. Then, the meta-action unit importance identification and optimization model was established according to the influence factors weight vector, optimization factors weight vector, meta-action unit importance matrix, and meta-action unit comprehensive optimization weight vector. A typical domestic electromechanical product was taken as the analysis object, and the effectiveness of the new method is verified by the comparison of various methods. The proposed method is helpful to reduce the blindness of enterprises in selecting analysis objects, and also lays a foundation for improving the reliability of electromechanical products.

The quality of CNC (computer numerical control) machine tool is the key to the survival of manufacturing enterprises. How to comprehensively and accurately evaluate and analyze its quality is very important for the timely discovery and improvement of machine tool defects. The current research either only evaluates and analyzes a certain quality characteristic of CNC machine tool, or ignores the dynamic nature of CNC machine tool quality parameters, which reduces the accuracy of quality analysis results. To address this problem, firstly, reliability, maintainability and supportability were taken as the comprehensive evaluation indexes of CNC machine tool quality characteristics, so as to improve the comprehensiveness of the analysis. Secondly, on the basis of considering the dynamic characteristics of machine tool reliability, the ADC (availability, dependability, capability) model was improved to obtain a comprehensive quality evaluation index function E RMS with time-varying characteristics. Finally, the characteristics of E RMS were analyzed, and its specific evaluation criteria were also given. Several CNC machine tools were tracked, and the method proposed in this paper was applied. The E RMS of the machine tools was obtained, and its characteristics were analyzed. The results verify the correctness of the proposed method, and provide theoretical basis and technical support for the improvement of the quality of CNC machine tool and the market competitiveness of manufacturing enterprises.

In this paper, traveling waves with different frequencies and velocities can be constructed by three wave method. Some new exact solitary and periodic solitary solutions are obtained for the Fifth-Order Sawada–Kotera equation using three wave type method via Hirota bilinear form. The solutions investigated by three wave method are more than solutions by others method such as homoclinic test method.

The paper generalizes the analytical solutions for the thermal-eigenstrain-induced elastic field in two joined half-space solids or a bimaterial with an interface of coupled dislocation-like and force-like imperfects. The present model permits quantitative jumps in displacements and/or stresses from one medium to the other. The model also leads to a set of explicit closed-form expressions for the dilatation-induced elastic fields in half-spaces I and II joined by such an imperfect interface. Cases for the elastic fields subjected to an ellipsoidal, a spherical, a spherical shell, and a cylindrical thermal inclusion are analyzed, and key results are validated by comparison with existing experimental results. The influences of several types of interfaces, such as the perfectly bonded, dislocation-like, and force-like interfaces, on the stress and displacement transmissions are further discussed.

Stress distributions and plastic deformation zones are factors directly influencing the fatigue life of components under cyclic contact. An effective approach to improving the resistance of a steel to contact fatigue failure is surface hardening, which builds gradient yield strength from the surface of the steel to the bulk. When using the distortion energy theory as the criterion to identify failure initiation for a case-hardened steel, contact yield starts in the subsurface wherever the von Mises stress reaches the local material strength, rather than at the point of the maximum von Mises stress in the subsurface. If the yield strength changes from the surface to the bulk following a straight line, the location of yield initiation should occur at the tangency of the strength line and the von Mises stress curve. Analyses on circular, rectangular, and elliptical contacts are presented to reveal the locations of contact yield initiation for such case-hardened steels subjected to rolling contact stresses, for which the influence of friction can be ignored. A group of formulas relating contact yield initiation, in terms of the critical pressure, location of the first yield, and plasticity index (transition to plasticity) to case-hardening parameters, such as the case slope, the minimum case depth, and surface and bulk strengths, are derived to facilitate contact element designs using case-hardened materials. The results are applied to examine the rolling contact behaviors of several case-hardened steels, and the data correlation suggests that their rolling contact fatigue lives are related to a nondimensional case-hardening slope besides external loading.

Purpose d-psicose-3-epimerase (DPEase) catalyses the isomerisation of d-fructose to d-psicose, a rare sugar in nature with unique nutritional and biological functions. An effective industrial-scale method is needed for d-psicose production. Herein, the expression of a neutral and a slightly acidic pH DPEase in Bacillus subtilis was evaluated. Methods Two DPEase genes from Clostridium bolteae and Dorea sp. were separately expressed in B. subtilis via plasmid pSTOP1622, and an extra P43 promoter was employed to the expression cassette. The fermentation conditions of the engineered B. subtilis strains were also optimised, to facilitate both cell growth and enzyme production. Result The introduction of P43 promoter to the two DPEase genes increased enzyme production by about 20%. Optimisation of fermentation conditions increased DPEase production to 21.90 U/g at 55 °C and 24.01 U/g at 70 °C in B. subtilis expressing C. bolteae or Dorea sp. DPEase, equating to a 94.67% and 369.94% increase, respectively, relative to controls. Conclusion Enhanced DPEase production was achieved in B. subtilis expressing C. bolteae or Dorea sp. DPEase genes.

