Mathematical Sciences

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A finite difference study of radiative mixed convection MHD heat propagating Casson fluid past an accelerating porous plate including viscous dissipation and Joule heating effects
(Elsevier, 2024-04) Reddy, B. Prabhakar; Matao, P.M.; Sunzu, J.M.
A finite difference numerical simulation scrutiny is executed to evaluate the combined impacts of heat generation, buoyancy forces, viscous dissipation and Joule heating in unsteady hydromagnetic mixed convective chemically reactive and radiative Casson fluid flowing along an exponentially accelerating permeable vertical plate engrossed in a porous media by considering ramp surface concentration and temperature. The dimensionless non-linear coupled PDEs describing the flow model are dealt numerically by adopting the competent implicit Crank-Nicolson finite difference procedure. The variance of velocity, temperature, and concentration distributions are exposed via graphical representations due to the dissimilarity of the flow restrained parameters. Computational outcomes of the skin-friction, Nusselt and the Sherwood numbers are portrayed in the tabular pattern. The final outcomes of the research exposed that the impacts of thermal radiation, viscous dissipation, and heat production parameters enlarges the temperature and velocity distributions. The fluid motion deflates for growing Casson parameter and magnetic field intensity. The rising chemical reaction parameter suppresses the concentration and velocity distributions. Very importantly it is distinguished that fluid momentum, temperature, and concentration are quicker in the instance of isothermal plate temperature than ramp wall temperature. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc.
Actuarial modelling of severity claims in motor insurance by fitting probability distributions: a case of Dar es salaam
(The University of Dodoma, 2017) Nganzi, Erick
The purpose of this study was to find out the appropriate probability distributions that fit suitable to the motor insurance claims in respect of motorcycles, cars, and heavy vehicle insurance claimed amounts. The specific objectives were: to estimate the probability distributions considered, to identify appropriate model that fit best to the motor insurance claims amounts among eight distributions and to test the goodness of fit of the fitted probability distribution models. Daily data were collected from Britam Insurance Company Limited (T) from January 2007 to December 2016 of Dar es Salaam region. The estimates of parameters of the distributions were obtained by using maximum likelihood estimation method, and Kolmogorov-Sminov test statistic was used to fully assess the goodness of fit of eight probability distributions considered at 5% level of significance. Appropriate probability distribution model has been identified based on model selection criteria developed. Empirical Distribution Function (EDF) and Cumulative Distribution Function (CDF) plots were also used to visually assess the goodness of fit of the distribution models. The log likelihood values and Akaike’s information criterion were obtained and used as the selection criteria of the model that fit best the motor insurance claimed amounts. The model with large log likelihood value was considered to be the better model or the model with minimum AIC was considered to be the better model for motor insurance claimed amounts. These data were analysed by using SAS version 9.4, and SPSS version 21. The results showed that the Lognormal distribution fitted best to the motorcycle insurance claimed amounts and Inverse Gaussian distribution model fitted best to the car and heavy vehicle insurance claim amounts respectively.
Analysis and investigation of logical flaw of Zeno’s Achilles-Tortoise paradox
(Informa UK Limited, 2024-03-16) Mayila, Shega; Mpimbo, Marco; Rugeihyamu, Sylvester; Hari M. Srivastava
In this paper, we analyze the Achilles-Tortoise paradox, which denies the overtaking of the slowest runner (Tortoise) by the quickest runner (Achilles) because the pursuer must first reach the point whence the pursued started, so the slower must always hold the lead. The paradox translates into a requirement for the quicker to complete one by one an infinite sequence of distinct runs in a finite time to overtake the slower. This feat is impossible because the infinite sequence of distances contains no final distance to run, and the time to complete such a feat is not enough. However, we know better that in a race, the quickest always overtakes the slowest. Then why does the argument say otherwise? There should be logical flaws in its argumentation. Therefore, after an analysis of the paradox, we investigate the existence of such a flaw that exists in the argument itself or in the inferences its premises make. In addition to this, we present the new mathematical solution based on open balls in real Euclidean space, which shows that only a finite number of runs are needed by the quickest to overtake the slowest.
