In this paper we have taken the fuzzy differential equation with linear differential operator. We have used Adomian decomposition method (ADM) to find the approximate solution. We have given several numerical examples and by comparing the numerical results obtain from ADM with the exact solution, we have studied their accuracy.

The main objective of this paper is to use the reduced differential transform method (RDTM) for finding the analytical approximate solutions for solving systems of nonlinear partial differential equations (NPDEs). The approximate solutions obtained by RDTM is verified by comparison with the exact solutions to show that the RDTM is quite accurate, reliable and can be applied for many other nonlinear partial differential equations. The method considers the use of the appropriate initial or boundary conditions and finds the solution without any discretization, transformation, or restrictive assumptions. This method is a simple and efficient method for solving the nonlinear partial differential equations. The numerical results show that this method is a powerful tool for solving systems of NPDEs. The analysis shows that our analytical approximate solutions converge very rapidly to the exact solutions.

This paper concerns the solution for singularly perturbed via cubic spline in tension. The derived scheme leads to a tridiagonal system. The error analysis is proved and the method is shown to have a fourth order convergence for the particular choice of the parameters. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory.

The object detection systems in an image, refers to systems that will find an object in an image completely mechanized and automated. These systems are often searching a particular object (which is known) in a raw image. These systems are often involved in two separate categories: (a) image processing, and (b) pattern recognition. The first issue involves the extraction of meaningful and valuable features. While the second issue involved finding a suitable learning model, so that it separates the object data from non- object data in a favorable and acceptable way. In this study, we have reviewed by three-step method of learning objects and using a multi-layered combination model for detection and using heuristic algorithms association rules for feature selection step and finally using a combination category method similar to the intensification of the final step there. And by reviewing various evaluation models, we measured the quality of our models. In this study, we showed that using a majority vote model is the best way to detect an object.

Kharchenko A1, Bodnarchuk I2*, Galay I.1, Yatcyshyn V2 1 National Aviation University, Kosmonavta Komarova ave. 1, Kyiv, 03058, Ukraine 2 Ternopil Ivan Pul’uj National Technical University, Ruska str, 56, Ternopil, 46000, Ukraine , Tel.: +38-050-437 7606. E-mail: bodnarchuk_io@gmail.com (Received May 12, 2016, accepted September 20, 2016) The problems of a multi-criteria decision making model of software system architecture dealing with definition of criterion function and formalization of the trade-off estimation procedure are discussed. Taking into account the domain requirements and criteria values limitations, the universal scalar convolution is proposed where the weights of the quality criterion depends on its proximity to the limitation. An optimization model of "replacement-compensation" was used for solution of reengineering problems and directed selecting of software architecture.

This paper presents a method for control discrete-time system with time-delay. The main idea is a convert the discrete-time delay linear controllable system into the linear systems without delay. Then by using similarity transformations a state feedback matrix was obtained, so that time-delay has no effect on the system. The proposed technique is illustrated by means of numerical examples.

The product sold in different stores may be not same price, mainly caused by diverse retailers’ situations. Meanwhile, maximizing relative interests is the businesses’ common goal. Based on the 2-2 suppliers-retailers situation, this paper researches on the market by using dynamic price Stackelberg game model. We consider two cases, one is retailers under the win-win environment (case 1) and the other is they under the malicious competition environment (case 2). Through analyzing and comparing the two cases, this paper finds that the influence of different parameters on the Nash Equilibrium stable range in size is same, while the amplitude of stable range, the prices of goods, sales as well as the businessman profit are all different. These results will be revealed in a series of charts, including the stability diagram, bifurcation diagram, phase plot and histogram. And the conclusions may have a certain reference value for businesses on how to stabilize the market and which competitive measures should be taken.

Due to the extensive existence of time delay for natural population, it is necessary to take the effect of time delay into account in forming a biologically meaningful mathematical model. In view of this, a delayed predator-prey system with Holling type-IV functional response and impulsive dispersal between two patches is formulated. By using comparison theorem of impulsive differential equation and some analysis techniques, we obtain a predator-extinction periodic solution, which is globally attractive. Furthermore, it is proved that the investigated system is permanent. Numerical simulations are carried out to illustrate the theoretical results.