##### International Journal of Mathematical Sciences and Computing (IJMSC)

IJMSC Vol. 5, No. 2, Apr. 2019

#### MECS Press Journal

REGULAR PAPERS

##### Stability Analysis of Equilibrium Points of Newcastle Disease Model of Village Chicken in the Presence of Wild Birds Reservoir

DOI: https://doi.org/10.5815/ijmsc.2019.02.01, Pub. Date: 8 Apr. 2019

Newcastle is a viral disease of chicken and other avian species. In this paper, the stability analysis of the disease free and endemic equilibrium points of the Newcastle disease model of the village chicken in the absence of any control are studied. The Hurwitz matrix criterion is applied to study the stability of the Newcastle disease free equilibrium point,Q0. The result shows that the disease free equilibrium point is locally asymptotically stable iff the principle leading minors of the Hurwitz Matrix,   (for n∈ℝ+) are all positive. Using the Castillo Chavez Theorem we showed that, the disease free equilibrium point is globally asymptotically when R0<1. Furthermore, using the logarithmic function and the LaSalle’s Theorem, the endemic equilibrium point is found globally asymptotically stable for R0>1. Finally the numerical simulations confirm the existence and stability of the equilibrium points of the model. This reveals that, proper interventions are needed so as to decrease the frequently occurrence of the Newcastle disease in the village chicken population.

##### Category Specific Prediction Modules for Visual Relation Recognition

DOI: https://doi.org/10.5815/ijmsc.2019.02.02, Pub. Date: 8 Apr. 2019

Object classification in an image does not provide a complete understanding of the information contained in it. Visual relation information such as “person playing with dog” provides substantially more understanding than just “person, dog”. The visual inter-relations of the objects can provide substantial insight for truly understanding the complete picture. Due to the complex nature of such combinations, conventional computer vision techniques have not been able to show significant promise. Monolithic approaches are lacking in precision and accuracy due to the vastness of possible relation combinations. Solving this problem is crucial to development of advanced computer vision applications that impact every sector of the modern world. We propose a model using recent advances in novel applications of Convolution Neural Networks (Deep Learning) combined with a divide and conquer approach to relation detection. The possible relations are broken down to categories such as spatial (left, right), vehicle-related (riding, driving), etc. Then the task is divided to segmenting the objects, estimating possible relationship category and performing recognition on modules specially built for that relation category. The training process can be done for each module on significantly smaller datasets with less computation required. Additionally this approach provides recall rates that are comparable to state of the art research, while still being precise and accurate for the specific relation categories.

##### Sorting using a combination of Bubble Sort, Selection Sort & Counting Sort

DOI: https://doi.org/10.5815/ijmsc.2019.02.03, Pub. Date: 8 Apr. 2019

One of the most important problems in computer science is the ordering of the data. Although sorting is a very old computer science problem, it still attracts a great deal of research. Usually, when we face a problem, we’re concerned with finding the solution, then getting it out of our heads and into a text editor, white-board, or down on a piece of paper. Eventually, we start transforming that idea into code, and the code is pretty terrible the first time around. But at some point, once we’ve made it work and made it right, we find ourselves asking: Can I make it fast? Can I make it better? This paper presents an enhanced sorting algorithm which comprises of a combination of Bubble Sort, Selection Sort, and Counting Sort. The new algorithm is analyzed, implemented, tested, compared and the results were promising.

##### Comparative Analysis of Personnel Distributions in the Local Government Service in Ekiti-State, Nigeria, for Service Delivery

DOI: https://doi.org/10.5815/ijmsc.2019.02.04, Pub. Date: 8 Apr. 2019

It’s is no longer news that the Local Government (Third-tier of government in Nigeria) has not been able to optimally discharge its responsibilities according to its mandate. This had raised serious policy and research concerns that resulted to several reformative approaches in a bid to restructuring the system for efficient service delivery in the past decade. One major unpopular reason for inefficient service delivery was poor administration in the Local Government as a result of unbalanced distribution of personnel by cadre and gender in each local government in the state. This had not only hampered local government administration but also impeded adequate provision of expected services to local populace in line with its mandate as enshrined in the fourth schedule of the 1999 Constitution of the Federal Republic of Nigeria. Application of Statistical analysis using Chi-square Test of Independence showed that distribution of employees by cadre depends on local government in post in the year under study. Percentage distributions employed revealed that some local governments that are located around the capital city had more workers than those located outside the state capital city except some local governments with more viable socio-economic benefits. Sex ratio showed that there was gender imbalance as female personnel are more than their male counterpart in the local government service is.

##### Study of Memory Effect in an Inventory Model with Linear Demand and Shortage

DOI: https://doi.org/10.5815/ijmsc.2019.02.05, Pub. Date: 8 Apr. 2019

For real market studies of any business, inclusion of memory or past experience in inventory model has great impact. Memory means it depends on the past state of the process not only current state of the process. Indeed, the inventory system is an appropriate example as a memory affected system. Presence of long past experiences or short past experiences of any company or shop has different importance on increasing or decreasing profit. The description of the memory dependent inventory model is more appropriate process compared to the memory less inventory model. Depending on demand rate, a comparison between the minimized total average costs of different numerical example has been presented. Fractional order derivative and integration have been used to establish the model. Our considered numerical example establishes that if linear type demand rate is only time proportional, profit of the business is high compared to the linear type demand rate.