The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

This paper presents the derivation of a set of the novel closed-form solutions for the eigenstrain-induced elastic fields in two joined half-space solids with an interface of coupled dislocation-like and force-like imperfects. A model is proposed to characterize the interfacial discontinuity properties concerning displacements and stresses, which permits quantitative jumps of either the displacements or the stresses from one medium to the other. Basic Galerkin vectors in these two imperfectly joined half-spaces are derived based on the boundary conditions, and thus the elastic responses are obtained in explicit expressions. Taking advantage of the three-dimensional fast Fourier Transform algorithms for the convolution and correlation, the elastic fields subjected to one arbitrarily shaped inclusion or more can be efficiently and accurately evaluated. The influences of several types of interfaces, such as the perfectly bonded interface, the dislocation-like interface, and the force-like interface, on the stress and displacement transmissions are discussed. Cases for the elastic fields due to a cuboidal, a spherical, and an array of multiple cuboidal inclusions, are investigated.

The exact solutions for the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equations are investigated via Maple software. According to the Hirota bilinear form of the NNV equations, lump solutions are mainly obtained by the limit method of the heteroclinic test functions with initial values. Furthermore, the interaction solutions of the lump and N -soliton solutions are researched with the aid of new test functions which consist of the quadratic polynomial functions and the exponential functions. Especially, the sufficient conditions for the existence of the interactions solutions for NNV equations are given.

The finite dimension estimates of Hausdorff dimension and fractal dimension of the attractor of the dissipative quantum Zakharov equations are mainly studied by using the estimates of the Lyapunov exponents. The main results on the attractor are obtained through studying the linear system $\operatorname{DS}(t)$ , which is the differential system of solution operator $S(t)$ for the dissipative quantum Zakharov equations at the initial value $(m_{0},n_{0},E_{0})$ .

Random invariant manifolds are considered for a stochastic Swift-Hohenberg equation with multiplicative noise in the Stratonovich sense. Using a stochastic transformation and a technique of cut-off function, existence of random invariant manifolds and attracting property of the corresponding random dynamical system are obtained by Lyaponov-Perron method. Then in the sense of large probability, an approximation of invariant manifolds has been investigated and this is further used to describe the geometric shape of the invariant manifolds.

The NPS pollution is difficult to manage and control due to its complicated generation and formation mechanism, especially in the data sparse area. Thus the ECM and BTOPMC were, respectively, adopted to develop an easy and practical assessment method, and a comparison between the outputs of them is then conducted in this paper. The literature survey and field data were acquired to confirm the export coefficients of the ECM, and the loads of TN and TP were statistically analyzed in the study area. Based on hydrological similarity, runoff data from nearby gauged sites were pooled to compensate for the lack of at-site data and the water quality submodel of BTOPMC was then applied to simulate the monthly pollutant fluxes in the two sections from 2010 to 2012. The results showed agricultural fertilizer, rural sewage, and livestock and poultry sewage were the main pollution sources, and under the consideration of self-purification capacity of river, the outputs of the two models were almost identical. The proposed method with a main thought of combining and comparing an empirical model and a mechanistic model can assess the water quality conditions in the study area scientifically, which indicated it has a good potential for popularization in other regions.

A new test function is proposed to construct new exact solitary solution for nonlinear evolution equation. The (2 + 1)-dimensional Sawada–Kotera equation is employed as an example to illustrate the effectiveness of the suggested method and some new wave solutions with three different velocities and frequencies are obtained. Obviously, the method can be applied to solve other type of nonlinear evolution equations as well.

The statistical properties of annual runoff in major rivers of China are studied based on the theory of stochastic process and technology of time series analysis. These properties include the characteristics of intra-annual and inter-annual variations of runoff, trends, abrupt changes and periodicities. The new findings from the intensive calculations and appropriate analysis of data in longer period are as follows: (i) compared with the nonuniformity of intra-annual runoff before 1980, the nonuniformity of intra-annual runoff in China generally decreased after 1980, except for Huaihe River and Songhua River; (ii) compared with the annual runoff before 1980, the annual runoff in China generally decreased after 1980 except for WangJiaba station in Huaihe River and Ha-Erbin station in Songhua River; the frequency of continuous low flow and continuous high flow in Haihe River and the downstream of Yellow River is higher than those in other rivers in China; (iii) annual runoff shows a downward trend in major rivers of China especially in Haihe River, Liao River and the midstream and downstream of Yellow River; (iv) there exist certain abrupt changes of annual runoff in major rivers of China; the abrupt change-points are different among different river basins; and (v) almost periodicities of annual runoff sequences in major rivers of China are generally 20 years below, that is, 3~7 and 12~20 years. The reasons for these changes are mainly caused by climate change and human activities. Copyright © 2011 John Wiley & Sons, Ltd.

