School of Mathematics, Statistics and Actuarial Sciences
https://repository.maseno.ac.ke/handle/123456789/92
2024-03-29T11:00:24ZBijections of plane Husimi graphs and certain combinatorial structures
https://repository.maseno.ac.ke/handle/123456789/6061
Bijections of plane Husimi graphs and certain combinatorial structures
Kariuki, Yvonne Wakuthii
Plane Husimi graphs are combinatorial structures obtained when we replace edges
in plane trees with complete graphs such that the resultant structures are connected and cycle
free. The formula that counts these structures is known to enumerate other combinatorial
structures. In this paper, we construct bijections between the set of plane Husimi graphs and
the sets of plane trees, dissections of convex polygons, sequences satisfying certain properties,
standard Young tableaux, Deutsch paths and restricted lattice paths.
http://ejma.euap.org
2023-10-19T00:00:00ZBijections for classes of labelled trees
https://repository.maseno.ac.ke/handle/123456789/6060
Bijections for classes of labelled trees
Nyariaro, Albert P. Oloo; Okoth, Isaac .Owino
Trees are acyclic connected graphs. Plane trees, d-ary trees, binary trees, non
crossing trees and their generalizations, which are families of trees, have been enumerated by
many authors using various statistics. These trees are known to be enumerated by Catalan or
Catalan-like formulas (Fuss-Catalan numbers). One of the most common approaches to the
enumeration of these trees is by means of generating functions. Another method that can be
used to enumerate them is by constructing bijections between sets of the same cardinality. The
bijective method is preferred to other methods by many combinatorialists. So, in this paper, we
construct bijections relating k-plane trees, k-noncrossing increasing trees, k-noncrossing trees,
k-binary trees and weakly labelled k-trees.
2024-01-09T00:00:00ZEnumeration of plane and d-ary tree-like structures
https://repository.maseno.ac.ke/handle/123456789/5849
Enumeration of plane and d-ary tree-like structures
Onyango, Christopher Amolo; Okoth, Isaac Owino; Kasyoki, Donnie Munyao
Trees are generalized using various approaches such as considering tree-like structures. Some of the tree-like structures are Husimi graphs, cacti and oriented cacti. These graphs have been enumerated according to number of vertices, blocks, block types and degree sequences. Noncrossing and plane counterparts have also been enumerated by number of vertices, blocks and block types. In this paper, we enumerate plane Husimi graphs, cacti and oriented cacti according to root degree, outdegree of a given vertex and outdegree sequence. The d-ary tree like structures are also introduced in this paper and enumerated according to number of vertices, blocks, block types, outdegree sequence and number of leaves.
2023-08-26T00:00:00ZReachability in complete t-ary trees
https://repository.maseno.ac.ke/handle/123456789/5848
Reachability in complete t-ary trees
Abayo, Sylvester Arthur; Okoth, Isaac Owino; Kasyoki, Donnie Munyao
Mathematical trees such as Cayley trees, plane trees, binary trees, noncrossing trees, t-ary trees among others have been studied extensively. Reachability of vertices as a statistic has been studied in Cayley trees, plane trees, noncrossing trees and recently in t-ary trees where all edges are oriented from vertices of lower label towards vertices of higher label. In this paper, we obtain closed formulas as well as asymptotic formulas for the number of complete t-ary trees in which there are paths of a given length such that the terminal vertex is a sink, leaf sink, first child and non-first child. We also obtain number of trees in which there is a leftmost path of a given length.
2023-10-01T00:00:00ZOn the Numerical Solution of Boundary Value Problem (BVP) of the Ordinary Differential Equation (ODE) - The Case of Steady-State Bio-Heat Equation with Combined Heat Transfer Coefficient by Pseudo-Spectral Collocation Method
https://repository.maseno.ac.ke/handle/123456789/5795
On the Numerical Solution of Boundary Value Problem (BVP) of the Ordinary Differential Equation (ODE) - The Case of Steady-State Bio-Heat Equation with Combined Heat Transfer Coefficient by Pseudo-Spectral Collocation Method
Odongo, Benard A; Manyonge, Alfred W; Owego, Dancun O; Opiyo, Richard O
Spectral methods for the solution of a boundary value problem of an ordinary differential equation are reviewed with particular emphasis laid on pseudo-spectral collocation method. The pseudo-collocation method is then used to solve the one dimensional bio-heat equation with metabolic heat generation in cylindrical coordinates applied to human tissue. It was noticed that an increase in heat transfer coefficient (hA), enhanced the temperature but a decrease in the tissue thickness was observed when this coefficient was increased. The effects of the combined heat transfer coefficient are analyzed and the results indicate that the obtained solution can be used in the study of the thermal behaviour of a biological system with the potential to locate tumours in the living tissue.
2023-09-15T00:00:00ZRecursive Relation for Zero Inflated Poisson Mixture Distributions
https://repository.maseno.ac.ke/handle/123456789/5468
Recursive Relation for Zero Inflated Poisson Mixture Distributions
Anyango, L. Cynthia, Edgar Otumba
The paper extends the work of Sarguta who derived recursive re lations for univariate distributions by considering the ZIP continuous
mixtures. The paper gives a recursive formular which can be used to
evaluate the mixed distributions which can be used when the probabil ity distribution functions cannot be evaluated explicitly. Integration by
parts is often employed when deriving the recursive formulas. From sec tion two up to section seven, we derived the recursive formulas for ZIP
mixture distributions using Rectangular, Exponential, Gamma with two
parameters, Poisson- Beta and Inverted - Beta as mixing distributions.
