American Journal of Applied Mathematics and Statistics

The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies bi-directionally. It is assumed that the plate is clamped on all the four edges and that the thickness varies linearly in one direction and parabolically in another direction. Using the separation of variables method and Rayleigh-Ritz technique with a two-term deflection function, the governing differential equation has been solved for vibration of visco-elastic parallelogram plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection is made. Visco-elastic of the plate is taken of the “Kelvin Type”. Time period and deflection function at different point for the first two modes of vibration are calculated for various values of taper constant, aspect ratio and skew angle and results are presented in tabular form. Alloy “Duralumin” is considered for all the material constants used in numerical calculations.

American Journal of Applied Mathematics and Statistics. 2013, 1(5), 103-109. DOI: 10.12691/ajams-1-5-5
Pub. Date: November 22, 2013

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Robustness and Power of the Kornbrot Rank Difference, Signed Ranks, and Dependent Samples T-test

by Norman N. Haidous and Shlomo S. Sawilowsky

Original Research

The purpose of the study was to compare the power and accuracy of the Kornbrot rank difference test to classical parametric and nonparametric alternatives when the assumption of normality is not met, the data are ordinal, and the sample size is small. Although the procedure is robust, there was no evidence the rank difference test had power advantages over Wilcoxon Signed-Ranks test.

American Journal of Applied Mathematics and Statistics. 2013, 1(5), 99-102. DOI: 10.12691/ajams-1-5-4
Pub. Date: October 29, 2013

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An Assessment of the Changing Climate in Northern Nigeria Using Cokriging

by U. Usman, S. A. Yelwa, S.U. Gulumbe and A. Danbaba

Original Research

The aim of this paper is to test the applicability of Co-Kriging (CK) on the study of the changing climate in Northern Nigeria. Indices were derived from climatic variables (Rainfall and Temperature) obtained from Nigerian Meteorological Agency (NIMET) and remotely sensed data covering the period from 1981 to 2010 in the form of Normalised Difference Vegetation Index (NDVI) data derived from National Oceanic Atmospheric Administration-Advanced Very High Resolution Radiometer (NOAA-AVHRR). Because of the strong relationship between NDVI and Rainfall, CK method of data interpolation was tested with R-Statistical software. A digital elevation model (DEM) of the study area at 90-meter spatial resolution was used as a supplement in an overlay procedure using the IDRISI Remote sensing and GIS software so as to derive the correct altitude values of the Met stations for comparison with the coefficient of variation of the rainfall dataset. Results from the derived CK prediction maps showed that there are high variability in NDVI and rainfall across the time-series. Furthermore, spatial average variability in the growing season rainfall was 60% with a mean temperature of 4% although coefficient of variation in rainfall for the individual climatic station's ranged from 18.15 to 60.98 per cent. While the highest coefficient of variation in temperature for the entire time series (1981-2010) was located around Katsina area, the lowest was located around Minna. From the results of this analysis it is evident that the higher prediction variance values particularly for vegetation NDVI and rainfall are located in the southern part of the study area particularly around Kaduna, Minna, and Jos as compared to the northern part of the study area falling around Maiduguri, Sokoto and Katsina which indicated relatively lower prediction values. However, further studies should also be undertaken using the raster NDVI dataset in a GIS environment to buttress our view that there were changes in the general ecosystems within the study area as result of climatic impact.

American Journal of Applied Mathematics and Statistics. 2013, 1(5), 90-98. DOI: 10.12691/ajams-1-5-3
Pub. Date: October 22, 2013

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Cost Effectiveness Statistic: A Proposal to Take Into Account the Patient Stratification Factors

by Ciro D'Urso

Original Research

The formula here proposed can be used to conduct economic analysis in randomized clinical trials. It is based on a statistical approach and aims at calculating a revised version of the incremental cost-effective ratio (ICER) in order to take into account the key factors that can influence the choice of therapy causing confounding by indication. Let us take as an example a new therapy to treat cancer being compared to an existing therapy with effectiveness taken as time to death. A challenging problem is that the ICER is defined in terms of means over the entire treatment groups. It makes no provision for stratification by groups of patients with differing risk of death. For example, for a fair and unbiased analysis, one would desire to compare time to death in groups with similar life expectancy which would be impacted by factors such as age, gender, disease severity, etc. The method we decided to apply is borrowed by cluster analysis and aims at (i) discard any outliers in the set under analysis that may arise, (ii) identify groups (i.e. clusters) of patients with "similar" key factors.

American Journal of Applied Mathematics and Statistics. 2013, 1(5), 87-89. DOI: 10.12691/ajams-1-5-2
Pub. Date: October 16, 2013

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Wavelet-Galerkin Method and Some Numerical Method for Lane-Emden Type Differential Equation

by Jafar Biazar and Fereshteh Goldoust

Letter To Editor

In this paper, we will compare the performance of Adomian decomposition method and the wavelet-Galerkin method applied to the Lane-Emden type differential equation. The Galerkin Wavelet method (GWM), which is known as a numerical approach is used for the Lane- Emden equation, as an initial value problem. This approach consists of using integral operator, to convert the Lane- Emden equation in to an integral equation, then applying Galerkin Wavelet method to solve the resulted integral equation. The properties of Galerkin Wavelet method (GWM) and the Adomian Decomposition Method are also addressed. Although the Adomian decomposition solution required slightly more computational effort than the wavelet-Galerkin solution, it resulted in more accurate results than the wavelet-Galerkin method. To illustrate the methods two examples are provided and the results are in good agreement with exact solution.

American Journal of Applied Mathematics and Statistics. 2013, 1(5), 83-86. DOI: 10.12691/ajams-1-5-1
Pub. Date: October 15, 2013

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