Probability Density Functions for Prediction Using Normal and Exponential Distribution

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

Pressure-Velocity Coupling Schemes for Bouyancy Driven Flow in a Differentially Heated Cavity Using F.V.M and Matlab

Numerical analysis of fluid flow is anchored on the laws of conservation. A challenge in solving the momentum equation arises due to the unavailability of an explicit pressure equation. To avoid solving the pressure term most researchers have eliminated it by cross differentiating the x and the y two dimensional momentum equations and subtracting them. This method introduces more variables to be solved in comparison to the primitive variables and is restricted to two-dimensional flows as streamlines do not exist in three-dimension. This method thus presents a serious limitation in analysis of fluid flow. In this study an equation for computing pressure has been developed using pressure - velocity coupling and used in solving the governing equations. The performance of three pressure velocity schemes namely; the Semi Implicit Method for Pressure linked Equation (SIMPLE), SIMPLE Revised (SIMPLER) and SIMPLE Consistent (SIMPLEC) for laminar buoyancy driven flow has been tested in order to establish the scheme that gives results consistent with bench mark data. The equations governing the flow are solved iteratively using finite volume method together with the central difference interpolating scheme. The solutions are presented for Rayleigh numbers of 103, 104, and 105. This resulted in the velocity profiles for the SIMPLE, SIMPLER, and SIMPLEC algorithm for a Rayleigh number of 104 and 105 converging to the same path. At a Rayleigh number of 103 however, SIMPLER algorithm undergoes a degradation in convergence with grid refinement at the baffle region. Results predicted by using the SIMPLEC algorithm are thus able to effectively compute the velocity of fluid flow in a differentially heated square enclosure with baffles for both low and higher Rayleigh numbers irrespective of the grid size.

Parameter Estimation of a dc Motor-Gear-ac Generator Mathematical Model

Mathematical models and there parameters are essential for designers to predict the close loop behaviors of the plant so that systems are stable. A block model is develop in the MATLAB/simulink for the DC Motor-Gear-AC-Generator mathematical model in this paper, the block built is used to estimate the parameters in the estimation node using the gradient descent, simplex search and nonlinear least square algorithm. Gradient descent curve match that of the experimental data and its values are used in the DC Motor-Gear-AC Generator mathematical model. Objective: To built block simulink Estimate the parameters of the DC Motor-Gear-Generator mathematical model.

Analyticity of the Resolvent Function

Analytic dependence on a complex parameter appears at many places in the study of differential and integral equations. The display of analyticity in the solution of the Fredholm equation of the second kind is an early signal of the important role which analyticity was destined to play in spectral theory. The definition of the resolvent set is very explicit, this makes it seem plausible that the resolvent is a well behaved function. Let T be a closed linear operator in a complex Banach space X. In this paper we show that the resolvent set of T is an open subset of the complex plane and the resolvent function of T is analytic. Moreover, we show that if T is a bounded linear operator, the resolvent function of T is analytic at infinity, its value at infinity being 0 (where 0 is the bounded linear operator 0 in X). Consequently, we also show that if T is bounded in X then the spectrum of T is non-void.

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

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: ut − α2uxxt + c0ux + 3uux + γuxxx + λ(u − α2uxx) = α2(2uxuxx + uuxxx).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.

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

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 {2m, 2m + 1, 2m+1 - 1, 2m+1 + 1, 2m+1 + k, 22m - k, 22m + 1} where k is the number of the information moduli set used. The information moduli set is {2m, 2m + 1, 2m+1 - 1} and the redundant moduli is {2m+1 + 1, 2m+1 + k, 22m - k, 22m + 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.

Power Law Fluid Model for Thermal Elastohydrodynamic Lubrication

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.

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

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.

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

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 Sm+n, S2m and Smn for all m,nÎZ+ with fewer relations than the existing literature from the presentations of Sm and Sn. 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.

Statistical Modelling with Birnbaum-Saunders Distribution

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.