The algebro-geometric solutions for Degasperis-Procesi hierarchy

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker-Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy.Comment: 65 pages. arXiv admin note: text overlap with arXiv:solv-int/9809004 by other author

Misalignment of Renminbi Exchange Rate Revaluation: Estimation and Implications

For the past several years, the revaluation of the renminbi has been a hot topic among policy makers and economists as well as market participants inside and outside the PRC against the background of internal and external disequilibrium of the PRC economy. Based upon the history of the exchange rate system, current arguments made by various stakeholders, and surveys of different theoretical approaches, the authors develop a two-country general equilibrium model to determine the exchange rate, taking particular account of the implications of price rigidity for the policy independence of each country. An empirical test is also introduced to identify the current degree of misalignment of the renminbi compared to its estimated equilibrium rate

Infrastructure and regional development in the People's Republic of China

This paper investigates the relationship between infrastructure and rural economic development. It begins by reviewing the progress of Chinese economic and rural reform and analyzes the challenges faced by the government of the People's Republic of China (PRC). Then, based on the review, an endogenous growth model is created to show the channel and mechanism of public infrastructure impacting production and consumption. Next, an empirical study is carried out in order to identify the role of different kinds of infrastructure in rural development. The paper also discusses the interaction between institutional arrangement (soft infrastructure) and hard infrastructure. Finally, some suggestions and implications beneficial to the rural development of the PRC are drawn from theoretical and empirical studies

Modeling Private Sector Development in the People's Republic of China

In this paper, a simplified mathematical model based on the behavioral pattern of firms in the PRC is used to discuss the impact of marketization and privatization on private sector development. The model demonstrates that private enterprises, SOEs, and other entities undergoing reform in the PRC are entities with multiple objectives. This pattern of behavior leads to firms that tend to use more capital and labor to produce more output compared with pure profit-maximizing firms, but which earn fewer profits or even register losses. The impacts of firms’ non-profit objectives and the “costs of entry” on the size and number of firms are also discussed. The problem of matching between managerial ability and firm size is introduced to explain why gradual reform in PRC has succeeded, whereas the “Big Bang” in Russia failed

Effects of Hydraulic Gradient, Intersecting Angle, Aperture, and Fracture Length on the Nonlinearity of Fluid Flow in Smooth Intersecting Fractures: An Experimental Investigation

This study experimentally investigated the nonlinearity of fluid flow in smooth intersecting fractures with a high Reynolds number and high hydraulic gradient. A series of fluid flow tests were conducted on one-inlet-two-outlet fracture patterns with a single intersection. During the experimental tests, the syringe pressure gradient was controlled and varied within the range of 0.20–1.80 MPa/m. Since the syringe pump used in the tests provided a stable flow rate for each hydraulic gradient, the effects of hydraulic gradient, intersecting angle, aperture, and fracture length on the nonlinearities of fluid flow have been analysed for both effluent fractures. The results showed that as the hydraulic gradient or aperture increases, the nonlinearities of fluid flow in both the effluent fractures and the influent fracture increase. However, the nonlinearity of fluid flow in one effluent fracture decreased with increasing intersecting angle or increasing fracture length, as the nonlinearity of fluid flow in the other effluent fracture simultaneously increased. In addition, the nonlinearities of fluid flow in each of the effluent fractures exceed that of the influent fracture

The Reduced Order Method for Solving the Linear Complementarity Problem with an M-Matrix

In this paper, by seeking the zero and the positive entry positions of the solution, we provide a direct method, called the reduced order method, for solving the linear complementarity problem with an M-matrix. By this method, the linear complementarity problem is transformed into a low order linear complementarity problem with some low order linear equations and the solution is constructed by the solution of the low order linear complementarity problem and the solutions of these low order linear equations in the transformations. In order to show the accuracy and the effectiveness of the method, the corresponding numerical experiments are performed

Research and Application of PDM Borehole Technology for HDD

AbstractBy introducing the structure character and working principle of PDM, borehole technologies of PDM directional drilling were studied in this text, including borehole technology principle, directional method, technology flow, drilling technology parameters, branch borehole technology etc. Shaanxi Tingnan Coal .Ltd field application was taken as an example to do a simple introduction on PDM matching equipment and technology promotion. The borehole technology and related result can be used as reference for horizontal directional drilling research and construction

Vibration analysis of a cylinder with slight diameter and thickness variations

The cross section of circular cylinder in their dynamic model is always considered as a perfect circle, which means radii at every point on the circle are the same. In real engineering structure, there are slight fluctuations in shape of the circular cylinder which is different from those in ideal model. Meanwhile, effects of structural fluctuations on its dynamic characteristic are rarely analyzed before. To study problem mentioned above, the geometric shape of a typical, apparently symmetrical cylinder is examined experimentally to demonstrate that a small variation in diameter and thickness indeed exists in practice firstly. Because fluctuations in diameter and thickness of the cylinder are related to each other, we need to separate effects of a slight variation in its diameter and thickness on structural dynamic characteristics to search the key factor of influence. Then, two simplified modes, which are modeled by finite element method, are used to study the effects of diameter or thickness variation alone on the natural frequencies and modal shapes of the free cylinder. It is revealed that the diameter variation described by the simplified model captures the key influencing elements which affect the modal characteristics of the free cylinder. Finally, a free cylinder with both variations is analyzed numerically and the results are verified experimentally. This work illustrates that significant discrepancies inevitably exist between the measured results of an actual free cylinder and an assumed symmetrical model even if there is only a very slight variation in its geometric shape

Algebro-geometric Solutions for the Degasperis--Procesi Hierarchy

Though the completely integrable Camassa--Holm (CH) equation and Degasperis--Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker--Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker--Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy

Gradient-based compressive sensing for noise image and video reconstruction

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a convex minimisation problem, and propose a new compressive sensing based on gradient-based method for noise image and video. Secondly, to improve the computational efficiency of gradient-based compressive sensing, they formulate the convex optimisation of noise signal reconstruction under Lipschitz gradient and replace the iteration parameter by the Lipschitz constant. With this strategy, the convergence of our FGB-CS is reduced from O(1/k) to O(1/k2 ). Experimental results indicate that their FGB-CS method is able to achieve better performance than several classical algorithms