Some Problems of Qualitative Researches on Ultrahyperbolic Equations

The prensent paper is a resume in the qualitative researches of the ultrahyperbolic equation,it involves a new proof of Asgeirsson's mean value theorem,extensions of mean value theorem,non-analyticity of the generalized potential solution,extensionality of solution,boundary problems and the elementary solution. Especially,we suggest to study ultrahyperbolie equation by means of the elementary solution,which is a natural way.

SOLVABILITY RESULTS OF A CONDITIONAL INPUT-OUTPUT EQUATION BASED ON A TYPE OF NONLINEAR LEONTIEF MODEL

A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.

Multi-scale Chaotic Analysis of the Characteristics of Gas-Liquid Two-phase Flow Patterns

Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtained gray-scale time series is decomposed by the Empirical Mode Decomposition (EMD) method, the various scales of the signals are processed by Hurst exponent method, and then the dual-fractal characteristics are obtained. The scattered bubble and the bubble cluster theories are applied to the evolution analysis of two-phase flow patterns. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length and Shannon entropy) are obtained. Resulting term of these properties, the dynamic characteristics of gas-liquid two-phase flow patterns are quantitatively analyzed. The results show that the evolution paths of gas-liquid two-phase flow patterns can be well characterized by the integrated analysis on the basis of the gray-scale time series of flowing images from EMD, Hurst exponents and Recurrence Plot (RP). In the middle frequency section (2nd, 3rd, 4th scales), three flow patterns decomposed by the EMD exhibit dual fractal characteristics which represent the dynamic features of bubble cluster, single bubble, slug bubble and scattered bubble. According to the change of diagonal average lengths and recursive Shannon entropy characteristic value, the structure deterministic of the slug flow is better than the other two patterns. After the decomposition by EMD the slug flow and the mist flow in the high frequency section have obvious peaks. Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns using the multi-scale non-linear analysis method based on image gray-scale fluctuation signals.

Analytic Solution to Nonlinear Dynamical System of Dragon Washbasin

Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinate of multi-degree-of-freedom self-excited vibration induced by dry friction of piecewise-smooth nonlinear systems is derived by means of average method, the results of which agree with those of the numerical solution. An effective and reliable analytical method investigating piecewise-smooth nonlinear systems of multi-degree-of-freedom has been given. Furthermore, this paper qualitatively analyses the curves about stationary amplitude versus rubbing velocity of hands and versus natural frequency of hands, and about angular frequency versus rubbing velocity of hands. The results provide a theoretical basis for identifying parameters of the system and the analysis of steady region.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.

Global Optimization Algorithm for Nonlinear Sum of Ratios Problems

In this paper, a global optimization algorithm is proposed for nonlinear sum of ratios problem （P）. The algorithm works by globally solving problem （P1） that is equivalent to problem （P）, by utilizing linearization technique a linear relaxation programming of the （P1） is then obtained. The proposed algorithm is convergent to the global minimum of （P1） through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming. Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems （P）.

Preparation of Fe-Mn/K/Al2O3 Fischer-Tropsch Catalyst and Its Catalytic Kinetics for the Hydrogenation of Carbon Monoxide

A K promoted iron-manganese catalyst was prepared by sol-gel method,and subsequently was tested for hydrogenation of carbon monoxide to light olefins.The kinetic experiments on a well-characterized Fe-Mn/K/Al2O3 catalyst were performed in a fixed-bed micro-reactor in a temperature range of 280-380 ℃,pressure range of 0.1-1.2 MPa,H2/CO feed molar ratio range of 1-2.1 and a space velocity range of 2000-7200 h-1.Considering the mechanism of the process and Langmuir-Hinshelwood-Hogan-Watson（LHHW） approach,unassisted CO dissociation and H-assisted CO dissociation mechanisms were defined.The best models were obtained using non-linear regression analysis and Levenberg-Marquardt algorithm.Consequently,4 models were considered as the preferred models based on the carbide mechanism.Finally,a model was proposed as a best model that assumed the following kinetically relevant steps in the iron-Fischer-Tropsch（FT） synthesis：（1） CO dissociation occurred without hydrogen interaction and was not a rate-limiting step;（2） the first hydrogen addition to surface carbon was the rate-determining steps.The activation energy and adsorption enthalpy were calculated 40.0 and -30.2 kJ.mol-1,respectively.

Nonlocality of Two-Qubit and Three-Qubit Schmidt-Correlated States

We investigate the nonlocality of Schmidt-correlated （SC） states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser-Horne-Shimony-Holt （CHSH） inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequaJity is only a sumcient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence, and relative entropy entanglement are discussed.

Three-dimensional Information Decoupling System Based on PSD and Deviation Correction

Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.

New Ansaetze for Obtaining Exact Solutions of Nonlinear Schroedinger-Type Equation

We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schrodinger equation which describe the femtosecond pulse propagation in monomode optical fiber. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.

