Marshal Sampson | Akwa Ibom State University (original) (raw)

Papers by Marshal Sampson

March, 2024

In this paper, we present a novel algorithm for efficiently computing canonical images of objects... more In this paper, we present a novel algorithm for efficiently computing canonical images of objects under the action of finite permutation groups. Our approach builds upon previous work utilizing Graph Backtracking, an extension of Jeffrey Leon's Partition Backtrack framework. By generalizing both Nauty and Steve Linton's Minimal Image algorithm, our method achieves significant improvements in computational efficiency and accuracy. We introduce a systematic exploration of the permutation group structure to guide the canonical image computation process, resulting in enhanced performance compared to existing methods. Through rigorous theoretical analysis and empirical evaluation, we demonstrate the effectiveness and scalability of our algorithm across diverse application scenarios.

IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 10, Issue 6 Ver. V (Nov - Dec. 2014), PP 30-33 www.iosrjournals.org , 2014

In this paper, we present the Mathematical model of the effect of complacency in HIV/AIDS prevent... more In this paper, we present the Mathematical model of the effect of complacency in HIV/AIDS preventions. The model was formulated under six (6) assumptions which resulted in a system of first order differential equations. Using methods from dynamical systems theory for analysis, it was shown that the disease free state is stable, the condition for this to be possible is: 1 < (µ +), that is, sum of the rate of progression to AIDS and rate of natural death is greater than 1(one). Also the endemic equilibrium state is asymptotically stable.At this point, the disease will not invade the community; otherwise the disease will invade the community. This means that there should be a bound on the rate of progression to AIDS; this is possible if the tempo of campaign against HIV/AIDS is not relaxed.

IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 14, Issue 4 Ver. II (Jul - Aug 2018), PP 68-71 www.iosrjournals.org, 2018

The rank of direct product of Brant SemigroupB(G, n) where n≥ 2 and | | ≥ 1, is presented as a cl... more The rank of direct product of Brant SemigroupB(G, n) where n≥ 2 and | | ≥ 1, is presented as a class of Algebra in comparison to the sum. This study is also extended to the computation of the rank of direct product of cancellativesemigroups.

IJRTI | Volume 8, Issue 7 | ISSN: 2456-3315, 2023

We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to... more We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to ascertain the relevance of the concept of independence. There are cases where the concept of independence fails to be useful for this purpose. One would expect the basis element to be the maximal independent subset of a given semigroup. However, we construct examples for infinite, commutative and non-commutative semigroups, where there exists finite basis and the number of independent elements is larger than the basis.

International Journal of Computer Science and Mathematical Theory (IJCSMT) E-ISSN 2545-5699 P-ISSN 26951924 Vol 10. No.1 2024 www.iiardjournals.org, 2024

This paperreviews the work ofM.I. Sampson et. Al (2023) [7], and delves into the intricate relati... more This paperreviews the work ofM.I. Sampson et. Al (2023) [7], and delves into the intricate relationship between minimal generating sets and independence in semigroups by examining the comparability of elements induced by orderings on the semigroup. It demonstrates that the existence of a minimal generating set implies independence, and conversely, independence implies the existence of a minimal generating set. Additionally, the paper presents two new algorithms: one for determining minimal generating sets for countable systems of semigroups and another for any given semigroup. These algorithms offer practical solutions for semigroup theorists and

International Journal of Applied Science and Mathematical Theory E- ISSN 2489-009X P-ISSN 2695-1908, Vol. 10 No. 1 2024 www.iiardjournals.org, 2024

This research investigates the divisibility properties of coprime integers, building upon the fou... more This research investigates the divisibility properties of coprime integers, building upon the foundational work of Dillip Kumar Dash and Nduka Wolu (2020) regarding the sum of coprime integers and its divisibility by certain integers. While Dash and Wolu established a result concerning the divisibility of the sum of coprime integers byan integer, we provide the converse of this result, revealing insights into the relationship between prime integers and the divisibility of coprime integer sums. Our study introduces a generalized property of integers that underpins these divisibility properties and provides a theoretical framework for understanding the phenomenon. Additionally, we present a computational illustration for generating coprime integers to test our theoretical findings, offering practical insights into the validity of our results. The research contributes to the understanding of the arithmetic properties of coprime integers and their implications for number theory.