New exact solutions including bright soliton solutions, breather and periodic types of chirped soliton solutions, kink-wave and homoclinic wave solutions for the 2D Ginzburg–Landau equation are obtained using the special envelope transform and the auxiliary function method. It is shown that the specially envelope transform and the auxiliary function method provide a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.

The high-order dispersive nonlinear Schrodinger equation is considered. The exact solutions were obtained by Zhang et al. [J.L. Zhang, M.L. Wang, X.Z. Li, Phys. Lett. A 357 (2006) 188-195] are analyzed. We can demonstrate that some solutions do not satisfy this equation. To obtain the correct solutions, the F-expansion method is applied to solve it.

Exact soliton solutions to the (2+1)-dimensional Ito equation are studied based on the idea of extended homoclinic test and bilinear method. Some explicit solutions, such as triangle function solutions, soliton solutions, doubly-periodic wave solutions and periodic solitary wave solutions, are obtained. It shows that the (2+1)-dimensional Ito equation has richer solutions. Besides, the elastic interactions of the solutions and their corresponding physical meaning are discussed.

An algebraic method is applied to obtain a series of exact solutions to the two-dimensional cubic Ginzburg–Landau equation with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. A Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method, is proposed to obtain the exact periodic solutions. It is shown that the periodic solutions obtained by using Jacobi elliptic function expansion method include some like-kink wave solutions and like-shock wave solutions.

Two types of soliton deflexion of (1 + 3)D Kadomtsev–Petviashvili (K–P) equation are considered. Using the Hirota bilinear form and the new technique of “homoclinic test”, a type of exact periodic soliton solution of the K–P equation with positive transverse dispersion effects is obtained. Another type of periodic soliton solution is found by means of the periodic soliton solution of the K–P equation with negative transverse dispersion effects and a temporal and spatial transformation. It is also investigated that the equilibrium solution u 0 = - 1 6 is an unique deflexion point, periodic soliton of traveling in different spatial directions will be interchanged with the solution varying from one side of - 1 / 6 to the other side.

Exact solitary-wave, kink wave and singular solitary-wave solutions for Kadomtsev–Petviashvili (KP) equation with p-power (p > 1) of nonlinearity are obtained using a novel auxiliary equation and homogeneous balance method.

In this paper, a novel identical reforming of differential equation and the Exp-function methods are used to construct solitary solutions and periodic solutions of (2+1)-dimensional cubic-quintic Ginzburg-Landau equation. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.

New approaches, homoclinic test approach (HTA) and extended homoclinic test approach (EHTA), are proposed to seek solitary-wave solution of high dimensional nonlinear wave system. Exact periodic solitary-wave, periodic soliton, cross solitary-wave and doubly periodic wave solutions for YTSF equation are obtained using HTA and EHTA, respectively.

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in H 0 1 .

New exact wave solutions including homoclinic wave, kink wave and soliton solutions for the 2D Ginzburg–Landau equation are obtained using the auxiliary function method, generalized Hirota method and the ansatz function technique under the certain constraint conditions of coefficients in equation, respectively. The result shows that there exists a kink-wave solution which tends to one and the same periodic wave solution as time tends to infinite.

In this paper, we obtain a new class of exact cross kink-wave and periodic solitary-wave solutions for Jimbo–Miwa equation by using two-soliton method, bilinear method and transforming parameters into complex ones. Moreover, we investigate singular and non-singular phenomenons of solutions. In addition, we study the resonance and non-resonance interactions between y – t periodic solitons and different line solitons.

The generlized complex Ginzburg-Landau equation (CGL) under periodic boundary condition is studied. The existence of global solution for this equation is established under appropriate assumption on a nonlinear σ, which rigorously establishes the foundation for further investigation of this type of model.

Logistics industry is becoming a more and more important field needed to be concentrated for all kinds of enterprises to reduce their own operation cost, and shorten their delivery time and so on. How to change the complicated logistics problem into abstract network model is elucidated here. Firstly, a directed graph G = (V, E) is used to describe the general logistics problem with some common restrictions such as cost and time etc. Secondly, considering the growth of logistics node, an improved network transport model was set forth. Thirdly, the combination of ant colony arithmetic with logistics network transport model is expounded, based on the similarity between logistics network transport model and Travelling Salesman Problem. Finally, the solution and analysis for the improved model is illustrated according to the ant colony arithmetic, and some related conclusions are detailed.

In present paper, we investigate a class of stochastic differential delay equations with Poisson jump and markovian switching.Constructing discrete approximate solution and continuous approximate solution by means of Euler-Maruyama scheme, we show the numerical solution converges to the true solution of stochastic differential delay equations with Poisson jump and Markovian switching in the sense of $L^{1}$-norm under one non-Lipschitz condition.

In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)ut=ρu−Δφ(u)−(1+iγ)Δu−νΔ2u−(1+iμ)|u|2σu+αλ1⋅∇(|u|2u)+β(λ2⋅∇)|u|2 is studied. The existence of global attractor for this equation with periodic boundary condition is established and upper bounds of Hausdorff and fractal dimensions of attractor are obtained.