##### Global Dynamics and Traveling Waves of a Delayed Diffusive Epidemic Model with Specific Nonlinear Incidence Rate

El Mehdi Lotfi, Khalid Hattaf, Noura Yousfi

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/BJMCS/2017/30573

In this paper, we investigate the global stability and the existence of traveling waves for a delayed diffusive epidemic model. The disease transmission process is modeled by a specific nonlinear function that covers many common types of incidence rates. In addition, the global stability of the disease-free equilibrium and the endemic equilibrium is established by using the direct Lyapunov method. By constructing a pair of upper and lower solutions and applying the Schauder fixed point theorem, the existence of traveling wave solution which connects the two steady states is obtained and characterized by two parameters that are the basic reproduction number and the minimal wave speed. Furthermore, the models and main results studied the existence of traveling waves presented in the literature are extended and generalized.

##### Modeling of Tomato Prices in Ashanti Region, Ghana, Using Seasonal Autoregressive Integrated Moving Average Model

Francis Ohene Boateng, John Amoah-Mensah, Martin Anokye, Lot Osei, Paul Dzebre

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2017/30535

The pricing of seasonal and perishable crops such as tomatoes is of paramount concern to emerging economies. In this paper, we have formulated a model for the prices of tomatoes in the Ashanti Region of Ghana. We applied time series on the tomatoes price data recorded over the period of 1994 to 2015, sourced from the Ministry of Food and Agriculture (MoFA) Research Directorate, Kumasi. We analyzed the data using Seasonal Autoregressive Integrated Moving Average (SARIMA) by regrouping the data into quarters for each year. Consequently, the best fitted model was found to be SARIMA (0, 1, 1)x(0,1,1). The model predicted that in 2016, the prices of tomatoes will increase with second quarter providing the highest price. However, after a huge rise in price at the second, price is expected drop in both the third and fourth quarter of 2016 all things being equal. This has been the price trend in all second quarters for the period considered in the analysis with exception of 2015 where price fell by almost GHC 5.00 compared the first quarter.

We have formulated this model to assist stakeholders including government to take informed decisions and formulate pricing policies that will guarantee farmers stable price.

##### Algorithms for Solving Some Inverse Problems from Combinatorial Number Theory

Elias Abboud

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2017/30619

In this paper we use the characteristic property of sumsets which states that there exists a proper subset tiling the set by translates to solve by an algorithmic methods, for finite sets, some inverse problems in combinatorial number theory.

##### Design and Comparison of Equiripple Bandpass Filter for Wireless Applications at Varying Bandwidths

Pooja Mehra, Savita Shivani, R. P. Gupta

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2017/30605

This paper presents the design of equiripple programmable bandpass filter for wireless applications. The designed filter covers a wide range of bandwidth compared to what can be achieved by a simple microcontroller. This bandwidth covers a variety of digital wireless applications like TETRA, IS-95, GSM to TACS. The responses of the designed filter are discussed and compared at varying bandwidths. Also the time required to evaluate the performance of designed filter also reduces drastically compared to a simple MAC unit.

##### A New Efficient Hybrid String Matching Algorithm to Solve the Exact String Matching Problem

Sinan Sameer Mahmood Al-Dabbagh, Nawaf Hazim Barnouti

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2017/30497

The string matching algorithms are considered one of the most studied in the computer science field because the fundamental role they play in many different applications such as information retrieval, editors, security applications, firewall, and biological applications. This study aims to introduce a new hybrid algorithm based on two well-known algorithms, namely, the modified Horspool and SSABS hybrid algorithms. Two factors used to analyze the proposed algorithm which is the total number of character comparisons and total number of attempts. The ABSBMH algorithm which is the name chosen for the proposed hybrid algorithm was tested on different types of standard datatype. The ABSBMH algorithm shows less number of character comparisons when compared to the results of other algorithms, while show almost no big different in the results of number of attempts this is due to the proposed hybrid algorithm preprocessing phase based on SSABS algorithm which is the same preprocessing phase of the Quick Search algorithm, so for all these reasons the results of the ABSBMH and other algorithms in terms of total number of attempts have been shown a small different, this is because it use different pattern lengths which are selected randomly from the databases. The experiential results expose that performance of the hybrid algorithm influenced by the type of the dataset used, the DNA sequence shows the worst result, while the English text datatype show the best results in terms of total number of character comparisons.

##### mcga: R Implementation of the Machine-coded Genetic Algorithms

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/BJMCS/2017/30894

Genetic Algorithms (GAs) are global optimization and search algorithms that mimic the natural selection and genetic processes. Floating-point GAs (FPGAs) are other type of GAs which directly operate on real-vectors without requiring a geno-type pheno-type distinction and encoding-decoding processes. However, the classical crossover and mutation operators are not directly applicable on the real-vectors. As a result of this, new types of genetic operators are developed for FPGAs. Machine-coded GAs (MCGAs) apply byte-based genetic operators on the byte representations of the candidate solutions. This natural encoding scheme makes classical crossover operators applicable on the real-vectors. Addition to this, MCGAs report more precise results in larger domains of decision variables. Mutation operation on the byte representations of variables have also similar e ects with its binary counterpart. The R package mcga defines plug-in versions of byte-based operators that can be integrated with the recently developed function ga in package GA. Low level utility functions are written in C++ and wrapped with the Rcpp and .Call interface of R. Advantages and disadvantages of using byte-based operators are discussed and demonstrated on some univariate and multivariate optimization problems.

##### The Generalized Reed-Muller Codes in a Modular Group Algebra

Harinaivo Andriatahiny, Vololona Harinoro Rakotomalala

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2017/30145

We study some properties of the modular group algebra of the additive group of a Galois ring over a finite field. A description of the Generalized Reed-Muller codes in this group algebra is presented.