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In this paper, the KdV-Sawada-Kotera-Ramani(KdVSKR) equation in various dimensions are studied. The bilinear form of the (1+1)-dimensional and (2+1)-dimensional KdVSKR equation are obtained by the independent transformation. Based on the Hirota bilinear method, we constructed new interaction solutions by studying the unknown nonlinear differential equations for the corresponding parameters. Three dimensional plots, density plots and contour plots provide us with a better understanding of visualizing the dynamic behavior of solutions.

While links in simple networks describe pairwise interactions between nodes, it is necessary to incorporate hypernetworks for modeling complex systems with arbitrary-sized interactions. In this study, we focus on the hyperlink prediction problem in hypernetworks, for which the current state-of-art methods are latent-feature-based. A practical algorithm via topological features, which can provide understandings of the organizational principles of hypernetworks, is still lacking. For simple networks, local clustering or loop reflects the correlations among nodes; therefore, loop-based link prediction algorithms have achieved accurate performance. Extending the idea to hyperlink prediction faces several challenges. For instance, what is an effective way of defining loops for prediction is not clear yet; besides, directly comparing topological statistics of variable-sized hyperlinks could introduce biases in hyperlink cardinality. In this study, we address the issues and propose a loop-based hyperlink prediction approach. First, we discuss and define the loops in hypernetworks; then, we transfer the loop-features into a hyperlink prediction algorithm via a simple modified logistic regression. Numerical experiments on multiple real-world datasets demonstrate superior performance compared to the state-of-the-art methods.

Social interaction between individuals constantly affects the development of their personal opinions. Previous models such as the Deffuant model and the Hegselmann-Krause (HK) model have assumed that individuals only update their opinions after interacting with neighbors whose opinions are similar to their own. However, people are capable of communicating widely with all of their neighbors to gather their ideas and opinions, even if they encounter a number of opposing attitudes. We propose a model in which agents listen to the opinions of all their neighbors. Continuous opinion dynamics are investigated in activity-driven networks with a tolerance threshold. We study how the initial opinion distribution, tolerance threshold, opinion-updating speed, and activity rate affect the evolution of opinion. We find that when the initial fraction of positive opinion is small, all opinions become negative by the end of the simulation. As the initial fraction of positive opinions rises above a certain value —about 0.45— the final fraction of positive opinions sharply increases and eventually equals 1. Increased tolerance threshold δ is found to lead to a more varied final opinion distribution. We also find that if the negative opinion has an initial advantage, the final fraction of negative opinion increases and reaches its peak as the updating speed λ approaches 0.5. Finally we show that the lower the activity rate of individuals, the greater the fluctuation range of their opinions.

Annealing effects on structural and compositional performances of Al2O3 thin films on 4H–SiC substrates are studied comprehensively. The Al2O3 films are grown by atomic layer deposition through using trimethylaluminum and H2O as precursors at 300 °C, and annealed at various temperatures in ambient N2 for 1 min. The Al2O3 film transits from amorphous phase to crystalline phase as annealing temperature increases from 750 °C to 768 °C. The refractive index increases with annealing temperature rising, which indicates that densification occurs during annealing. The densification and grain formation of the film upon annealing are due to crystallization which is relative with second-nearest-neighbor coordination variation according to the x-ray photoelectron spectroscopy (XPS). Although the binding energies of Al 2p and O 1s increase together during crystallization, separations between Al 2p and O 1s are identical between as-deposited and annealed sample, which suggests that the nearest-neighbour coordination is similar.

Surface leakage currents of AlGaN/GaN high electron mobility transistors are investigated by utilizing a circular double-gate structure to eliminate the influence of mesa leakage current. Different mechanisms are found under various passivation conditions. The mechanism of the surface leakage current with Al2O3 passivation follows the two-dimensional variable range hopping model, while the mechanism of the surface leakage current with SiN passivation follows the Frenkel-Poole trap assisted emission. Two trap levels are found in the trap-assisted emission. One trap level has a barrier height of 0.22 eV for the high electric field, and the other trap level has a barrier height of 0.12 eV for the low electric field.

Since a shell structure contains a wealth of information, it is not only very important for understanding the transport properties of the network, but also essential to identify influential spreaders in complex networks. Nodes within each shell can be classified into two categories: protected nodes and unprotected nodes. In this paper, we propose a generalization of the localized attack, modified localized attack, which means that when a randomly chosen node (root node) is under attack, protected nodes will not be removed, but unprotected nodes in the nearest shells will fail. We numerically and analytically study the system robustness under this attack by taking an Erdos-Renyi (ER) network, a regular random (RR) network and a scale-free (SF) network as examples. Moreover, a fraction of nodes belonging to giant component S and a critical threshold q c , where S approaches to zero, are given. The result implies that increasing connection density has been found to be useful to significantly improve network robustness.

We study both analytically and numerically the robustness ofninterdependent networks with partial support-dependence relationship, which reflects real-world networks more realistically. For a starlike network ofnErd˝os-Renyi (ER) networks, we find that the system undergoes from second-order to first-order phase transition as coupling strengthqincreases. Moreover, we notice that the region of the first-order transition becomes larger, while the region of the second-order transition becomes smaller as the number of networksnincreases. However, for a starlike network ofnscale-free (SF) networks, the system undergoes from second-order through hybrid-order to first-order phase transition asqincreases. Furthermore, we also observe that the region of the first-order transition remains constant and appears only forq= 1, however, the region of hybrid-order transition gradually becomes larger and the region of the second-order transition becomes smaller asnincreases. For a looplike network ofnER networks, we find the giant componentp ! to be independent of the number of networks. Additionally, when the average degree of networks increases, the region of the first-order transition becomes smaller and the region of the second-order transition becomes larger. For the case ofnER networks with partial support-dependence relationship, as average supported degree ˜ !" ,ncoupled networks become independent and only second-order transition is observed, which is similar toq= 0. Copyright c !EPLA, 2013