Articles: Department of Mathematics and Statistics

• Modelling and Simulation of Competition for Students’ Population with Holling Type II Response 

  Odhiambo, Brian; Ngari, Cyrus; Kimani, Patrick; Njori, Peter (UoEm, 2023)

  Te increase in the country’s population attracted the establishment of more schools, both public and private schools, to cater for the increasing number of students. However, there have been dynamics of students’ population ...
• Transitivity Action of An on (n=4,5,6,7) on Unordered and Ordered Quadrupples 

  kimani, Gachago j; N, Kinyanjui J.; j, Rimberia; kimani, Patrick; muchemi, Jacob kiboi (UoEm, 2015)

  In this paper, we study some transitivity action properties of the alternating group An(n=4,5,6,7 ,) acting on unordered and ordered pairs from the set X = {1,2,...,n} through determination of the number of disjoint equivalence ...
• Rank and Subdegrees of P GL(2, q) Acting Cosets of P GL(2, e) for q an Even Power of e 

  Kimani, Patrick; Kamuti, Ireri; Rimberia, Jane (UoEm, 2019)

  The action of projective general group on the cosets of its maximal subgroups has been studied. For instance, [9] studied the action of G on the cosets of P GL(2, e) when q is an odd prime power of e. In this paper, we ...
• Predicting the Number of Tourists in-Flow to Kenya Using Seasonal Autoregressive Integrated Moving Average Model 

  Gechore, Dennis; Atitwa, Edwin; Kimani, Patrick; Wanyonyi, Maurice (UoEm, 2022-12)

  Tourism is the leading source of revenue to the Kenyan Government, contributing about 8.8% to the Kenya’s Gross Domestic Product. Based on the 2019 report released by the ministry of tourism and wildlife, tourism industry ...
• On the Number of Cyclotomic Cosets and Cyclic Codes over Z13 

  Hussein, Lao; Kivunge, Benard; Kimani, Patrick; Muthoka, Geoffrey (UoEm, 2018-06)

  Let Zq be a finite field with q element and x n − 1 be a given cyclotomic polynomial. The number of cyclotomic cosets and cyclic codes has not been done in general. Although for different values of q the polynomial x n ...
• Enumeration of cyclic codes over GF(17) 

  Hussein, Lao; Kivunge, Benard; Muthoka, Geoffrey; Mwangi, Patrick (UoEm, 2015-05)

  In this paper we seek the number of irreducible polynomials of xn− 1 over GF(17). We factorize Xn− 1 over GF(17)into irreducible polynomials using cyclotomic cosets of 17 modulo n . The number of irreducible polynomials ...
• Cycle Index Formulas for Dn Acting on Ordered pairs 

  Muthoka, Geoffrey; Kamuti, Ireri; Kimani, Patrick; Hussein, Lao (UoEm, 2016-04)

  The cycle index of dihedral group Dn acting on the set of the vertices of a regular n-gon was studied by Harary and Palmer in 1973 [1]. Since then a number of researchers have studied the cycle indices dihedral group ...
• Cycle Index Formulas for Dn Acting on Unordered Pairs 

  Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; kimani, patrick (UoEm, 2015)

  The cycle index of dihedral group Dn acting on the set X of the vertices of a regular -gon was studied (See [1]). In this paper we study the cycle index formulas of Dn acting on unordered pairs from the set x . In ...
• Action ofPGL (2 ,q ) on the Cosets of the Centralizer of an Eliptic Element 

  Kimani, patrick; Adicka, Daniel (UoEm, 2021)

  Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroupsCq+1. In this paper, we consider the action ofPGL (2, ) centralizer of an elliptic ...
• Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered 4-Element and 5- Element Subsets 

  Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Lao, Hussein; Kimani, Jacob (UoEm, 2015)

  Ranks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply ...
• Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered Pairs and on Ordered Triples 

  Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Lao, Hussein (UoEm, 2014)

  Ranks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply ...
• Ranks and Subdegrees of External Direct Product of Cn Dr Acting on X Y 

  Mutua, Felix Mutinda; Kamaku, Peter Waweru; Kimani, Patrick Mwangi (UoEm, 2020)

  In this paper, transitivity, ranks and subdegrees of the action of ex- ternal direct product of Cyclic and Dihedral group on Cartesian Product of two sets are determined. The action is proved to be transitive. Also, it's ...
• Rank and Subdegrees of PGL(2; q) Acting Cosets of PGL(2; e) for q an Even Power of e 

  Kimani, Patrick Mwangi; Kamuti, Ireri; Rimberia, Jane (UoEm, 2019)

  The action of projective general group on the cosets of its maximal subgroups has been studied. For instance, [9] studied the action of G on the cosets of PGL(2; e) when q is an odd prime power of e. In this paper, we ...
• Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups 

  Agwanda, Siahi Maxwell; Kimani, Patrick; Kamuti, Ireri (UoEm, 2020)

  The action of affine groups on Galois field has been studied. For instance, [3] studied the action of 𝐴𝑓𝑓 (𝑞 ) on Galois field 𝐺𝐹 (𝑞) for 𝑞 a power of prime 𝑝. In this paper, the rank and subdegree of the direct ...
• Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered 4-Element and 5- Element Subsets 

  Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Lao, Hussein; Kimani, Jacob (UoEm, 2015)

  Ranks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply ...
• Cycle Index Formulas for D n Acting on Unordered Pairs 

  Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; Kimani, Patrick Mwangi (Uoem, 2015)

  The cycle index of dihedral group D n acting on the set of X the vertices of a regular n- gon was studied (See [1]). In this paper we study the cycle index formulas of D n acting on unordered pairs from the set . In each ...
• Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered Pairs and on Ordered Triples 

  Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Muthoka, Geoffrey (Uoem, 2014)

  Ranks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply ...
• Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element 

  Kimani, Patrick Mwangi; Adicka, Daniel (Uoem, 2021-08-19)

  Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroups. In this paper, we consider the action of PGL(2,q) centralizer of an elliptic ...
• MODELING DISPROPORTIONAL EFFECTS OF EDUCATING INFECTED KENYAN YOUTH ON HIV/AIDS 

  Ronoh, Marilyn; OGANA, WANDERA; Chirove, Faraimunashe; Wairimu, Josephine (journal of biological systems, 2020)

  We formulate an age and sex-structured deterministic model to assess the effect of increasing comprehensive knowledge of HIV/AIDS disease in the infected Adolescent Girls and Young Women (AGYW) and, Adolescent Boys and ...
• Modeling the effects of insecticides resistance on malaria vector control in endemic regions of Kenya 

  Wairimu, Josephine; Ronoh, Marilyn; Malonza, David M; Chirove, Faraimunashe (Elsevier Ltd., 2018-12)

  We present a model to investigate the effects of vector resistance to control strategies. The model captures the development of resistance as well as loss of resistance in mosquitoes and how these affect the progress in ...

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