Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u=2(ln f)_x and u=2(ln f)_{xx}, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations

Equivalence of the Initialized Riemann-Liouville Derivatives and the Initialized Caputo Derivatives

Initialization of fractional differential equations remains an ongoing problem. In recent years, the initialization function approach and the infinite state approach provide two effective ways to deal with this problem. The purpose of this paper is to prove the equivalence of the initialized Riemann-Liouville derivatives and the initialized Caputo derivatives with arbitrary orders. By synthesizing the above two initialization theories, the diffusive representations of the two initialized derivatives with arbitrary orders are derived. Laplace transforms of the two initialized derivatives are shown to be equal. As a result, the two most commonly used derivatives are proved to be equivalent when initial conditions are properly imposed.Comment: 17 page

Hereditary effects of exponentially damped oscillators with past histories

Hereditary effects of exponentially damped oscillators with past histories are considered in this paper. Nonviscously damped oscillators involve hereditary damping forces which depend on time-histories of vibrating motions via convolution integrals over exponentially decaying functions. As a result, this kind of oscillators are said to have memory. In this work, initialization for nonviscously damped oscillators is firstly proposed. Unlike the classical viscously damped ones, information of the past history of response velocity is necessary to fully determine the dynamic behaviors of nonviscously damped oscillators. Then, initialization response of exponentially damped oscillators is obtained to characterize the hereditary effects on the dynamic response. At last, stability of initialization response is proved and the hereditary effects are shown to gradually recede with increasing of time

Analytical Results of k-core Pruning Process on Multi-layer Networks

Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer networks are especially useful when describing the systems with several kinds of interactions. In this paper we study the analytical solution of $\textbf{k}$-core pruning process on multi-layer networks. $k$-core decomposition is a widely used method to find the dense core of the network. Previously the Nonbacktracking Expand Branch (NBEB) is found to be able to easily derive the exact analytical results in the $k$-core pruning process. Here we further extend this method to solve the $\textbf{k}$-core pruning process on multi-layer networks by designing a variation of the method called Multicolor Nonbacktracking Expand Branch (MNEB). Our results show that, given any initial multi-layer network, Multicolor Nonbacktracking Expand Branch can offer the exact solution for each intermediate state of the pruning process, these results do not only apply to uncorrelated network, but also apply to networks with either interlayer correlations or in-layer correlations

Using NonBacktracking Expansion to Analyze k-core Pruning Process

We induce the NonBacktracking Expansion Branch method to analyze the k-core pruning process on the monopartite graph G which does not contain any self-loop or multi-edge. Different from the traditional approaches like the generating functions or the degree distribution evolution equations which are mathematically difficult to solve, this method provides a simple and intuitive solution of the k-core pruning process. Besides, this method can be naturally extended to study the k-core pruning process on correlated networks, which is among the few attempts to analytically solve the problem

H2CO and H110{\alpha} observations towards NH3 sources

We observed the H2CO(110-111) absorption lines and H110{\alpha} radio recombination lines (RRL) toward 180 NH3 sources using the Nanshan 25-m radio telescope. In our observation, 138 sources were found to have H2CO lines and 36 have H110{\alpha} RRLs. Among the 138 detected H2CO sources, 38 sources were first detected. The detection rates of H2CO have a better correlation with extinction than with background continuum radiation. Line center velocities of H2CO and NH3 agree well. The line width ratios of H2CO and NH3 are generally larger than 1 and are similar to that of 13CO. The correlation between column densities of H2CO and extinction is better than that between NH3 and extinction. These line width relation and column density relation indicate H2CO is distributed on a larger scale than that of NH3, being similar to the regions of 13CO. The abundance ratios between NH3 and H2CO were found to be different in local clouds and other clouds.Comment: accepted for publish in Astrophysics and Space Science, DOI:10.1007/s10509-014-1922-

An Analytical Solution to the kk-core Pruning Process

$k$-core decomposition is widely used to identify the center of a large network, it is a pruning process in which the nodes with degrees less than $k$ are recursively removed. Although the simplicity and effectiveness of this method facilitate its implementation on broad applications across many scientific fields, it produces few analytical results. We here simplify the existing theoretical framework to a simple iterative relationship and obtain the exact analytical solutions of the $k$-core pruning process on large uncorrelated networks. From these solutions we obtain such statistical properties as the degree distribution and the size of the remaining subgraph in each of the pruning steps. Our theoretical results resolve the long-lasting puzzle of the $k$-core pruning dynamics and provide an intuitive description of the dynamic process

