In this paper, the dynamical behaviors and projective synchronization of a five-dimensional hyperchaotic Lorenz system are investigated. First of all, a hyperchaotic system is constructed by introducing two state variables into the Lorenz chaotic system. Secondly, the dynamical behaviors of the proposed system, such as the dissipative property and equilibrium point, are discussed. Thirdly, based on the stability theory, the projective synchronization of the systems can be achieved. Finally, some numerical simulations are given to verify the projective synchronization scheme.

In this paper, the problem of existence of periodic solution is studied for the second order delay differential equation with a singularity of repulsive type

In this paper, the perturbed compound Poisson-Geometric risk model with constant interest and a threshold dividend strategy are considered. Firstly, the integro-differential equations with boundary conditions for the Gerber-Shiu function is discussed. Then the equation satisfying the ruin probability studied when the claim size is exponential function. Finally, Integro-differential equations with certain boundary for the moment-generation function of the present value of total dividends until ruin is derived.

In this paper, we review a nonlinear matching pursuit approach (Hou and Shi, 2013), a data- driven time-frequency analysis method, which is looking for the sparsest representation of multiscale data over a dictionary consisting of all intrinsic mode functions (IMFs). In many practical problems, signals are non-integer period sampled. In other words, the time window may not contain exactly an integer number of signal periods. We consider the sparse time-frequency decomposition of non-integer period sampling signals by the nonlinear matching pursuit method and estimate the error. The estimation show that the relative error depends on the separation factor, the frequency ratio, and the number of periods of the IMF.

Obtaining economic situation of the group is a key step in understanding the socio-economic situation like the division of the rich and the poor. But the traditional way to obtain economic situation of the group is based on the survey data of professionals and mathematical models. Such methods are time- consuming and too dependent on professionals. Therefore, the use of data mining techniques to judge and predict the economic situation of the group came into being. Such methods are efficient that can overcome the shortcomings of the traditional methods. In this paper, we started by acquiring the individual's economic level and finally established a personal economic level prediction model. Through large-scale access to the individual's economic level, the economic level of the group can be obtained. We analyzed the Chinese text data published on the network by Individuals with logistic regression model to explore whether the above text data can reflect a person's economic status. The experimental results indicate that personal created textual data is able to forecast the individual's economic level accurately and certain categories of vocabulary have an impact on the individual's economic level.

Rescue workers and fire fighters’ job mostly require entering to disaster zones such as factories accident areas, collapsed mines, or burned buildings to perform rescue operations. In addition to human caused disasters, the aftermath of natural disasters such as tornados, earthquakes and tsunamis requires them to be present in order to contain the disaster, help injured victims, and guide trapped victims to a safe exit. The lives of the rescue workers and fire fighter are always at risk in such accidents, since they have no prior knowledge of accident source, environment, and location. Thereby, Search and Rescue Robot (SRR) is an excellent alternative, in which it can perform certain tasks of rescue workers and fire fighters without endangering their life. In a case of disaster, SRR can be sent directly to the danger zones to navigate and provide helpful information regarding the cause of the accident, location of the hazard spots, number of trapped or injured victims, the conditions inside the danger zone, and several other functions. The use of SRR will improve the quality of rescue missions because it can provide important data from the heart of the accident where it is too risky for human to go in. In addition, it can identify the number and the status of the trapped victims and even supply basic equipment, which in some cases can be lifesaving, such as masks and fire blankets in accident which include fires. In this project we designed and fabricated a prototype of search and rescue robot that can perform multiple tasks and can navigate in rough surfaces. The SRR can be controlled from a distance station where the operator can manipulate the SRR movement and its grapping arm while monitoring the surrounding environment using video camera and different sensors. The fabricated prototype successfully passed all the tests that was set to examine its performance.