by Charles- Ogan and Gladys Ibibo
Review Article
Technology has grown rapidly in today’s world and so the teaching and learning of mathematics have become more and more necessary. A new technological software- GeoGebra is to make the teaching and learning of the subject more practical, easy and simple to understand. Calculus is the mathematics of change. Calculus is an important branch of mathematics which many students find difficult and complex to comprehend. GeoGebra as a dynamic software, easy-to-use which promotes learning and enhance understanding of calculus concepts. It is a free new technological tool, a new means of utilizing technology with visual aids to assist students to interact with mathematical concepts independently or in teams, in the classroom or at home. This study demonstrated practical ways of constructing calculus concepts. Showed the simulations of tracing and identifying the solutions of solving problems in Calculus. The study suggested that Mathematics Teachers should be encouraged to use GeoGebra and other technological tools to improve the quality of teaching Mathematics. Also, GeoGebra should be introduced to Mathematics educators in Nigeria to enable students to explore the world of mathematics in a wider spectrum and think more creatively.
American Journal of Applied Mathematics and Statistics. 2018, 6(3), 115-120. DOI: 10.12691/ajams-6-3-5
Pub. Date: July 10, 2018
8979 Views1119 Downloads
by Narender Singh, Dalip Singh and Meenaxi
Original Research
This paper express reliability measures of a cold standby system which have two units. In cold standby system one unit operative and other unit kept as a spare. In the system both the unit kept as non-identical. The each operative unit fails due to snowstorm with different failure rate. The system completely failed when the both two units are failed. The failed unit cannot be operative directly by the repairman. The failed unit under the snow, first digging out from the snow then hospitalize (repair) the unit after that the unit becomes operative. Some properties of reliability system such as mean time to system failure, availability and profit have been computed. At last particular cases have been taken to explain the model.
American Journal of Applied Mathematics and Statistics. 2018, 6(3), 109-114. DOI: 10.12691/ajams-6-3-4
Pub. Date: June 22, 2018
5678 Views1573 Downloads
by K. Prudhvi
Original Research
In this paper, we prove a unique fixed point theorem for generalized d-cyclic contraction in dislocated metric spaces (d-metric spaces). Our result generalizes, extends and improves some known results existing in the references.
American Journal of Applied Mathematics and Statistics. 2018, 6(3), 107-108. DOI: 10.12691/ajams-6-3-3
Pub. Date: June 14, 2018
5740 Views1203 Downloads
by Ikeme John Dike and Chinyere Ogochukwu Dike
Original Research
Ebola Virus Disease (EVD) is a complex and unprecedented epidemic killer disease. Recently, the disease has caused serious loss of life, waste of economic and material resources in West African nations. The most prevalent countries are Guinea, Liberia and Sierra Leone. Compartmental models are traditional epidemiological mdels that try to explain epidemic problems through the use of specific compartments that are subsets of a given population. Analysis using the developed queueing based compartmental models for Ebola Virus Disease (EVD) resulted in estimates of R0= (2.2550, 3.5264, 2.2325) for Guinea, Liberia and Sierra Leone. R0 > 1 for each of the countries, implying that the transmission and control of the epidemic was unstable and needed urgent intervention. The developed SEILICDR model outperformed the existing SEIR model by 13.10%, 91.76%, and 83.14%, respectively on the basis of their RMSE. Finally, analysis using queueing in SEILICDR compartmental models led to the discovery that, at a probability of 0.4 in each compartment, the transmission of EVD can be controlled.
American Journal of Applied Mathematics and Statistics. 2018, 6(3), 96-106. DOI: 10.12691/ajams-6-3-2
Pub. Date: June 13, 2018
16483 Views2327 Downloads
by Dharmaratne MA and Attygalle MDT
Original Research
Good quality, timely and accurate statistics lie at the heart of a country's effort to improve development effectiveness. As a response to the challenge of measuring the institutional capacity of a country in producing timely and accurate statistics, the World Bank developed its framework for the Statistical Capacity Index (SCI). Although the World Bank's framework is acknowledged for its simplistic approach, it has received extensive critique for the ad-hoc allocation of weights. This research attempts to find a solution to this criticism using a statistical methodology. Country information used by the World Bank to create the SCI for the year 2014 was considered. The data consisted information on 25 categorical variables out of which 16 were binary variables and 9 were ordinal variables. Nonlinear Principal Component Analysis (NLPCA) was conducted on the categorical data to reduce the observed variables to uncorrelated principal components. Consequently, the optimally scaled variables were used as input for factor analysis with principal component extraction. The results of the factor analysis were used to weight the new SCI. The dimension, availability and periodicity of economic and financial indicators explained most of the variance in the data set. The research proposes a simpler version of the new SCI with only 23 variables. In the proposed new index, the variables enrolment reporting to UNESCO, gender equality in education and primary completion indicators were the three variables receiving the largest weight. These three indicators measure the periodicity of reporting data on educational statistics to UNESCO; periodicity of observing the gross enrolment rate of girls to boys in primary and secondary education; and periodicity of observing the PCR indicator which is the number of children reaching the last year of primary school net of repeaters respectively. This research represents the first attempt to create a SCI using multivariate statistical techniques and especially index construction with NLPCA. The research concluded with a comparison of the proposed new index and the index created by the World Bank, which justified that the proposed index be used as a solution for the arbitrary allocation of weights in creating the SCI.
American Journal of Applied Mathematics and Statistics. 2018, 6(3), 80-95. DOI: 10.12691/ajams-6-3-1
Pub. Date: May 22, 2018
13150 Views2801 Downloads