O.C. Okoli

Chukwuemeka Odumegwu Ojukwu University

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M. Laisin

Chukwuemeka Odumegwu Ojukwu University

Christian Moore

East Tennessee State University

W. Uwandu

A. C. Eze

Chukwuemeka Odumegwu Ojukwu University

Dozie Felix Nwosu

Federal Polytechnic Nekede

C. O. Aronu

Chukwuemeka Odumegwu Ojukwu University

T. Tiruneh Ababu

University of Eswatini

Charles N. Moore

Washington State University

Ababu Teklemariam Tiruneh

University of Eswatini

Amaka Monica Ezeonyebuchi

Chukwuemeka Odumegwu Ojukwu University

Cooperative Institutions

Chukwuemeka Odumegwu Ojukwu University

Nnamdi Azikiwe University

University of Eswatini

Federal Polytechnic Nekede

Petroleum Training Institute

East Tennessee State University

Washington State University

Mississippi State University

Kansas State University

Washington University in St. Louis

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Enumerative techniques for k-inseparable noninclusion and m-noninclusion arrangements

Applied Mathematical Sciences (2014)

Christian Moore O.C. Okoli M. Laisin W. Uwandu

Let X = {xt : t = 1, 2, . . . , N} be a finite collection and let K = {xti : i = 1, 2, . . . , k} and M = {xtj : j = 1, 2, . . . ,m} be sub-collections of X. Furthermore, we considered the problem of selecting r(r ≤ n) elements fromX with the k andm non-inclusion elements, such that the k noninclusion elements are always together in each selection. We constructed suitable mathematical formula in the combinatorial sense for enumerative purpose on certain kind of restriction called k-inseparable non-inclusion and m-non-inclusion on the sub-collections of elements of the set X = {xt : t = 1, 2, . . . , N}. Mathematics Subject Classification: 05A10

10.12988/ams.2014.311672

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A Unify Method for Solving Quadratic Equations

Tropical Journal of Applied Natural Sciences (2017)

O.C. Okoli

olynomial equations practically appears in different branches of study, physics, chemistry, economics etc.The general form of a polynomial equation of degree is given byWhere ; = 0,1,2,3, … , are the constant coefficients of the unknown variable .If = 1 and 1 ≠ 0, the polynomial equation of degree in 1.1 takes a special name known as LINEAR EQUATION which is given by 1 + 0 = 0; 1 ≠ 0 ---(1.2)If = 2 and 2 ≠ 0, the polynomial equation of degree in 1.1 takes a special name known as QUADRATIC EQUATION which is given by 2 2 + 1 + 0 = 0; 2 ≠ 0 ---(1.3)If = 3 and 3 ≠ 0, the polynomial equation of degree in 4.1 takes a special name known as CUBIC EQUATION which is given byFor the purpose of our study, we shall restrict our study for the case where ≤ 2. The results expressed in this work shall be of immense benefit to students interested in quadratic equations who has yearn for alternative approach for solving this equations.In order to incite the reader we begin with the very fundamentals.

Degree (music)

Cubic function

Independent equation

Constant (computer programming)

Equation solving

10.25240/tjans.2017.2.1.13

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Citations (1)

FURTHER ON KULKARNI’S AND RELATED UNIFIED METHODS FOR SOLVING GENERALPOLYNOMIAL EQUATIONS OF DEGREE LESS THAN FIVE

Journal of Mathematical Sciences & Computational Mathematics (2020)

O.C. Okoli T. Tiruneh Ababu A. C. Eze

For n ∈ a positive integer, let <mml:math display="block"><mml:msub><mml:mi>f</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover></mml:mstyle><mml:mo> </mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>j</mml:mi><mml:mo> </mml:mo></mml:mrow></mml:msub><mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msup></mml:math>; a n ≠ 0; n < 5 be a general polynomial equation of degree less than five in one variable. Before now, we are unaware of any known unified method for solving f n ( x ) = 0 ( n < 5) in radical until Kulkarni did so in 2006. However, it is quite ironical and contradicting to observe (one among many other issues) that the method introduced by Kulkarni fails if n = 1 (since n = 1 satisfies n < 5) which is the case of general polynomial equation of degree one. It is the purpose of this paper to address this issue and many more with an approach that is quite simple and novel.