International Journal for Research Trends and Innovation (IJRTI) | Volume 8, Issue 8 | ISSN: 2456-3315 , 2023

A class of *-bisimple ample-semigroups whose certain *-classes contain no regular elements was co... more A class of *-bisimple ample-semigroups whose certain *-classes contain no regular elements was considered in [3], this class of *-bisimple ample-Semigroups are seen to be generalized. The characterization of this class of semigroups rather involves the use of bisystems with certain structure mappings and a binary multiplication together with some closure axioms. The characterization of this class of semigroups were given in [4]. This paper is a follow up of [3] and [4] which presents a generalized theorem for a semigroup in this class. Moreover, a typical example of a semigroup in this class of *-bisimple ample-semigroups is constructed to offer an insight into this class of semigroups.

International Journal of Scientific Research and Engineering Development-– Volume 6 Issue 4, July- Aug 2023 , 2023

This paper extends the paper results by (Effiong and Co, 2023) on intersection of coset of Cyclic... more This paper extends the paper results by (Effiong and Co, 2023) on intersection of coset of Cyclic Subsemigroup to obtain algorithm for minimal generators of semigroup. A semigroup generating set is subset of semigroups which determines the whole semigroup through algebraic closure. The minimal generating set isthat which does not have a proper generating subset. The paper also shows an idea about the infiniteness of the independent elements in an infinite semigroup. An example is given to show how relatively small the minimal generating sets of such infinite semigroups are.

International Journal of Mathematical Analysis and Modelling, Volume 6, Issue 2, October-November 2023, pages 377 – 388 , 2023

This paper studies independence in semigroup by exploring the relationship between the concepts o... more This paper studies independence in semigroup by exploring the relationship between the concepts of "minimal generating set" as compared to "minimum generating set" using comparability of elements, as induced by the orderings on the semigroup. It is shown that minimal generating set implies independence and vice versa. Two concluding results which are algorithms respectively for determining minimal generating sets for countable systems of semigroups and for any given semigroups, are given.

.IOSR Journal of Mathematics (IOSR-JM) , 2023

There is an existing theorem showing that not every group has a minimal generating set, by relyin... more There is an existing theorem showing that not every group has a minimal generating set, by relying on a claim that all Proper Subgroups of infinite − Group (a group in which the order, () of its element is the power of some primes) are finite and cyclic. This paper shows as one of its objectives that not all Proper Subgroups of an infinitely generated − Group are finite and cyclic. Furthermore, the concepts of Maximal Independent sets and Minimal Generating Set are investigated for condition under which both concepts coincide. It is also shown that in the additive semigroup of integers, there are infinite minimal generating sets with different number of elements. This gives the implication that the dimension of vector spaces do not have analog in semigroups. Equivalently, these same examples serve as examples of infinite inequivalent maximal independent sets.

IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X., 2021

Dillip Kumar Dash and Nduka Wolu (2020) proved using the concept of Euler Phi Function that for a... more Dillip Kumar Dash and Nduka Wolu (2020) proved using the concept of Euler Phi Function that for all , divides the sum of all elements of , the set of all positive integers less than where the positive integers are relatively prime to. Our work gives the converse of this result as a direct implication of a generalised property of integers which we have also stated and proved. This further enables the conclusion that for any prime integer greater than , divides the sum of all integers less than if and only if is relatively prime to. A computerized illustration for generating values of coprime to test the result is also given.

IOSR Journal of Mathematics, 2014

In this paper, we formulate the mathematical model for the epidemiology of fowl pox infection tra... more In this paper, we formulate the mathematical model for the epidemiology of fowl pox infection transmission that incorporates discrete delay. The model results in a discrete delay system of ordinary differential equations with delay parameter ≥ 0. Analysing the system using theorems from differential and integral calculus, we discovered that the number of infectives after a very long time from the day of inception of the epidemic is constant.