Analysis of effects of agriculture intervention using propensity score matching
(Macrothink Institute, 2015) Josephat, Peter; Likangaga, Rose
Nowadays the agriculture extension programme s are practiced in many parts of the world. There is a mixture of results about the effects of agriculture intervention programmes. The literature shows that the interventions are ineffective and have limited diffusion. On the other side, it shows that interventions are effective. Following different arguments about the effects of agriculture extension, this paper adopted Propensity Score Matching (PSM) to analyze the effects of District Agricultural Sector Investment Project (DASIP) using agriculture data. The study was conducted in rural Tanzania areas. It covered five regions namely Kagera, Mwanza, Mara, Simiyu and Kigoma. The study focused on agro ecological zone where corn is cultivated. Two methods which are questionnaire administration and direct oral interview were used to collect primary data. The collection of data using the questionnaire was done from both participants (359) and non participants (519). Before running the independent t test, the estimation of propensity score was done using Logistic regression. Thirteen confounding variables were used to estimate propensity scores.The effects of the intervention were analysed by considering four items namely the earnings from corn production, value of livestock owned value of household assets owned, and value of farm assets owned. The results show that none of the four factors had significant result as the p values are greater than 0.05. This implies that the earning between farmers participating in DASIP are not significant different from those who do not participate in the programme. The study recommends that the group activities should last longer rather than changing them from time to time.
Anisotropic neutral models with van der waals Equation of state
(The University of Dodoma, 2017) Mahali, Kasongo Andefise
We find new exact solutions to Einstein-Maxwell field equation for neutral anisotropy stellar stars with Van der Waals equation of state. We adopted Sunzu, Maharaj and Ray‘s metric function and measure of anisotropy. The solutions are obtained after considering the transformed Einstein-Maxwell field equations for neutral anisotropic matter. In our models, we regain previous anisotropic and isotropic results as a special case. We consider the space-time geometry to be static spherically symmetry. The exact solutions to the Einstein-Maxwell field equations corresponding to our models are found explicitly in terms of elementary functions namely simple algebraic functions. The gravitational potentials and matter variables generated are well behaved. We also generate relativistic stellar masses consistent with the stars PSR J1614-2230, Vela X-1, 4U 1538-52, LMC X-4, SMC X-4, Cen X-3, Her X-1, SAX J1808.4-3658 and EXO 1785-248.
Application of Odd Lomax log-logistic distribution to cancer data
(Elsevier, 2024-03) Kailembo, Benson Benedicto; Gadde, Rao Srinivasa; Kirigiti, Peter Josephat
The effectiveness of the parental distribution is modified in this article by adding flexibility, allowing it to capture all characteristics of the provided real-world data sets. This is accomplished by using the T-X class of distributions to generalize the parental distribution. Odd Lomax loglogistic distribution or OLLLD in short, is the name of the generalized parental distribution. The fundamental statistical properties of OLLLD are explicitly expressed. The maximum likelihood estimation approach is used to estimate the unidentified OLLLD parameters. In order to investigate the fit of the approach employed in estimating the parameters of OLLLD, the data are generated and an investigation done. Again, the ability of OLLLD is evaluated by fitting it to the real survival time data set of breast cancer.
Asymptotic behavior of solutions of matrix lyapunov integro differential equations
(Korean Journal Publishing Service, 2014) Sarma, Goteti V.; Hugo, Alfred
The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.
Blow-up of solutions to problems for nonlinear hyperbolic equation.
(The University of Dodoma, 2016) Chillingo, Josiah Kidney
Different physical phenomena can be represented in terms of nonlinear problems for partial differential equations; however such problems are often subjected to singularities. Thus it gives rise to a permanent research interest to such problems. In the present study we provide reviews of essential approach applied to Cauchy problems and initial-boundary problems for hyperbolic equations based on latest results in this ﬁeld.