Influence of Pipe-Diameter on Water Hammer Phenomenon

The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes its influence in essential hydraulic topics such as head loss, in pipelines. In this paper, the objective is to analyze the inner-diameter influence on water hammer phenomenon. An analytical algorithm for solving the unsteady-one-dimensional water hammer model had been applied. It had allowed estimating the instantaneous head at any point of a single pipeline. The model was solved by mean of the Laplace＇s Transformed application and the anti-transforming procedure into the complex field. To determinate the influence of internal-diameter conduit on the pressure oscillation, four distinct inside-diameter values were introduced into the solution, successively. The first overpressure-peak at each case was tabulated along with the corresponding inner^liameter and a mathematical relation had been founded. The obtained results show a close dependence between both, over-pressure peaks and internal-pipe diameter. It was founded that this dependence is given in terms of a non-linear relation between them. It was further founded that the wave frequency is sensitive to the variation of the pipe-diameter.

Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

In this paper an efficient computational method based on extending the sensitivity approach(SA) is proposed to find an analytic exact solution of nonlinear differential difference equations.In this manner we avoid solving the nonlinear problem directly.By extension of sensitivity approach for differential difference equations(DDEs),the nonlinear original problem is transformed into infinite linear differential difference equations,which should be solved in a recursive manner.Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained.Numerical examples are employed to show the effectiveness of the proposed approach.

Analytical Solution of Helmholtz Equation in Anisotropic and Nonhomogeneous Region

The analytical solution of Helmholtz equation for magnetic vector potential in anisotropic and nonhomogeneous region is presented. The solution is built of a combination of both Bessel and power functions. There are developed two examples that proof the accuracy of the proposed analytical solution. First example is showing the electromagnetic field analysis in slot of ferromagnetic rotor of electrical induction machine. The second example approaches electromagnetic field wave in resonator of the form of rectangular cavity The analytical solution presented is treated as an exact one and is being compared with the numerical solution, e.g., given by finite element method. The analytical solution can be used as a benchmark test for numerical algorithms,

Unified analytical solutions for a circular opening based on non-linear unified failure criterion

Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.

Analytic approximation to nonlinear hydroelastic waves traveling in a thin elastic plate floating on a fluid

An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large floating structure(VLFS)on the surface of deep water.A convergent analytical series solution for the plate deflection is derived by choosing the optimal convergencecontrol parameter.Based on the analytical solution the efects of diferent parameters are considered.We find that the plate deflection becomes lower with an increasing Young’s modulus of the plate.The displacement tends to be flattened at the crest and be sharpened at the trough as the thickness of the plate increases,and the larger density of the plate also causes analogous results.Furthermore,it is shown that the hydroelastic response of the plate is greatly afected by the high-amplitude incident wave.The results obtained can help enrich our understanding of the nonlinear hydroelastic response of an ice sheet or a VLFS on the water surface.

(2+1)-Dimensional Analytical Solutions of the Combining Cubic-Quintic Nonlinear Schrdinger Equation

We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.

Orbit control strategy for Lagrange point orbits based on an analytical method

The periodic or quasi-periodic orbits around collinear Lagrange points present many properties that are advantageous for space missions. These Lagrange point orbits are exponentially unstable. On the basis of an analytical method, an orbit control strategy that is designed to eliminate the dominant unstable components of Lagrange point orbits is developed. The proposed strategy enables the derivation of the analytical expression of nonlinear control force. The control parameter of this strategy can be arbitrarily selected provided that the parameter is considerably lower than the negative eigenvalue of motion equations, and that the energy required keeps the same order of magnitude. The periodic or quasi-periodic orbit of controlled equations remains near the periodic or quasi-periodic orbit of uncontrolled equations.

Analytical Solution for Peristaltic Transport of Viscous Nanofluid in an Asymmetric Channel with Full Slip and Convective Conditions

The peristaltic ttow of nanofluids is a relatively new area of research. Scientists are of the opinion that the no-slip conditions at the boundaries are no longer valid and consequently, the first and the second order slip conditions should be addressed. In this paper, the effects of slip conditions and the convective boundary conditions at the boundary walls on the peristaltic flow of a viscous nanofluid are investigated for. Also, the exact analytical solutions are obtained for the model. The obtained results are presented through graphs and discussed. The results reveal that the two slip parameters have strong effects on the temperature and the nanoparticles volume fraction profiles. Moreover, it has been seen that the temperature and nanoparticles volume fraction profiles attain certain values when the first slip condition exceeds a specified value. However, no limit value for the second slip parameter has been detected. Further, the effects of the various emerging parameters on the flow and heat transfer characteristics have been presented.

Multi-objective optimization for deepwater dynamic umbilical installation analysis

We suggest a method of multi-objective optimization based on approximation model for dynamic umbilical installation. The optimization aims to find out the most cost effective size, quantity and location of buoyancy modules for umbilical installation while maintaining structural safety. The approximation model is constructed by the design of experiment (DOE) sampling and is utilized to solve the problem of time-consuming analyses. The non-linear dynamic analyses considering environmental loadings are executed on these sample points from DOE. Non-dominated Sorting Genetic Algorithm (NSGA-II) is employed to obtain the Pareto solution set through an evolutionary optimization process. Intuitionist fuzzy set theory is applied for selecting the best compromise solution from Pareto set. The optimization results indicate this optimization strategy with approximation model and multiple attribute decision-making method is valid, and provide the optimal deployment method for deepwater dynamic umbilical buoyancy modules.