10.15864/jmscm.1306

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Recursion Formula for the Probability Distribution of Sum of (vu+ 1)-sided die and some of its Properties

Tropical Journal of Applied Natural Sciences (2017)

O.C. Okoli

Déjà vu

10.25240/tjans.2017.2.1.14

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Modified Geometric Distribution of Certain Order and Some of its Properties

Tropical Journal of Applied Natural Sciences (2018)

O.C. Okoli

hilippou et al. (1983) introduced the distribution of the number of trials until the first occurrence of consecutive k successes in Bernoulli trials with success probability p which they called a negative binomial distribution of order k.This distribution have caught the interested of researchers, owning to the work of Philippou et al., (1983) whose contribution in this field seems to be very important.Philippou et al. (1984) studied a negative binomial distribution of order k and defined a Poisson distribution of order k, attention has been paid to interrelationships among the so called discrete distributions of order k and their exact distribution theory has been developed extensively by many researchers.For any fixed positive integer , let denote the number of independent trials with success probability p ( = 1 -) until the first occurrence of consecutive k successes.Philippou gave the following definition for the probability mass function of the event { = } (where { 1 = } reduces to the standard geometric distribution); Definition 1.1 random variable is said to have a geometric distribution of order with parameter if the probability mass function () is given byWhere the summation is taken over all non-negative integers 1 , 2 , … , satisfying the condition 1 + 2 2 + ⋯ + = -.Ever since then, related concepts has been introduced, reliability theory of the consecutive-k-out-of-n:F systems and studied by Kontoleon (1980), Chiang and Niu (1981) and Derman, Lieberman and Ross (1982).Several related concepts on discrete distributions of order k were studied by Lambiris and Papastavridis (1985), Fu (1985;1986a;1986b), Fu andBeihua (1987), Aki P

Bernoulli trial

Geometric distribution

Bernoulli distribution

Binomial distribution

Symmetric probability distribution

Poisson binomial distribution

Binomial (polynomial)

10.25240/tjans.2018.2.2.19

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Generalized falling factorial and associated binomial coefficient identities of Pascal's type

Applied Mathematical Sciences (2013)

Charles N. Moore O.C. Okoli W. Uwandu M. Laisin

Binomial coefficient

Factorial

Falling (accident)

10.12988/ams.2013.310546

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Construction of hyper-geometric mass function in the sample spaces S_{N,r}^p (S_{N,r}^c) of r-permutations/r-combinations

Applied Mathematical Sciences (2013)

Christian Moore M. Laisin O.C. Okoli W. Uwandu

Sample (material)

10.12988/ams.2013.38431

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Generalized r-Permutation and r-Combination Techniques for k-Separable Inclusion Condition

International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statistics (2011)

Christian Moore M. Laisin O.C. Okoli

In this paper, we provide elegant mathematical formula for the k-inclusion condition on rpermutations and r-combinations. We believe the formula to be novel as we have not come across such in literature.

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Unified Functional Method for Solving General Polynomial Equations of Degree Less Than Five

MALAYSIAN JOURNAL OF COMPUTING (2021)

Dozie Felix Nwosu O.C. Okoli Amaka Monica Ezeonyebuchi Ababu Teklemariam Tiruneh

A unified method for solving that incorporate a computational formula that relate the coefficients of the depressed equation and the coefficients of the standard polynomial equation is proposed in this study. This is to ensure that this method is valid for all It shall apply the undetermined parameter method of auxiliary function to obtain solutions to these polynomial equations of degree less than five in one variable. In particular, the result of our work is a unification and improvement on the work of several authors in the sense that only applicable for the case of polynomial equation of degree one. Finally, our results improve and generalize the result by applying standard formula methods for solving higher degree polynomials. It is recommended that the effort should be made toward providing other variant methods that are simpler and friendly.

Degree (music)

Unification

Equation solving

10.24191/mjoc.v6i2.11922

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Ratio estimator for double sampling procedure with non-response: An empirical study

International Journal of Basic and Applied Science (2024)

S. K. Oguagbaka O.C. Okoli C. O. Aronu

This study proposes a ratio-type estimator for population mean estimation using auxiliary variables with double sampling in the presence of non-response. The study provides expressions for the constant, bias, and mean square errors (MSE) of the proposed estimator and compares it with ten existing estimators. The study employed the secondary source of data collection to evaluate the efficiency of the proposed and existing estimators by analyzing five natural populations from three different sources. The performance of ten (10) estimators was considered in this study. The findings suggest that the proposed estimator and the H estimator provide more accurate and precise estimates of the population mean using an auxiliary variable. Additionally, the study found significant differences amongst the mean values of the constant and bias for the different estimators. A Dunn Kruskal-Wallis multiple comparison tests with the Bonferroni method was performed to ascertain the pair of estimators that contributed to the significant difference observed. When estimating the population means using an auxiliary variable, the proposed estimator outperformed other existing estimators that were taken into consideration in the study

10.35335/ijobas.v12i4.281

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