Kazeem Oare Okosun; Oluwole Daniel Makinde

In this paper, we derive and analyse a deterministic model for the transmission of childhood disease perform optimal control analysis of the model. The model is found to exhibit multiple equilibria. However, a unique endemic equilibrium exists when there is no disease induced death. We also derive and analyse the necessary conditions for the optimal control of the disease. In addition, we investigate the cost-effectiveness of the controls to determine the most effective strategy to control childhood disease with minimum costs. Finally, we present the numerical solutions.]]>

Shiye Wang; Zhezhou Yu; Xiangchun Yu

More and more attention has been paid to linear-time online action detection and video segmentation, due to wide application in the fields of human-computer interaction, games and surveillance. In this paper we propose a new descriptor which can be adopted for action recognition, online action detection and segmentation. In addition, we propose the improved efficient linear search (improved ELS) whose scheme is modified to solve the problem of the existence of many action classes' maximum subarray sums exceeding their thresholds. Then we evaluated our approach on MSRC-12 and MSR-Action3D datasets. The results show that our descriptor achieves the state-of-the-art results on action recognition and the performance of the improved ELS is much higher than that of the ELS.]]>

Ilham Djellit; Wissame Selmani

The dynamic behaviour of a dynamical system, described by a planar map, is analytically and numerically explored. We examine the analytical conditions for the stability and bifurcation of the fixed points of the system and by using the numerical methods, we compute bifurcation curves of fixed points and cycles with orders up to five under variation of three parameters, and compute all codimension-1 and codimension-2 bifurcations on the corresponding curves. These curves form stability boundaries of various types of cycles which emanate around codimension-2 bifurcation points. Mathematical underpinnings and numerical simulations confirm our results and contribute to reveal further complex dynamical behaviours.]]>

Chao Wei; Chaobing He

This paper is concerned with the parameter estimation problem for partially observed nonlinear stochastic system. The suboptimal estimation of the state is obtained by constructing the extended Kalman filtering equation. The likelihood function is provided based on state estimation equation. The strong consistency of the estimator is proved by applying maximal inequality for martingales, Borel-Cantelli lemma and uniform ergodic theorem. An example is provided to verify the effectiveness of the method.]]>

Anant Kant Shukla; T.R. Ramamohan; S. Srinivas

The objective of this article is to obtain analytical solutions for a set of nonlinear problems by using 'further generalisation of HAM'. In comparison to the Homotopy analysis method (HAM) solutions, more accurate solutions are obtained by introducing an extra term in the frame of HAM. We consider a set of three nonlinear problems of which first two are governed by single nonlinear ordinary differential equation (they are two cases of the forced Van der Pol Duffing oscillator) and third one is governed by a system of four coupled nonlinear ordinary differential equations. A maximum reduction of approximately 25% in the square residual error is obtained by using the generalised form of HAM compared to the square residual error without the generalised form.]]>

Lanfang Zhang; Juanjuan Ji; Julang Jiang; Chaolong Zhang

The KZK parabolic nonlinear wave equation is one of the most widely employed nonlinear models for propagation of 3D diffraction sound beams in dissipative media. In this paper, the exact analytical solutions of (3 + 1)-dimensional time fractional KZK equation have been constructed in the sense of modified Riemann-Liouville derivative and the (G′/G)-expansion method, the simplest equation and the fractional complex transform. As a result, some new exact analytical solutions are obtained, and the effects of diffraction, attenuation and nonlinearity are researched deeply using the obtained exact analytical solutions.]]>

L. Lakshmi; P. Bhaskara Reddy; C. Shoba Bindu; N. Aravind Kumar

Most of the web search queries submitted by users are short, uncertain and ambiguous. The information retrieval process is very complicated today as it depends on many factors like classification of a web query; number of phrases present in the query, number of in-links and out-links to and from the documents, vocabulary, changing nature of the meaning of words. Information retrieval process mainly involves two steps, retrieval of relevant documents for user queries and retrieved documents are sorted using efficient page rank algorithms. Most of the existing systems use static navigation of the web query and ranking. They mainly depend on the number of in links and out links of a web page. In this paper, we proposed dynamic navigation of web query using B-tree to retrieve relevant documents efficiently by reducing nonrelevant documents and resulting documents are sorted by using an improved page rank algorithm.]]>

Guihua Li; Pengxiang Ge

Fish scales were unique structural materials that served as a form of natural armour and affected the mechanical properties which had important applications in bionics. Digital image correlation (DIC) method was used to determine the mechanical properties, but it took a long time to calculate the uniaxial tensile deformation. In this investigation a DIC optimisation algorithm method based on speeded-up robust features (SURF) and Newton-Raphson (N-R) was conducted on specimens prepared from the scales. First, the SURF algorithm was used to detect the matched points and their coordinate values in the digital images before and after deformation. Then, the initial displacement of the interest point was estimated from the affine transformation fitted to the matched feature points inside the subset area. Last, the zero-mean normalised sum of squared differences (ZNSSD) metric function was optimised by the N-R iterative method, and the optimised displacement value of the interest points would be gained. The numerical translation experiments and simulation results showed that this method improved the search speed and the measurement accuracy effectively. So the deformation of fish scales for axial tension would be calculated by this method.]]>