Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems

In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.

Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem

The concept of the deferred Nörlund equi-statistical convergence was introduced and studied by Srivastava et al. [Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112 (2018), 1487–1501]. In the present paper, we have studied the notion of the deferred Nörlund statistical convergence and the statistical deferred Nörlund summability for sequences of real numbers defined over a Banach space. We have also established a theorem presenting a connection between these two interesting notions. Moreover, based upon our proposed methods, we have proved a new Korovkin-type approximation theorem with algebraic test functions for a sequence of real numbers on a Banach space and demonstrated that our theorem effectively extends and improves most of the earlier existing results (in classical and statistical versions). Finally, we have presented an example involving the generalized Meyer–König and Zeller operators of a real sequence demonstrating that our theorem is a stronger approach than its classical and statistical versions.

Pangolin v1.0, a conservative 2-D advection model towards large-scale parallel calculation

To exploit the possibilities of parallel computers, we designed a large-scale bidimensional atmospheric advection model named Pangolin. As the basis for a future chemistry-transport model, a finite-volume approach for advection was chosen to ensure mass preservation and to ease parallelization. To overcome the pole restriction on time steps for a regular latitude–longitude grid, Pangolin uses a quasi-area-preserving reduced latitude–longitude grid. The features of the regular grid are exploited to reduce the memory footprint and enable effective parallel performances. In addition, a custom domain decomposition algorithm is presented. To assess the validity of the advection scheme, its results are compared with state-of-the-art models on algebraic test cases. Finally, parallel performances are shown in terms of strong scaling and confirm the efficient scalability up to a few hundred cores.

Can An Algebraic Diagnostic Test be Used to Predict Final Grades in an Introductory Statistics Class?

The Department of Mathematics and Statistics at California State University Sacramento has been using the Intermediate Algebra Diagnostic (IAD) test as a proxy tool to screen students intending to enroll in an introductory statistics course (Stat 1). However, the use of an algebraic test as a diagnostic tool for a statistics course has been questioned by some faculty members and students at this university. The regression models used in this study (simple linear regression, hierarchical linear regression, and logistic regression) show that higher IAD scores are related to higher final grades in Stat 1, even after adjusting for different instructors. Inferences were also made in this study to predict a passing grade and passing rates in Stat 1 based on the bounds of the confidence and prediction intervals obtained for the IAD scores with these models. KEYWORDS: Linear Regression, Logistic Regression, Statistics Diagnostic Test, Algebra Diagnostic Test, MDTP, Introductory Statistics

Structural Analysis and Mobility Test of Fourteen Links Kinematic Chain Using Graph Theory

The present work is focused on the graph theory which is used for structural analysis of kinematic chain and identification of degree of freedom. A method based on graph theory is proposed in this paper to solve structural problems by using a suitable example of fourteen links kinematic chain. Purpose of this paper is to give an easy and reliable method for structural analysis of fourteen links kinematic chain. Here, a simple incidence matrix is used to represent the kinematic chain. The proposed method is applied for determining the characteristic polynomial equation of fourteen links kinematic chain. An algebraic test based on graph theory is also used for identifying degree of freedom of kinematic chain whether it is total, partial or fractionated degree of freedom.