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Now showing 1 - 5 of 14

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The Ecological Effects of Wood Fuel Extraction on the Gazetted Forests within Koibatek Zone, Mau Forests Complex, Kenya
(International Journal of Innovative Research & Development, 2019) Keith Kipng’etich Rono; Raphael Achola Kapiyo; Esnah Kerubo Bosire
Despite the importance of woodfuel in Kenya’s economic development, the ecological effects of its extraction on forests (particularly gazette forests) remain unclear. Studies contradicts each other on effects of woodfuel extraction on for ests with some indicating that it leads to loss of biodiversity and forest degradation while othersstating that woodfuel extraction is a forest cleaning activity and a part of good forest management. Little has been done to establish the area of forests lost due to woodfuel extraction as well as changes in distribution of preferred tree species from gazette forests in Kenya. The objective of this paper was to establish the ecological effects of woodfuel extraction on the gazette forests within Koibatek Zone, Mau Forests Complex-Kenya.Cross-sectional descriptive research design was adopted with all the 8 gazetteblocks within the Zone purposely selected. Stratified random sampling was used to select 384 woodfuel extractors and 8 FGDs were conducted each comprising of 10 participants. World Bank (2009) was used to convert volumes of woodfuel to equivalent forest cover required/ consumed in gazetted forests from 2006-2014. Forest cover change for 2006-2014 was examined by analyzing satellite images acquired from the United States Geological Survey Global Visualization viewer.The estimated volume of woodfuel from gazetted forests between 2006 and 2014 was 260,746.1m3 out of which 113,289.59m3was firewood and 147,456m3 was charcoal. The forest cover lost due to woodfuel was equivalent mature trees contained in 3902.6ha of closedcanopy forests. This is equivalent to 7.6% of closed forests of the gazette blocks within Koibatek Forests Zone. About 13 tree species were preferred for woodfuel; 8 indigenous species and 5 exotic species. Indigenous trees preferred had reduced as indicated by 89% of extractors while distribution of exotic species remained constant as reported by 68% of extractor s
Matrices of the Zero Divisor Graphs of Classes of 3-Radical Zero Completely Primary Finite Rings
(SCIENCE MUNDI, 2024) Frank Omondi Ndago; Maurice Owino Oduor; Michael Onyango Ojiema
The study of finite completely primary rings through the zero divisor graphs, the unit groups and their associated matrices, and the automorphism groups have attracted much attention in the recent past. For the Galois ring R ′ and the 2-radical zero finite rings, the mentioned algebraic structures are well understood. Studies on the 3-radical zero finite rings have also been done for the unit groups and the zero divisor graphs Γ(R). However, the characterization of the matrices associated with these graphs has not been exhausted. It is well known that proper understanding of the classification of zero divisor graphs with diameter 2 and girth 3 can provide insights into the structure of commutative rings and their zero divisors. In this study, we consider a class of 3-radical zero completely primary finite rings whose diameter and girth are 2 and 3 respectively. We enhance the understanding of the structure of such rings by investigating their Adjacency, Laplacian and Distance matrices.
On the Structure of a Class of Galois Ring Module Idealization
(2024) Owino Maurice Oduor
Let Ro be a Galois ring and U is a finitely generated Ro− module. Consider an idealization of U expressed as R = Ro ⊕U endowed with a suitable multiplication. We explore the structure of R through its group of units R × and the graph of its zero divisors Γ(R). The study involves an investigation on the overarching interplay between the ring theoretical properties of R, the group theoretic properties of R × and the graph theoretic properties of Γ(R). Since R is a finite ring with identity, the convention that each element of R is either a unit or a zero divisor has been extensively used to drive the concept of classification of the elements of R. The units of R have been classified, the automorphisms of R have been determined and the zero divisors of R have been characterized.
The Wiener Index and Related Indices of the Zero Divisor Graphs of Certain Classes of Completely Primary Finite Rings
(Asian J. Math. Appl. (2025) 2025:11, 2025) Frank Omondi Ndago; Maurice Oduor Owino
Studies on zero divisor graphs of completely primary nite rings R have been extensively done from Galois rings to other rings whose sets of zero divisors Z(R) coincides with the Jacobson radical J (R). The studies have focused on graph geometric properties such as the girth, clique number, chromatic number and diameter among others. Some ndings are also evident on matrices of zero divisor graphs on certain classes of rings. The classes of completely primary nite rings considered in the various studies are square radical zero, cube radical zero and power four radical zero. In this paper we have advanced the study on zero divisor graph Γ(R) of completely primary nite rings by investigating the Wiener Index and its invariants such as the Average disorder number and Distance index. Further, we analyse the binding number and some bounds on the Zagreb indices of the rings satisfying the conditions (Z(R))3 = (0) and (Z(R))2 ≠ (0), (Z(R))4 = (0) and (Z(R))3 ≠ (0).
Zero divisor graphs of classes of five radical zero commutative completely primary finite rings
(Int. J. Nonlinear Anal. Appl. In Press, 1–10, 2024-05) Hezron Saka Were; Maurice Owino Oduor
This paper provides a characterization for zero divisor graphs of a completely primary finite ring R satisfying the conditions (Z (R))5 = (0) ; (Z (R))4 ̸= (0) where Z(R) is its subset of all zero divisors (including zero). This has been achieved through Anderson and Livingston’s zero divisor graphs by precisely determining the graph invariants, including diameter, girth and the binding number, and graph characteristics including completeness, connectedness and partiteness.