SPAS Publications 2022/2023

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

2023-08-04T11:33:30Z

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach Vincent, K.; Sammy, M. W; Jeremiah, K Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that ifis a contraction mapping on a complete metric space then there exists a unique fixed point in. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of , the Sierpinski triangle also with contraction constant of . On the other hand, a mapping on such that is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

2023-08-04T09:24:06Z

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach KoechVincenta; MusundiW.Sammy; KinyanjuiJeremiah Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that ifis a contraction mapping on a complete metric space then there exists a unique fixed point in. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of , the Sierpinski triangle also with contraction constant of . On the other hand, a mapping on such that is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.

Finite Elemente basiertes Modell zur Abschätzung von induzierten Eigenspannungen und Schnittkräften in einer AISI 1020 (S 275 JR) Stahllegierung

2023-08-04T09:32:55Z

Finite Elemente basiertes Modell zur Abschätzung von induzierten Eigenspannungen und Schnittkräften in einer AISI 1020 (S 275 JR) Stahllegierung Bosire R. N; Muvengei O. M. |; Mutua J. M; KimothoJ. K. The application of finite element models is a promising method for ensuring part quality during machining to accurately predict induced residual stresses and cutting forces. The present study applied Analysis System software to formulate a 3D model to predict induced residual stress and forces for AISI 1020 alloy. Taguchi method was applied in the design of the experiment with three levels and three factors selected: Cutting speed, feed rate and depth of cut. For validation, stresses are measured using an x-ray diffractometer from the surface to a depth of 0.6 mm in steps of 0.2 mm. The cutting forces are determined using a force dynamometer. Simulation results showed that cutting speed, feed rate and depth of cut contributed 94.76%, 0.048%, and 0.11% respectively. The predictive model equations were statistically significant with a p-value of <0.005. The average induced residual stress on the superficial layer from the experiment and simulation were 367.7 MPa and 365.6 MPa respectively. The average residual stresses obtained at depths of 0.2 mm, 0.4 mm, and 0.6 mm were 260 MPa, 233 MPa, and 211 MPa, respectively. The proposed model offers a potential solution to reducing the costs of experimental me

Moderating Influence Of External Environment On The Link Between Transformational Leadership And Performance Of Microfinance Banks In Kenya

2023-08-01T15:30:23Z

Moderating Influence Of External Environment On The Link Between Transformational Leadership And Performance Of Microfinance Banks In Kenya Muthoni N; Cheluget J; Mwikya J Retention of the desired staff is a key determinant of success in microfinance institutions in the modern competitive world. Notably, these institutions experience poor staff retention due to inappropriate leadership. Investigations on the effect of transformational leadership on staff retention have largely considered transformational leadership as a unidimensional construct than its respective dimensions of idealized influence, inspirational motivation, intellectual stimulation and individualized consideration. This study therefore investigated the effect of transformational leadership on staff retention in microfinance institutions in Nairobi City County, Kenya, specifically the effect of idealized influence, inspirational motivation, intellectual stimulation and individual consideration on staff retention. The underpinning theories were Transformational Leadership Theory, Leader-Member Exchange Theory, Social Exchange Theory, and Resource-Based View Theory. The study was guided by the positivism philosophy and descriptive and explanatory research designs. A total of 298 respondents was obtained through census sampling from the 12 accessible microfinance institutions licenced by the Central Bank of Kenya in Nairobi City County. Primary data was collected from senior, middle and lower-level management staff in the headquarters of these institutions, using structured questionnaires. The data were analysed using descriptive and inferential statistics, while hypotheses were tested at 5% significance level using regression analysis. The study established that transformational leadership significantly predicts staff retention through idealized influence, intellectual stimulation and individualized consideration. The study recommends that the policy makers in the microfinance institutions should align transformational leadership practices with the staff retention strategies for the success of these institutions.