Department of Mathematics and PhysicsContains PDF journal articles for this departmenthttp://ir.tum.ac.ke/handle/123456789/1812024-02-23T16:39:46Z2024-02-23T16:39:46ZON THE CYCLE INDICES OF FROBENIOUS GROUPSMunywoki, MichaelKamuti, IreriKivunge, Benardhttp://ir.tum.ac.ke/handle/123456789/174262024-02-21T00:00:42Z2010-01-01T00:00:00ZON THE CYCLE INDICES OF FROBENIOUS GROUPS
Munywoki, Michael; Kamuti, Ireri; Kivunge, Benard
There are several very useful formulas, which give the cycle indices of
the binary operation of the sum, product, composition and power group of M and H
in terms of cycle indices of M and H. One very useful binary operation on groups,
which has not been exploited, is the semidirect product.
Suppose G = M ⋊H, a semi direct product; the question is: how can we express
the cycle index of G in terms of the cycle indices of M and H? This work partially
answers this question by considering the cycle indices of some particularly semidirect
product groups; namely – Frobenious groups.
2010-01-01T00:00:00ZEvaluation of Sea-Water Intrusion in Coastal Aquifers Using both Numerical Methods and Causal Research: A Case Study of Mombasa, KenyaMusingi, Dorcas MutheuMunywoki, Michael MbindyoMusingi, Benjamin Musyimihttp://ir.tum.ac.ke/handle/123456789/174252024-02-21T00:00:42Z2021-07-02T00:00:00ZEvaluation of Sea-Water Intrusion in Coastal Aquifers Using both Numerical Methods and Causal Research: A Case Study of Mombasa, Kenya
Musingi, Dorcas Mutheu; Munywoki, Michael Mbindyo; Musingi, Benjamin Musyimi
This research carried out in Mombasa Island links research done in 2020 on the effects of sea-water intrusion and the current state. The aquifer in Mombasa Island is semi-confined and consists of limestone and coral rock. Water samples were collected and tested from 32 boreholes to determine chemical qualities. Results showed that chloride levels ranged from 74 mg/l to 412 mg/l, with 34% of boreholes having high chloride concentration. After modelling using MT3D program results indicated that the boreholes near the ocean were interfered by sea-water intrusion because chloride concentration was high. Control measures to prevent further sea-water intrusion should be put in place. Therefore, from a practical point of view, individuals who have sunk boreholes since 2020 try to mitigate the problem by installing Reverse Osmosis systems within their facilities, to reduce chloride levels from borehole water. The current research analyses the impact of intrusion on the installed RO systems on Mombasa Island, including cost implications, with the view of proposing viable mitigation measures. The reverse osmosis system though expensive would save a lot of chloride entering the bore holes. It is a little bit expensive though but the end results are positive and the chloride levels will reduce the cost of using too much soap.
DOI: 10.4236/eng.2021.137028
2021-07-02T00:00:00ZTHE NUMBER OF DISTINCT FUZZY SUBGROUPS OF THE GROUP r p q Z n × Z m × Z FOR DISTINCT PRIMES p, q, r AND m, n ∈ Z+Munywoki, MichaelMakamba, Babingtonhttp://ir.tum.ac.ke/handle/123456789/174232024-02-21T00:00:57Z2022-01-01T00:00:00ZTHE NUMBER OF DISTINCT FUZZY SUBGROUPS OF THE GROUP r p q Z n × Z m × Z FOR DISTINCT PRIMES p, q, r AND m, n ∈ Z+
Munywoki, Michael; Makamba, Babington
The equivalence relation ‘~’ defined by Murali and Makamba is used
to find the number of the distinct fuzzy subgroups of the group
r ,
p q
Z n × Z m × Z where p, q, r are distinct primes with m and n as
Received: October 25, 2021; Accepted: November 30, 2021
2020 Mathematics Subject Classification: Primary 20N25, 03E72; Secondary 20K01, 20K27.
Keywords and phrases: maximal chain, equivalence, fuzzy subgroups.
How to cite this article: Michael Munywoki and Babington Makamba, The number of distinct
fuzzy subgroups of the group r
Zpn × Zqm × Z for distinct primes p, q, r and , m, n ∈ Z+
Advances in Fuzzy Sets and Systems 27(1) (2022), 111-138.
DOI: https://doi.org/10.17654/0973421X22006
2022-01-01T00:00:00ZClassifying fuzzy subgroups of the abelian group Zp1× Zp2×···× Zpn for distinct primes p1, p2,···, pnMunywoki, Michael MMakamba, Babington Bhttp://ir.tum.ac.ke/handle/123456789/174182024-02-21T00:00:50Z2017-01-01T00:00:00ZClassifying fuzzy subgroups of the abelian group Zp1× Zp2×···× Zpn for distinct primes p1, p2,···, pn
Munywoki, Michael M; Makamba, Babington B
In this paper, we classify the fuzzy subgroups of the group G= Zp1× Zp2×···× Zpn where p1, p2,···, pn are distinct primes and n∈ Z+. We develop an algorithm for counting the distinct fuzzy subgroups of the group G using the criss-cut counting technique. This is achieved by using the maximal chains of subgroups of G and the equivalence relation given by Murali and Makamba in their research papers on equivalent fuzzy subgroups
2017-01-01T00:00:00Z