##### Regression-type Imputation Class of Estimators using Auxiliary Attributes

A. Audu, O. O. Ishaq, A. Abubakar, K. A. Akintola, U. Isah, A. Rashida, S. Muhammed

Asian Research Journal of Mathematics, Page 1-13
DOI: 10.9734/arjom/2021/v17i530296

Several imputation schemes and estimators have been proposed by different authors in sample survey. However, these estimators utilized quantitative information of auxiliary characters. In this study, some imputation methods were studied using qualitative information of auxiliary characters and two new imputation schemes using auxiliary attribute have been suggested. The mean squared errors of the proposed estimators were derived up to first order approximation using Taylor series approach. Numerical illustrations with two populations were conducted and the results revealed that the proposed estimator is more efficient.

##### More Connections on Valuated Binary Tree and Their Applications in Factoring Odd Integers

Xingbo Wang, Yuequan Jin

Asian Research Journal of Mathematics, Page 14-34
DOI: 10.9734/arjom/2021/v17i530297

This paper continues investigating connections on a valuated binary tree. By defining three types of new connections, the paper derives several new properties for the new connections, and proves that odd integers matching to the new cases can be easily and rapidly factorized. Proofs are presented for the new properties and conclusions with detail mathematical reasoning and numerical experiments are made with Maple software to demonstrate the fast factorization by factoring big odd composite integers that are of the length from 101 to 105 decimal digits. Source codes of Maple programs are also list for readers to test the experiments.

##### Pseudo-Lindley Family of Distributions and its Properties

U. U. Uwadi, E. E. Nwezza

Asian Research Journal of Mathematics, Page 35-49
DOI: 10.9734/arjom/2021/v17i530298

In this study, we proposed a family of distribution called the Pseudo Lindley family of distributions. The limiting behaviors of the density and hazard rate function of the new family are examined. Statistical properties of the proposed family of distributions derived include quantile function, moments, order statistics, and Renyi’s entropy. The maximum likelihood method was employed in obtaining the parameter estimates of the Pseudo Lindley family of distribution. Bivariate extension of the proposed family is discussed. Some special members of the family are obtained. The shape of the density function of special members could be unimodal, bathtub shaped, increasing and decreasing.

##### Analytic Inversion of Closed form Solutions of the Satellite’s J2 Problem

Alessio Bocci, Giovanni Mingari Scarpello

Asian Research Journal of Mathematics, Page 50-68
DOI: 10.9734/arjom/2021/v17i530299

This report provides some closed form solutions -and their inversion- to a satellite’s bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the J2 spherical zonal harmonic. The equatorial track of satellite motion- assuming the co-latitude φ fixed at π/2- is investigated: the relevant time laws and trajectories are evaluated as combinations of elliptic integrals of first, second, third kind and Jacobi elliptic functions. The new feature of this report is: from the inverse t = t(c) we get the period T of some functions c(t) of mechanical interest and then we construct the relevant c(t) expansion in Fourier series, in such a way performing the inversion. Such approach-which led to new formulations for time laws of a J2 problem- is benchmarked by applying it to the basic case of keplerian motion, finding again the classic results through our different analytic path.

##### A Continuous Poisson-Rayleigh Distribution: Its Properties and Applications

Abraham Iorkaa Asongo, Innocent Boyle Eraikhuemen, Emmanuel Remi Omoboriowo, Isa Abubakar Ibrahim

Asian Research Journal of Mathematics, Page 69-84
DOI: 10.9734/arjom/2021/v17i530300

This article proposed a Poisson based continuous probability distribution called Poisson-Rayleigh distribution. Some properties of the new distribution such as quantile and reliability functions and other useful measures were obtained. The model parameters were estimated using the method of maximum likelihood. The usefulness of the new distribution was proven empirically using real life datasets.

##### On the Stability Analysis of Linear Unperturbed Non-integer Differential Systems

Ubong D. Akpan

Asian Research Journal of Mathematics, Page 85-89
DOI: 10.9734/arjom/2021/v17i530301

In this paper, the stability of non-integer differential system is studied using Riemann-Liouville and Caputo derivatives. The stability notion for determining the stability/asymptotic stability or otherwise fractional differential system is given. Example is provided to demonstrate the effectiveness of the result.

##### The Influence of Circulatory Forces on the Stability of Undamped Gyroscopic Systems

Ubong D. Akpan

Asian Research Journal of Mathematics, Page 90-94
DOI: 10.9734/arjom/2021/v17i530302

In this paper, the effects of circulatory forces on undamped gyroscopic systems have been studied. The stability or otherwise of arising MGKN systems have been analysed using eigenvalue method and Lyapunov method. Bottema-Lakhadanov-Karapetyan theorem is also employed to further analyze the systems. Examples are given to illustrate the use of these methods in determining the stability or otherwise of undamped gyroscopic circulatory systems.

##### The Existence of Entire Positive Solutions to Monge-Ampere Type Equations

Shuangshuang Bai

Asian Research Journal of Mathematics, Page 95-103
DOI: 10.9734/arjom/2021/v17i530303

Aims/ Objectives: In this paper, we study the Monge-Ampere type equation det D2u + αu = p(|x|)f(u)(x ∈ Rn)

In the previous articles, the equation with Monge-Ampere operator or Laplace operator has been studied extensively. However, the research about the combination of two kinds of operator is scarce. We would like do some research on this topic. We obtain a sufficient condition of the existence of entire positive solutions for the equation.

Study Design: Study on the existence of solutions.

Place and Duration of Study: Department of Mathematics and Physics, North China Electric Power University, September 2019 to present.

Methodology: We prove the existence of the solution by constructing Euler’s break line, combining the idea of transformation and the method of mathematical analysis. Results: We obtain a sufficient condition of the existence of entire positive solutions for the equation.

Conclusion: We prove the existence of entire positive solutions to Monge-Ampere type equation det D2u + αu = p(|x|)f(u)(x ∈ Rn) and obtain the sufficient condition for the existence of solutions.