The Impact of Multinational Auto Manufacturers on the Market Structural of Chinese Saloon Car Industry

The paper studies the structural characteristics of Chinese Saloon Car market of 1993-2002 by three market structural indexes: rate of market concentration, HHI index and logarithm variance of manufacturer scale. We prove that the Saloon Car market that once was largely occupied by several monopolies has gradually developed into a multivariate competitive market. Although the multinational auto manufacturers still have a strong control of national auto market, the violent reaction of oligopoly with the continuing opening of the market is emerging. After WTO accession, the recombining situations of Chinese auto industry, which are participated by multinational auto manufacturers, have been fixed on the whole, but it is not the result of sufficient market competition. The Chinese auto market will still face danger of being shuffled after the transitional period of WTO. It is possible to create a more stable and mature market structure only after Chinese Saloon Car industry carries through a reconstruction which based on a more fairness and orderly competition. Keywords: Multinational Enterprise, Market Structure, Rate of Market Concentration, Saloon Car Industry Résumé: Ce texte étudie les caractéristiques structurales du marché chinois de berline entre 1993 et 2002 à l’aide de trios index structuraux : vitesse de concentration du marché , index HHI , et la variance logarithmique de l’échelle de fabricant . On constate que le marché de berline , occupé aurapavant largement par plusieurs monopoles , est devenu graduellement un marché concurrentiel multivariant . Bien que les fabricants multinationaux d’automobile aient encore un contrôle fort sur le marché national de voiture , la réaction forte d’oligopole avec l’ouverture continuelle du marché est en train de s’émerger . Après l’accession à l’OMC , la fusion de l’industrie chinoise d’automobile , participée par les fabricants multinationaux d’automobile a été déterminée dans l’ensemble , mais ce n’est pas le résultat de la concurrence du marché . Le marché chinois d’automobile fera face à la recomposition après la période de transition de l’OMC . Il est possible de créer une structure plus stable et mûr du marché après la traversée de reconstruction de l’industrie chinoise de berline . Cette reconstruction doit se baser sur la concurrence plus juste et plus ordonnée . Mots-clés: enterprise multinationale , structure du marché , vitesse de concentration du marché , industrie de berlin

The Reconstruction Algorithm Study of 2D Interpolating Resistive Readout Structure

Systematic investigations including both simulation and prototype tests have been done about the interpolating resistive readout structure with GEM (Gaseous Electron Multiplier) detector. From the simulation, we have a good knowledge of the process of charges diffusion on the surface of the readout plane and develop several reconstruction methods to determine the hit position. The total signal duration time of a typical event with the readout structure is about several hundred nanoseconds, which implied an ideal count rate up to 106Hz. A stable worked prototype was designed and fabricated after the simulation. Using 55Fe 5.9keV X-Ray, the image performance of the prototype is examined with flat field image and some special geometry shapes, meanwhile, an energy resolution of about 17% is obtained

Size-dependent radiosensitization of PEG-coated gold nanoparticles for cancer radiation therapy

Gold nanoparticles have been conceived as a radiosensitizer in cancer radiation therapy, but one of the important questions for primary drug screening is what size of gold nanoparticles can optimally enhance radiation effects. Herein, we perform in vitro and in vivo radiosensitization studies of 4.8, 12.1, 27.3, and 46.6 nm PEG-coated gold nanoparticles. In vitro results show that all sizes of the PEG-coated gold nanoparticles can cause a significant decrease in cancer cell survival after gamma radiation. 12.1 and 27.3 nm PEG-coated gold nanoparticles have dispersive distributions in the cells and have stronger sensitization effects than 4.8 and 46.6 nm particles by both cell apoptosis and necrosis. Further, in vivo results also show all sizes of the PEG-coated gold nanoparticles can decrease tumor volume and weight after 5 Gy radiations, and 12.1 and 27.3 nm PEG-coated gold nanoparticles have greater sensitization effects than 4.8 and 46.6 nm particles, which can lead to almost complete disappearance of the tumor. In vivo biodistribution confirms that 12.1 and 27.3 nm PEG-coated gold nanoparticles are accumulated in the tumor with high concentrations. The pathology, immune response, and blood biochemistry indicate that the PEG-coated gold nanoparticles do not cause spleen and kidney damages, but give rise to liver damage and gold accumulation. It can be concluded that 12.1 and 27.3 nm PEG-coated gold nanoparticles show high radiosensitivity, and these results have an important indication for possible radiotherapy and drug delivery.Comment: 14 pages, 9 figure