Carleman estimates to solutions of direct and inverse problems for hyperbolic equations
(The University of Dodoma, 2015) Ngomaitala, Hussein Rajabu
A number of phenomena in modern science can be conveniently described in terms of problem for hyperbolic equation with Carleman estimates to the solution of inverse problem. The purpose of this study is to give a survey of the solution of the inverse problems for hyperbolic equation by Carleman estimates. We extend the results and prove the Carleman estimate focusing on an inverse problem for a simple hyperbolic equation. Also we derive the Lipschitz's stability by energy estimate; we obtain tomographic images by sent x-ray in different directions and measured at different places.
Charged anisotropic composite stellar object with strange, polytropic and gaseous matter
(Elsevier, 2024-08) Olengeile, Lilian; Sunzu, Jefta M.; Mkenyeleye, Jason M.
In this study, we build a charged star model with three layers with distinct equations of state. The core, intermediate layer, and envelope layer obey linear, polytropic, and Chaplygin equations of state, respectively. The model satisfies the physical requirements for the matter variables, gravitational potentials, and stability conditions. We have generated within-acceptable range masses and radii for stars. We also recover the masses and radii for the stars PSRJ1903+0327, PSRJ1614-2230, SAXJ1808.4-3658, Vela X-1, and EXO1785-248 from earlier investigations which shows astrophysical significance of our model.
Charged anisotropic models for quark stars
(Springer, 2014) Sunzu, J. M.; Maharaj, S. D.; Ray, S.
We perform a detailed physical analysis for a class of exact solutions for the Einstein-Maxwell equations. The linear equation of state consistent with quark stars has been incorporated in the model. The physical analysis of the exact solutions is performed by considering the charged anisotropic stars for the particular nonsingular exact model obtained by Maharaj, Sunzu and Ray. In performing such an analysis we regain masses obtained by previous researchers for isotropic and anisotropic matter. It is also indicated that other masses and radii may be generated which are in acceptable ranges consistent with observed values of stellar objects. A study of the mass-radius relation indicates the effect of the electromagnetic field and anisotropy on the mass of the relativistic star
Charged anisotropic models via embedding
(Springer, 2021) Mathias, Alberto K.; Maharaj, Sunil D.; Sunzu, Jefta M.; Mkenyeleye, Jason M.
We generate exact solutions to the Einstein–Maxwell field equations by analysing the embedding condition. We obtain a relationship between gravitational potentials that helps to solve the embedding condition and integrate the field equations. Our choice of the measure of anisotropy and electric field are physically realistic. Our model contains several previously known solutions as special cases. These include the investigations of interior Schwarzchild metric, Finch and Skea, Hansraj and Maharaj, Feroze and Siddiqui, and Manjonjo, Maharaj and Moopanar. We also describe the structure and properties of the relativistic star by including graphical representations. Our analysis shows that the body is stable, all energy conditions are satisfied, the regularity condition is not violated, forces under equilibrium condition are balanced, all matter variables are well behaved and the matching conditions are satisfied at the boundary of the relativistic star.
