Journal of Advances in Mathematics and Computer Science

Comparing Calibration Product Type Estimators of Population Mean In Stratified Sampling under Two Constraints Using Different Distance Measures

2021-10-25T02:45:21+00:00

Calibration approach adjusts the original design weights by incorporating an auxiliary variable into it, to make the estimator be in the form of a regression estimator. This method was employed to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure using double constraints. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators using a secondary data set and simulated data under underlying distributional assumptions of Gamma, Normal and Exponential distributions with varying sample sizes of 10%, 15%, 20% and 25% were carried out. The result with the real life data showed that the calibration product type estimator from chi-square distance measure estimated the population mean with minimum bias than and obtained from the other distance measures. The result from real life data also revealed that the estimator obtained from chi-square distance measure under two constraints was more efficient than the other three estimators. The result from simulation studies showed that the proposed calibration product type estimators outperform the conventional product type estimator in term of efficiency, consistency and reliability under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better under normal distribution. It was also observed that as sample size increases there was no significant change in the performance of these proposed estimators which justifies the preference with small sample size.

Action of Finite Group Presentations on Signal Space

2021-10-28T03:20:41+00:00

The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, that is, different types of signal has different transformation combination. This paper aimed at studying representation of finite groups via their actions on Signal space and to use more than one transformation to process a signal within the context of group theory. The objective is achieved by using group generators as actions on Signal space which produced output signal for every corresponding input signal. It is proved that the subgroup presentations act on signal space by conjugation. Hence, a different approach to signal processing using group of transformations and presentations is established.

Statistical Modelling with Birnbaum-Saunders Distribution

2021-10-30T02:52:19+00:00

In this article, it is assumed that the distribution of the error terms is the Birnbaum-Saunders distribution in the process of one-way ANOVA. The Birnbaum-Saunders distribution has been widely used in reliability analysis especially in fatigue-life models. In reliability analysis, nonnormal distribution is much more common than the normal distribution. We obtain the estimation of the parameters og interest by maximum likelihood method. We also propose new test statistics based on these estimators . The efficiencies of the maximum likelihood estimators and the Type I errors obtained by using the proposed estimators are compared with normal theory via Monte Carlo simulation study. At the end of the study, the real life example is given just for the illustration of the method.

A Constructive Method for Generating Short Presentations for the Symmetric Groups Sm+n, S2m and Smn

2021-11-13T05:02:07+00:00

A long-standing problem is how to create a short-length presentation for finite groups of degree n. This paper aimed at presenting a concrete method for generating presentations for the groups S_m_+n, S_2m and S_mn for all m,nÎZ⁺ with fewer relations than the existing literature from the presentations of S_m and S_n. The aim is achieved by considering finite groups acting on sets and Cartesian product of groups which lead to the construction of multiple transformations as representatives of some finite groups.

Two-step Tensor Splitting Iteration Method for Multi-linear Systems

2021-11-22T13:38:41+00:00

In this paper, we construct two-step tensor splitting iteration method for multi-linear systems. Moreover, we present convergence analysis of this method. Finally, we give two numerical examples to show that this new method is more ecient than the existing methods.

Power Law Fluid Model for Thermal Elastohydrodynamic Lubrication

2021-11-30T09:10:15+00:00

The aim of this paper is to analyse thermal elastohydrodynamic lubrication (TEHL) line contact of rolling a bearing using a non-Newtonian uid that is described by the power law model. The performance characteristics of the rolling bearing are determined for various index for dilatant, Newtonian and pseudo plastic uids. The one-dimensional Reynolds and energy equations are both modied to incorporate the non-Newtonian nature of the lubricant. The coupled system of governing equations are discretized using the finite difference method and solved simultaneously. The results show that the pressure, film thickness and temperature for dilatant uids increased with increase in the ow index as compared to pseudo plastic uids. The in uence of thermal effects on pressure and lm thickness is more significant compared with that under isothermal elastohydrodynamic lubrication especially on the case of dilatant uids. The viscosity of the lubricant increases with increase in pressure and reduces with increment in temperature. The surface roughness in the bearing surface increases the lm thickness of the lubricant. The uid pressure, film thickness and temperature increases with increase in the bearing speed. To truly re ect the characteristics of EHL models, thermal effects should be considered.

An Enhanced Error Detection and Correction Scheme for Enterprise Resource Planning (ERP) Data Storage

2021-11-30T09:11:35+00:00

In this research paper, a Redundant Residue Number System (n,k) code is introduced to enhance Cloud ERP Data storage. The research findings have been able to demonstrate the application of Redundant Residue Number System (RRNS) in the concept of Cloud ERP Data storage. The scheme contributed in addressing data loss challenges during data transmission. The proposed scheme also addressed and improved the probability of failure to access data compared to other existing systems. The proposed scheme adopted the concept of Homomorphic encryption and secret sharing whiles applying Redundant Residue Number System to detect and correct errors.The moduli set used is {2^m, 2^m + 1, 2^m+1 - 1, 2^m+1 + 1, 2^m+1 + k, 2^2m - k, 2^2m + 1} where k is the number of the information moduli set used. The information moduli set is {2^m, 2^m + 1, 2^m+1 - 1} and the redundant moduli is {2^m+1 + 1, 2^m+1 + k, 2^2m - k, 22^{m + 1}}. The proposed scheme per the simulation results using python reveals that it performs far better in terms of data loss and failure to access data related concerns. The proposed scheme performed better between 41.2% for data loss to about 99% for data access based on the combination of (2, 4) and (2, 5) data shares respectively in a (k, n) settings.

Global Weak Solutions for the Weakly Dissipative Dullin-Gottwald-Holm Equation

2021-11-30T09:11:16+00:00

In this paper, we are concerned with the existence and uniqueness of global weak solutions for the weakly dissipative Dullin-Gottwald-Holm equation describing the unidirectional propagation of surface waves in shallow water regime:
u_t − α²u_xxt + c₀u_x + 3uu_x + γu_xxx + λ(u − α²u_xx) = α²(2u_xu_xx + uu_xxx).
Our main conclusion is that on c0 = − γ/α² and λ ≥ 0, if the initial data satisfies certain sign conditions, then we show that the equation has corresponding strong solution which exists globally in time, finally we demonstrate the existence and uniqueness of global weak solutions to the equation.