Journal of Advances in Applied Mathematics

3

Authors: Clement Boateng Ampadu

Recall from [1] the Green’s function is a solution to the following initial value problem ut(x, t) − kuxx(x, t) = 0 u(x, 0) = (x) where  is the Dirac Delta function, (x, t) 2 R×(0,1). In the present paper, inspired by the T −X family of distributions [2] and the following fundamental solution (x, t) = 1 p 4kt exp  − x2 4kt  we present a new solution to the above intitial value problem.

8

Authors: Xinfeng Li, Hao Deng

To study the return on education, R language and regression analysis were applied. First, the research background and research status at home and abroad were introduced. Then, the relevant theories and influencing factors of educational returns were analysed. Finally, taking Hunan Province as an example, using the data surveyed by the National Bureau of Statistics, a multiple linear regression model was established to study the educational returns of urban residents. The results showed that education, employment and the degree of regional development all affected educational returns. Therefore, the level of investment in education should be raised and the regional gap should be narrowed.

12

Authors: Michael Gr. Voskoglou

A Fuzzy Linear Programming problem differs from an ordinary one to the fact that the coefficients of its objective function and / or the technological coefficients and constants of its constraints are fuzzy instead of real numbers. In this work a new method is developed for solving such kind of problems by ranking the fuzzy numbers involved and by solving the obtained in this way ordinary Linear Programming problem with the standard theory. The values of the decision variables may then be converted to fuzzy numbers in order to facilitate a fuzzy expression of the problem’s optimal solution, but this must be strictly checked to avoid non-creditable expressions. Examples involving triangular and trapezoidal fuzzy numbers are also presented in the paper illustrating the applicability of our method to real-life applications.

15

Authors: Federico Talamucci

The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at a fixed distance from the corresponding pivot. The mathematical model is first written encompassing a large class of setting for the device (different sizes, different physical properties, ...). In order to carry on the problem of synchronization via analytical methods, we focus on the circumstance of identical pendula: in that case, some classical theorems concerning the zeroes of polynomial equations are used in order to locate the eigenvalues governing the process, so that the possibility of synchronization of the device can be better understood.

9

Authors: Huiliang Wang, Yangqi Cao

Based on the geometry theory and kinematics principle of gear form grinding machine, a mathematical model of gear form grinding machine vibration is established. Using the multiple scales method, the model is analyzed and solved, which provides a theoretical basis for the system study of the relationship between natural frequency and external excitation frequency. According to the theoretical analysis results, the test platform is set up on the YK7660 gear form grinding machine. By varying the parameters of grinding process, the data of vibration characteristics of gear form grinding is acquired and analyzed. The experimental results show that the change of grinding depth has great influence on the grinding force; meanwhile when the cutting depth is increased from 0.01mm to 0.02mm, the X axis vibration amplitude increases by 19% compared with the feed rate of the workpiece. The research of vibration characteristics of gear form grinding machine proves the validity of the grinding force derived by vibration theory, which provides the theoretical foundation for improving the accuracy of grinding gear in practical application.

18

Authors: Mohammed Harunor Rashid, Md. Zulfikar Ali, Alain Piétrus

Let X and Y be Banach spaces. Let be an open subset of X. Suppose that f : X ! Y is Fréchet differentiable in and F : X  2Y is set-valued mapping with closed graph. In the present paper, for solving the generalized equations 0 2 f(x) + F(x), an extended cubic method (ECM) is introduced and studied its convergence analysis. Indeed, we analyze semi-local and local convergence of the ECM.

4

Authors: Xilan Liu, Dejie Deng, Huijuan Wang

This paper is concerned with the oscillatory behavior of a class of neutral nonlinear difference equation with positive and negative coefficients. The oscillation criteria are given, which extended the results of known ones.

7

Authors: Ge Li, Yuncui Zhang, Yan Feng

Tensor is a high-level extension of the matrix, H-tensor is a special tensor and it is a new developed concept in tensor analysis. In this paper, we introduce some definitions and theorems firstly, then establish some implementable criteria in identifying nonsingular H-tensor, and at last give two numerical examples to prove the criteria are reliable.

13

Authors: Asim Timalsina, Gene Hou, Jin Wang

We present a new computational framework for fluid-structure interaction problems that involve rigid body motion. Based on a partitioned strategy, the fluid and structural dynamics are computed separately, and the solutions communicate at the interface. The immersed boundary method is employed to handle the fluid-structure interaction, and the direct-forcing technique is utilized to calculate the interaction force. In particular, the rigid body motion is directly and explicitly incorporated into the formulation and computation of the structural dynamics. We demonstrate our methodology by numerically simulating the motion of single and multiple rigid circular discs interacting with nonlinear viscous flow.

14

Authors: Mingwei LI

The widespread application of “Internet +” technology has enlightened the problemsolving of the increasingly heavy traffic in China. Thus the “Internet + traffic” has been pushed to the leading edge. The numerous researches in the “Internet + traffic” field mainly focus on the strategies of transformation and upgrading the existing traffic system to a more “internet” way, few have ever concerned about the demands on developing “Internet + traffic” of each cities, which was usually treated as for granted. However, as this paper finds out, different cities, based on their urban traffic development, have different levels of “Internet + traffic” development demand. Therefore, in this paper we discuss the development index and construction demand degree of the “Internet + traffic”. In addition, we build the multiple regression model and select data of 36 principal cities in China to make clear the construction level and key development areas of “Internet + traffic” under the requirements of urban traffic. Additionally, the prediction model is provided to evaluate the construction degree of separate cities when developing “Internet + traffic”. At last, suggestions would be put forward for a better development of the “Internet + traffic”.