Comparing evaluation methods of students’ performance in secondary schools in Mbulu district using statistical quality control grade and fixed grading
(The University of Dodoma, 2022) Alphonce, Filbert
Tanzania like other countries in the world is faced by challenges in secondary education system. There is enough evidence that, assessment of students’ performance is one of the challenges that face assessors in secondary schools. Despite the mitigations agreed to solve the challenges on evaluation of students’ performance in the country. Studies about evaluation of students’ performance that have been conducted in Tanzania have mainly focused on fixed grading method. To fill this gap, this quantitative study investigated students’ performance by comparing their performance using statistical quality control charts grade and fixed grading method. The study is guided by three specific objectives which were: to assess students’ performance of a subject by using individual control chart over fixed grading method, between subjects by using mean and S control chart over fixed grading method and within a school by using group control charts over fixed grading method. The study was conducted in ordinary secondary schools in Mbulu District. It employed secondary data which were collected from240 students’ sampled documents obtained from academic students’ progressive report from six ordinary secondary schools in Mbulu District. The students’ performance was analyzed as per specific objectives by using Minitab Statistical Software with the help of statistical quality control charts grade and fixed grading method. After the analysis of the collected data, the quality control charts grade revealed that more students were performing well as compared with the analysis done by fixed grading method. The findings implied that statistical quality control charts grade was a tool that caused a large number of students to pass their examinations as opposed to the fixed grading method in evaluation of students’ performance. This is because the statistical quality control charts grade lower the cut-off points of the students’ performance. These findings have an implication in evaluating students’ performance since secondary school teachers may use statistical quality control charts grade to increase individual students’ performance in each subject.
Comparing the logarithmic least square and eigen value methods in analytic hierarch process by using the best job example.
(The University of Dodoma, 2016) Revocatus, Ponsian
This dissertation centers on comparing two methods based on consistence and ranking preservation of alternatives in analytic hierarchy process (AHP) by using the best job example. These two methods logarithmic least square method (LLSM) and eigenvalue method (EM) are used to develop approximations of ratio scales from a positive reciprocal matrix. The measurement of consistency and rank preservation are the main criteria for comparison of these two methods. The priorities obtained for each method from the combination of the comparison matrices for all criteria with respect to all alternatives, the ranking of the alternatives were given against the four covering criteria, the results show that, the two methods namely LLSM and EM give different results on ranking the alternatives as shown by Saaty and Vargas(1984).
Competency and performance gap between executive and non-executive employees of banks in Kerala, India
(WJRR Journal, 2021) Balan, Ramkumar T.
This paper assesses the Competency and Performance of bank employees of Four banks in Kerala, India. The gap in the performance and competency of executive and non- executive employees of the banks were determined. The linear regression model is estimated on dimensions of this efficiency measures. Also logistic regression models on competency and performance for executive and non-executive employees were identified. The dimensions of effectiveness of employees in a banking work place on both groups were compared. The gap in the characteristics of two sets of employees is illustrated for various demographic groups.
The contribution of teaching aids (counting objects) in numeracy skills performance for standard two pupils: a case of Kiteto district
(The University of Dodoma, 2017) Mkonyi, Sarael Jonas
This study aimed at investigating the contribution of teaching aids (counting objects) in numeracy skills performance for standard two pupils. The main objective of this study was to introduce an effective intervention for enhancing pupils’ achievement levels in numeracy. The study revealed that there is a low numeracy skill which is caused by many reasons such as unsuitable teaching and learning environment, few teaching methods, negative attitude of pupils and parents towards numeracy, shortage of teaching and learning materials, negative interaction between teachers and pupils to mention few. Pupils who experience learning difficulties are not having low numeracy skills; rather the teaching methods may be the result of their low numeracy skills. This study uses qualitative and quantitative approaches. The study used purposive sampling and simple random sampling whereby purposive sampling used to select eight (8) teachers in eight (8) different schools who teach numeracy in standard two to fill the questionnaires and simple random sampling was used to select forty (40) pupils from four (4) schools (ten (10) pupils from each school) for focus group discussion (FGD). Data were collected through questionnaire, focused group discussion, observation and documentary review. The data obtained were analyzed and interpreted through short statements and other studies from different literature for qualitative data and Microsoft Excel for quantitative data. The study revealed that teaching aids used in teaching and learning numeracy are locally made; some of the teachers use it frequently and effective use of teaching aids in numeracy skills increases performance.