2017-01-01T00:00:00ZApplication of Continous Time Model in Prediction of Loss Reserves in Credit Insurance for Asset-Based Lending Companies
https://repository.maseno.ac.ke/handle/123456789/5465
Application of Continous Time Model in Prediction of Loss Reserves in Credit Insurance for Asset-Based Lending Companies
Etyang Isaac, Joshua Were
Asset-based lending companies and other loan providers are exposed to risk of loan defaults by borrowers. To reduce this risk, these companies acquire credit insurance. Thus when the borrower defaults in payment, the insurance company covers a percentage of the outstanding balance which generates a way to lessen and spread credit risk that the lender incurs. Therefore there are a number of methods put in place such as frequency-severity and hazard rate models used to value credit insurance. Valuing of credit insurance for asset-based lending companies is a challenging task especially in Kenyan market, where in the case of a borrower’s default, the process for recovering of the collateral will last a longer period of more than a year and where data on the borrower’s behavior of payment is of poor quality or generally unavailable. The existing methods do not consider the time to repossession of the collateral in case of loan default. Our proposed model takes into account time to repossession of the collateral and can be used in emerging market economies where other available methods may be either unsuitable or are too complex to implement due to lack of enough data. Therefore, this paper incorporates a continuous time model to forecast loss reserves in credit insurance for asset-based lending companies. First, we establish a discrete-time model to describe delinquency of credits in loan insurance product. Martingale properties, Replicating of asset portfolio strategy and Itô’s calculus are used to obtain results on expected values of future losses of credit insurance products. Secondly, we used the Black-Scholes model to develop a continuous-time model to forecast future losses in credit insurances. This is constructed by linking the latter from the discrete-time (Binomial) model using the methods of stochastic calculus. We estimated the loss reserves by applying the Geometric Brownian Motion on data of outstanding balances of 30% of 100 loanees from car loan business with assets valued at between 1 million and 10 million, to predict the probability of default of the borrower.
DOI: 10.4236/jmf.2022.123025
2022-01-01T00:00:00ZEmpowered schools embrace the competency based curriculum: sharing the Kenya connect empowered school model in Machakos county
https://repository.maseno.ac.ke/handle/123456789/5430
Empowered schools embrace the competency based curriculum: sharing the Kenya connect empowered school model in Machakos county
Kaleli, James. Musyoka
Rural public schools face many challenges and are severely under-resourced. Students are eager to learn and parents see schools as a means for upward mobility for their children. However, public schools struggle due to lack of resources, overcrowded classes, and outdated teaching methodologies. Kenya Connect, a Non-Governmental Organization in Wamunyu, Machakos County has been working to enrich education for the last twenty years. In 2019, we piloted an “Empowered School” program with Sofia primary school participating. This program provides the creation of Professional Learning Communities among the teachers, resources to the schools including art supplies, rulers, educational posters, after-school LitClubs in partnership with LitWorld plus Level-Up Village STEM classes, refurbishing the classrooms with fresh and bright paint, cork-boards and strips to hang student work. In order to be an “Empowered School” all teachers and the head teacher agreed to participate in weekly professional development and other Kenya Connect programs. The Parent Management Committee was also consulted and needed to give their support. Teachers are now using strategies to facilitate a student-centered classroom and are seeing a deeper engagement in learning. We have been monitoring the test scores and noted that the Empowered Schools have higher student achievement than our other partner schools. In 2020, our Empowered Schools scored a mean score of 320 out of 500 against our regular schools who scored 280 out of 500 in the Kenya Certificate of Primary Education. As well, teachers are reporting that students are using critical thinking and problem solving skills, in addition to being more creative.
2021-01-01T00:00:00ZAnalysis of the factors affecting farm-level output of mangoes among small-scale farmers in Mwala Sub-County, Kenya
https://repository.maseno.ac.ke/handle/123456789/5429
Analysis of the factors affecting farm-level output of mangoes among small-scale farmers in Mwala Sub-County, Kenya
Isaboke, Hezron N. Musyoka, Kennedy
The factors affecting farm-level output of mangoes among small-scale farmers in
Mwala Sub-County, Kenya were examined. The first stage of regression analysis resulted
that family and hired labour, amount of pesticides and manure had positively significant
affected on mango farm-level output. The results on the second stage of the factor affecting
mango output was household size, farming income, area allocated to mango farming (farm
size), amount of credit, and extension contacts which exhibited positively affected on
mango output, while cost of pesticides and manure precipitated had negatively affected.
The study recommended that relevant authorities should strengthen the extension contact
for encouraging farmers to practice the best and recommended management practices on
mango farming to improve production. Furthermore, small-scale mango farmers accessed
to functional input markets would enhance farm-level mango output.
Available online http://www.ijat-aatsea.com
2022-01-01T00:00:00ZBijections of k-plane trees
https://repository.maseno.ac.ke/handle/123456789/5424
Bijections of k-plane trees
Owino, Isaac. Okoth
A k-plane tree is a tree drawn in the plane such that the vertices are labeled by integers in the set
{1, 2, . . . , k}, the children of all vertices are ordered, and if (i, j) is an edge in the tree, where i and j are labels
of adjacent vertices in the tree, then i + j ≤ k + 1. In this paper, we construct bijections between these trees and
the sets of k-noncrossing increasing trees, locally oriented (k − 1)-noncrossing trees, Dyck paths, and some
restricted lattice paths.
https://pisrt.org/psrpress/j/odam/2022/1/bijections-of-k-plane-trees.pdf
2022-01-01T00:00:00Z