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International Journal of Mathematics and Mathematical Sciences publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.
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Impact of Using Double Positive Samples in Deming Regression
In the method comparison approach, two measurement errors are observed. The classical regression approach (linear regression) method cannot be used for the analysis because the method may yield biased and inefficient estimates. In view of that, the Deming regression is preferred over the classical regression. The focus of this work is to assess the impact of censored data on the traditional regression, which deletes the censored observations compared to an adapted version of the Deming regression that takes into account the censored data. The study was done based on simulation studies with NLMIXED being used as a tool to analyse the data. Eight different simulation studies were run in this study. Each of the simulation is made up of 100 datasets with 300 observations. Simulation studies suggest that the traditional Deming regression which deletes censored observations gives biased estimates and a low coverage, whereas the adapted Deming regression that takes censoring into account gives estimates that are close to the true value making them unbiased and gives a high coverage. When the analytical error ratio is misspecified, the estimates are as well not reliable and biased.
A Stochastic Approach to Modeling Food Pattern
In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in the human organism with a deficient immune system, during consecutive intakes of contaminated food. This process quantifies the exposure to toxins of subjects living with comorbidity (children not breastfed, the elderly, and pregnant women) to food-borne diseases. The Adomian Decomposition Method and the fractional integration of Riemann Liouville are used in the modeling processes.
Sine-Weibull Geometric Mixture and Nonmixture Cure Rate Models with Applications to Lifetime Data
In this study, two new distributions are developed by compounding Sine-Weibull and zero-truncated geometric distributions. The quantile and ordinary moments of the distributions are obtained. Plots of the hazard rate functions of the distributions show that the distributions exhibit nonmonotonic failure rates. Also, plots of the densities of the distributions show that they exhibit decreasing, skewed, and approximately symmetric shapes, among others. Mixture and nonmixture cure rate models based on these distributions are also developed. The estimators of the parameters of the cure rate models are shown to be consistent via simulation studies. Covariates are introduced into the cure rate models via the logit link function. Finally, the performance of the distributions and the cure rate and regression models is demonstrated using real datasets. The results show that the developed distributions can serve as alternatives to existing models for survival data analyses.
A Note on Constant Mean Curvature Foliations of Noncompact Riemannian Manifolds
We aimed to study constant mean curvature foliations of noncompact Riemannian manifolds, satisfying some geometric constraints. As a byproduct, we answer a question by M. P. do Carmo (see Introduction) about the leaves of such foliations.
A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay
In this paper, we design and investigate a higher order -uniformly convergent method to solve singularly perturbed parabolic reaction-diffusion problems with a large time delay. We use the Crank–Nicolson method for the time derivative, while the spatial derivative is discretized using a nonstandard finite difference approach on a uniform mesh. Furthermore, to improve the order of convergence, we used the Richardson extrapolation technique. The designed scheme converges independent of the perturbation parameter (-uniformly convergent) and also achieves fourth-order convergent in both time and spatial variables. Two model examples are considered to demonstrate the applicability of the suggested method. The proposed method produces better accuracy and a higher rate of convergence than some methods that appear in the literature.
A Note about Young’s Inequality with Different Measures
The key purpose of this paper is to work on the boundedness of generalized Bessel–Riesz operators defined with doubling measures in Lebesgue spaces with different measures. Relating Bessel decaying the kernel of the operators is satisfying some elementary properties. Doubling measure, Young's inequality, and Minköwski’s inequality will be used in proofs of boundedness of integral operators. In addition, we also explore the relation between the parameters of the kernel and generalized integral operators and see the norm of these generalized operators which will also be bounded by the norm of their kernel with different measures.