Department of Mathematics
https://repository.maseno.ac.ke/handle/123456789/1935
2024-03-29T00:56:25ZBijections 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.
2023-09-15T00:00:00ZBijections 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
2022-01-01T00:00:00ZRefined enumeration of k-plane trees and k-noncrossing trees
https://repository.maseno.ac.ke/handle/123456789/5284
Refined enumeration of k-plane trees and k-noncrossing trees
Isaac Owino Okoth, Stephan Wagner
A k-plane tree is a plane tree whose vertices are assigned labels between 1 and k in such a way that the sum of the labels along any edge is no greater than k+1. These trees are known to be related to (k+1)-ary trees, and they are counted by a generalised version of the Catalan numbers. We prove a surprisingly simple refined counting formula, where we count trees with a prescribed number of labels of each kind. Several corollaries are derived from this formula, and an analogous theorem is proven for k-noncrossing trees, a similarly defined family of labelled noncrossing trees that are related to (2k+1)-ary trees.
https://arxiv.org/pdf/2205.01002.pdf
2022-01-01T00:00:00ZApplication of binary logistic regression model: determinants of contraceptive utilization.
https://repository.maseno.ac.ke/handle/123456789/4977
Application of binary logistic regression model: determinants of contraceptive utilization.
Caleb Okeyo Oyala
Contraceptives uptake among the youth has been a sensitive and controversial issue in the society that has resulted to various
social problems that include unwanted pregnancies and sexual transmitted infections among others. This requires intervention measures that
will promote contraceptive use in order to reduce unwanted pregnancies, sexual transmitted diseases and slow down the spread of sexually
transmitted diseases and infection among university students. This study focuses on analysis of clinical data of contractive utilization on
youth using binary logistic regression. Stratified random sampling was applied to identify 453 undergraduate students participants . The
study established that based on gender, more than 45% females are likely to use contraceptives compared to men, undergraduate students who
were from religions like catholic 27% are more likely, protestants 24% more likely and other Christian denomination are 52% less likely to
use contraceptives unlike their Muslim counterparts who are 72% more likely to use contraceptives. Use of alcohol does not have association
with use of contraceptives though 1% of students who take alcohol are less likely to use contraceptives compared to those who don’t take
alcohol. Sexually active are 16% more likely to use contraceptives
2020-01-01T00:00:00ZThree Dimensional Mathematical Models for ConvectiveDispersive Flow of Pesticides in Porous Media
https://repository.maseno.ac.ke/handle/123456789/4924
Three Dimensional Mathematical Models for ConvectiveDispersive Flow of Pesticides in Porous Media
Seth H. W. Adams, Alfred Manyonge
The transport of solutes through porous media where chemicals undergo adsorption or change process on the surface of the
porous materials has been a subject of research over years. Usage of pesticides has resulted in production of diverse quantity and
quality for the market and disposal of excess material has also become an acute problem. The concept of adsorption is essential in
determining the movement pattern of pesticides in soil in order to assess the effect of migrating chemical, from their disposal
sites, on the quality of ground water. Most studies made of movement of pesticides in the ground environment, the mathematical
models so far developed emphasis axial movement and in a few cases both axial and radial movements. Soil processes have a 3D
character; modeling therefore in principle, should employ three dimensions. It should also be noted that the appropriate number of
dimensions is closely related to the required accuracy of the research question. The 1D and 2D approaches are limited since they
are not capable of giving dependable regional influence of pesticides movement in the porous media and ground water. They give
us only theoretical results which are devoid of the reality in the field due to lumping of parameters. In this publication, three
dimensional formulas are developed so that it can enhance our capacity to analyze the realistic regional impact of adsorption of
pesticides in a porous media and the ground water in the field condition. The methodology will involve determining the
comprehensive dispersion equation accounting for 3D movement of solutes in the porous media and finding the solution of the
governing equation using Alternate Direction Implicit method (ADI) which is unconditionally stable for 3D equations of Douglas
and Gunn approach
2018-01-01T00:00:00ZNorm Properties of S -Universal Operators
https://repository.maseno.ac.ke/handle/123456789/4836
Norm Properties of S -Universal Operators
MUHOLO Joshua, BONYO,Job
We investigate the norm properties of a generalized derivation on a norm ideal J in B(H), the algebra of
bounded linear operators on a Hilbert space H. Specifically, we extend the concept of S−universality from the
inner derivation to the generalized derivation context, establish the necessary conditions for the attainment of the
optimal value of the circumdiameters of numerical ranges and the spectra of two bounded linear operators on H.
Moreover, we characterize the antidistance from an operator to its similarity orbit in terms of the circumdiameters,
norms, numerical and spectra radii of a pair of S-universal operators.
DOI: 10.33434/cams.692820
2020-01-01T00:00:00Z