##### Deep Recurrent Q-learning Method for Area Traffic Coordination Control

Saijiang Shi, Feng Chen

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2018/41281

In order to improve the performance of Deep Q-learning when dealing with the area traffic control which is a partially observable Markov decision process. This paper introduces Deep Recurrent Q-learning by changing the fully connected network layers to LSTM layers. On the other hand, we use transfer learning to achieve the coordination of multiple intersections in the area. By the simulation experiments, this paper compares the average delay of our algorithm with the Deep Q-learning algorithm for three different saturation flows, respectively. We also compare our algorithm with another two popular traffic signal control algorithms, i.e., Q-learning and fixed time control algorithm. The experiment results show that the performance of our improved Deep Recurrent Q-learning algorithm is better than the other three algorithms.

##### Mean-periodic Functions Associated to a Family of Differential-refection Operators

Sami Rebhi

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2018/38207

We consider the family of differential-reflection operators ∧A,∈. We study the harmonic analysis associated with this operator. Next we de ne and characterize the mean-periodic functions associated with ∧A,∈.

##### Variation Mass Effects on the Stability of Libration Points of Restricted Three Body Problem (Laplace Transformation)

Sahar H. Younis, Fatma M. Elmalky, M. N. Ismail

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2018/40842

In this work a dynamical system of three bodies with decreasing mass with respect to time is deduced. The Jean’s law is applied onto equations of motion. The equations of motion in this case are differed from that with constant mass only by small perturbing force considered as the variation of mass. This system is solved by using Laplace and Inverse Laplace Transformation. An application is done on the Earth–Moon-|Spacecraft system. The results obtained are compared with the previous work obtained by Explicit Rung-Kutta method and it was in a good agreement.

##### New Approach to Exponential H∞ Filtering for Uncertain Singular Systems with Markovian Switchings

Mengzhuo Luo, Shouming Zhong

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/JAMCS/2018/40826

In this paper, the problem of exponential H filtering is investigated for uncertain singular Markovian jump systems(SMJSs) with time-varying delay. A mode dependent approach is presented to deal with it. By constructing a stochastic Lyapunov functional and employing some novel integral inequalities, a filtering design criterion is proposed under which the resulting filtering error system is robustly exponentially mean-square admissible with a prescribed H performance index. Based on this, the proper gain matrices and optimal H performance index can be efficiently obtained via solving a convex optimization problem subject to some linear matrix inequalties(LMIs). Finally, a numerical example is given to demonstrate the reduced conservatism and effectiveness of the presented general filtering technique.

##### Implicit Hybrid Points Approach For Solving General Second Order Ordinary Differential Equations With Initial Values

O. O. Olanegan, B. G. Ogunware, C. O. Alakofa

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2018/40447

This article focuses on the development of implicit hybrid method for the general solution of second order ordinary differential equations with initial values (IVPs). The method of collocation and interpolation of power series was used to derive the method, while Taylor series is used to develop and analyze the predictors The method is found to be consistent and zero-stable. The method shows to be more efficient and accurate when compared with existing work by other authors.