Control charts for monitoring process capability index using median absolute deviation for some popular distributions
(Multidisciplinary Digital Publishing Institute, 2019) Aslam, Muhammad; Rao, G. Srinivasa; AL-Marshadi, Ali Hussein; Ahmad, Liaquat; Jun, Chi-Hyuck
A control chart monitoring the process capability index (PCI) using median absolute deviation (MAD) is proposed to analyze the industrial process performance. Extensive simulation studies were carried out to evaluate the performance of MAD-based PCI control charts under the low, moderate, and high asymmetric conditions when the process characteristic follows Weibull, log-normal, and gamma distributions. The performance of the proposed control charts was evaluated based on the average run lengths. The practical implementation of the proposed charts was also illustrated with industrial data.
Demographic factors influencing the prevalence of HIV/AIDS in Mbeya region of Tanzania
(The University of Dodoma, 2017) Edward, Noel
This study is conducted in the aim to figure out the demographic factors that fueling prevalence of HIV/AIDS in 2011/2012-Mbeya region. Demographic data of the cross-sectional years 2011/2012 is used. The data encompass male and female individual age group of 15-49.The binary logistic regression model was employed and demographic factors that were considered to have an impact on the prevalence of the epidemic were included in my analysis. The result shows that demographic variables had significant effect on the prevalence of HIV/AIDS in the year 2011/2012-Mbeya region for all respondents. However, except for male circumcision for male individual, polygamous, travelers and pregnancy status for female individuals, the demographic parameters such as respondent’s age, respondent’s sex, place of residence, paid sex (commercial sex), and unsafe sex, had significant effect on the prevalence of HIV/AIDS in the year 2011/2012 in Mbeya region.
Design of sampling plan in terms of acceptable quality level (AQL) and sustainable quality region (SQR)
(The University of Dodoma, 2017) Kuhanga, Seleman Dominicus
Attribute sampling plans on quality indices like AQL and MAPD gives the way for Sustainable Quality Region SQR=MAPD-AQL especially for the product at initial stage of production, where the exact quality of the product was not well designed. Optimum information on Acceptable quality level (AQL) and Maximum allowable percent defective would be better for protecting both consumer and producer in terms of SQR along with AQL or MAPD. New single sampling plans were developed by suggesting a unique monotonic increasing function on operating ratio(R) based on SQR with either AQL or MAPD corresponding to acceptance numbers. This study suggests a new quality region called Sustainable Quality Region (SQR) which exceed AQL and precede MAPD. ie proportional defective falls between AQL and MAPD ( SQR ), ie SQR= ( MAPD-AQL). Also, optimum sampling plan was suggested by establishing the measures AQL and MAPD, which are more producer and consumer friendly. The OC curves of SQR plans were compared with other AQL plans. Another single sampling plan was developed by considering the relationship between the MAPD with SQR so as to obtain the quality level that will protect consumer from getting the product with poor quality. Also economic SSP was developed based on MAPD –Min(ATI) at AQL and SQR-Min(ATI) at MAPD which aims for developing the quality level that both consumer and producer will be protected from getting poor quality product (consumer’s risk) with minimal cost of inspection as well as high quality items not to be rejected (producer’s risk). Also interesting relationships of SQR with AQL, MAPD, LTPD, TQR, AOQL and MAAOQ were presented so as to evaluate the other quality indices of the prescribed and suitable examples were illustrated.
Designing of multiple dependent state repetitive sampling plan for type-II generalized half logistic distribution
(Springer Nature, 2021) Rao, Gadde Srinivasa; Jilani, S. D.; Rao, A. Vasudeva
In this article, we present a new multiple dependent state repetitive (MDSR) sampling plan for attributes based on consider Type-II generalized half logistic distribution (TGHLD) with known shape parameter is consider here. The optimal parameter of the proposed plan is used to determine the operating characteristic (OC) curve approach using two point’s method. The results are explained with tables. We have made the comparison of proposed design with the usual multiple dependent state (MDS) sampling plans, repetitive acceptance sampling plan (RASP) and single sampling plan (SSP) in Average Sample Number (ASN). The proposed plan is demonstrated with the help of real- life data.

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