http://ir.tum.ac.ke/handle/123456789/181 Contains PDF journal articles for this department Sat, 13 Jun 2026 17:24:09 GMT 2026-06-13T17:24:09Z http://ir.tum.ac.ke/handle/123456789/17600 COMPUTING FUZZY SUBGROUPS OF SOME SPECIAL CYCLIC GROUPS Makamba, Babington; Munywoki, Michael M. In this paper, we discuss the number of distinct fuzzy subgroups of the group Zpn × Zqm × Zr, m = 1, 2, 3 where p, q, r are distinct primes for any n ∈ Z + using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group G and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form. https://doi.org/10.4134/CKMS.c180341 Tue, 01 Jan 2019 00:00:00 GMT http://ir.tum.ac.ke/handle/123456789/17600 2019-01-01T00:00:00Z http://ir.tum.ac.ke/handle/123456789/17597 Operator Equations, Operator Inequalities and Power Bounded Operators in Hilbert Spaces Stephen, Ms Nyamusi Dorca; Kavila, Dr Mutie This is a study on some operator equations, operator inequalities and power bounded operators in Hilbert spaces. Looking at the operator equation TW = WS various properties on T, W and S such as; quasinormal, posinormal, hyponormal among others are satisfied, also on some operator inequalities the equivalence of constability of sequences of norms and its decomposition among other results are shown. Wed, 01 Nov 2017 00:00:00 GMT http://ir.tum.ac.ke/handle/123456789/17597 2017-11-01T00:00:00Z http://ir.tum.ac.ke/handle/123456789/17595 A little more on ideals associated with sublocales Ighedo, O.; Kivunga, G.W.; Stephen, D.N. As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the StoneCech compactification of ˇ L and the Lindel¨of coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper is to augment [12] by considering two other coreflections; namely, the realcompact and the paracompact coreflections. We show that M-ideals of RL indexed by sublocales of βL are precisely the intersections of maximal ideals of RL. An M-ideal of RL is grounded in case it is of the form MS for some sublocale S of L. A similar definition is given for an O-ideal of RL. We characterise M-ideals of RL indexed by spatial sublocales of βL, and O-ideals of RL indexed by closed sublocales of βL in terms of grounded maximal ideals of RL. https://doi.org/10.48308/cgasa.20.1.175 Mon, 01 Jan 2024 00:00:00 GMT http://ir.tum.ac.ke/handle/123456789/17595 2024-01-01T00:00:00Z http://ir.tum.ac.ke/handle/123456789/17499 Modelling Turbulence Using the Staggered Grid and Simplec Method KIMUNGUYI, J. K.; GATHER, F. K.; AWUOR, K. O. In a natural convection, local density differences and a resulting pressure gradient accelerate the fluid. In this paper a numerical study of a turbulent, natural convection problem is performed with an incompressible fluid in a rectangular enclosure. At the heated wall, the temperature distribution is a function of temperature gradients. The objective of this study is to conduct a numerical investigation of turbulent natural convection in a 3-D cavity using the staggered grid and the SIMPLEC method. The statisticalaveraging process of the mass, momentum and energy governing equations introduces unknown turbulent correlations into the mean flow equations which represent the turbulent transport of momentum, heat and mass, namely Reynolds stress () and heat flux (), which are modeled using k- SST model. The ReynoldsAveraged Navier-stokes (RANS), energy and k- SST turbulent equations are first non-dimensionalized and the resulting equations are discretized using a staggered and solved using SIMPLEC. From the results, both the experimental data and simulation using the staggered grid and SIMPLEC return a non-dimensional temperature of 0.5 at the core of the cavity and almost zero towards the cold and the natural turbulence flow is responsible for temperature distribution. Further, convective mass exchange is dominant in the centre of the enclosure. The investigated Rayleigh number of this study lies at Ra = 1.58. Fri, 01 May 2020 00:00:00 GMT http://ir.tum.ac.ke/handle/123456789/17499 2020-05-01T00:00:00Z