SIMC 2015

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http://hdl.handle.net/11071/3921

Conference Theme: Exploring Mathematics and its Applications

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Boundary element method for solving high frequency scattering problems for obstacles with no corners
(Strathmore University, 2015) Mokgolele, M.
We consider scattering of a time-harmonic acoustic incident plane wave by a sound soft smooth object with Lipschitz boundary. The application of conventional boundary or finite element methods, have computational cost that grows linearly respect to the frequency of the incident wave. Recent research has been devoted in finding methods which does not loose robustness as frequency of the incident wave increases. Arden, Chandler-Wilde and Langdon proposed a collocation method to solve a high frequency scattering by convex polygons. They use a boundary element method, and incorporating products of plane wave basis functions with piecewise polynomials supported on a graded mesh into approximation space. They demonstrated via numerical experiments the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to frequency. Here we proposed a collocation method for high frequency scattering by smooth objects (objects with no corners, e.g. a circle).We applied same approximations as theirs, but employing uniform mesh. We demonstrate through numerical experiments the logarithmical grow of the solutions as frequency increases, with much reduced computational cost.
Cocycle of multifunctions
(Strathmore University, 2015) Molaei, MohammadReza
In this paper we introduce cocycles of multifunctions, and we study the concept of attractors for them by using of semibornologies. We de_ne a kind of conjugate relation on them, and we show that a conjugacy takes an attractor to an attractor. We consider the role of semibornology on the existence of new attractors.
Effect of CD4+ T-Cells and CD8+ T-Cells on Psoriasis: a mathematical study
(Strathmore University, 2015) Datta, Abhirup; Kesh, Dipak Kumar; Roy, Priti Kumar
Psoriasis is a common chronic inflammatory skin disease that is differentiated by repeated occurrences of raised scaly and red skin plaques. It is generated through several applications of drugs, strains, physical wounds to the skin and also for infectivity. Psoriasis is identified by composite interactions of T-Cells, Dendritic Cells, Cytokines and downstream transcription factors (type 1 Cytokines network). The effects of T-Cells in dermal layer (CD4+ T-Cells) are well-studied in the disease dynamics of Psoriasis from mathematical as well as biological context. But the concept of T-Cells in epidermal layer (CD8+ T-Cells) for disease progression of Psori-asis has not yet been explored till now from mathematical avenue. Here we introduce both CD4+ and CD8+ T-Cell, Dendritic Cell and Keratinocyte population to notice the impact of them on immunopathogenic cell-biological mechanism of Psoriasis. Numerical simulation is also furnished to establish the analytical outcomes.
Eigenvalue approach to the solution of generalized thermoelastic interactions in an infinite body with cylindrical cavity
(Strathmore University, 2015) Lahiri, Abhijit; Sarkar, S.
A generalized thermoelastic problem with temperature- dependent modulus of elasticity and thermal conductivity has been considered in an infinite medium with a cylindrical cavity. After applying Laplace-transformation the basic equations are presented in the form of a vector-matrix differential equation and then are solved by eigen-value method. Finally, the expressions of radial displacement, temperature and stress distribution are shown graphically for two different cases to compare the situations between the temperature-dependent and temperature-independent material properties in the inverse Laplace domain.
Language practices involving two languages among trilingual undergraduate students of Mathematics
(Strathmore University, 2015) Njurai, E.W.
This paper presents language practices of some trilingual undergraduate students of mathematics as they engaged with a mathematics task. The paper draws from a larger study that was recently completed. The aim in this paper is to explore whether, how and why the trilingual students use languages in their repertoire to make sense of an algebra task. The two languages in focus are the home languages of the students and the Language of Learning and Teaching (LoLT), English. Research shows that there is a research gap on language practices in trilingual contexts. The study adapted a qualitative inquiry process. It was conducted in one public university with a focus on first year students undertaking mathematics in their programs. Data was collected using questionnaires, clinical and reflective interviews. Analysis followed Discourse analysis (Gee, 2005) with a focus on mathematical Discourses. Findings show that the students engaged with competent mathematical Dis- courses. Furthermore they used their home languages as resources in their repertoire to interpret and understand the task. There were multiple purposes for code switching be- tween the two languages in their solitary engagement. The findings are important to inform Language in Education Policy (LiEP) in Kenya how and why some undergraduate students of mathematics position the home languages when they engage with mathematics. In the global perspective, the findings contribute to the field of mathematics education in trilingual contexts.
Mathematical modelling of The East Africa Marine Systems (TEAMS) fiber optic
(Strathmore University, 2015) Bulinda, Vincent Major
The concept of high bandwidth capabilities and low attenuation characteristics make it ideal for gigabit data transmission possible because light energy can be modelled in a wave. Mathematics and communication plays an integral role in today's world economic platform especially in large scale transmission of data and voice. We consider a cylindrical dielectric waveguide made of silica glass. The discussion will be based on the nature and behaviour of some of the ordinary differential equations (ODE's) and the partial differential equations (PDE's) namely; Maxwell equations, Schrodinger's equations and the Bessel functions and their interactions and applications then investigate the fiber optics solutions theory in communication engineering which plays a vital role in transmission capacity than metallic cables and therefore suited to the increase demand for high transmission capacity and speed. The problem involves studying the motion of sound which is a wave subjected to a sinusoidal forcing function. In this case the focus will be on Kenya being one of the developing countries in communication to the rest of the East African countries: Uganda, Rwanda, Burundi and Tanzania through cross-border connectivity arrangements and how fiber cables have enabled this happen in sharing data as fast as possible. The differential equations used in describing pulse propagation in the dispersion-dominated nonlinear fiber channel should demonstrate an agreement between the analytical results and the numeric. This technique is aimed at simplification of digital signal processing of nonlinear impairments represented graphically.
On collaboration: an important skill for Mathematics educators for the 21st century
(Strathmore University, 2015) Olszewski, Peter T.; Owiti, Dickson S. O.
Mathematics, problem solving, and critical-thinking are key skills to innovation. Not only does the 21st century workforce require mathematics skills for success in everyday life but also for scientific advancement and technological development so as to enhance global competitiveness. Since teaching as an individual process in the 21st century classroom is no longer effective, mathematics educators should embrace practices that foster 21st century skills to their learners. Collaboration is a key skill that not only empowers teachers of mathematics in handling the bigger challenges of the 21st century education but also enables students to succeed in today's world. When we think about collaboration, many different types exist. Most of all major turning points in our history were motivated by a collaborative effort. With any new teacher entering the profession, one needs a mentor to help guide us through the first years of the profession. This is where collaborations start. However, collaborations in education should never stop and should always be on going, as there is always something new to learn. This presentation will outline why collaboration in education is important for both the mathematics educator and student. In addition, the presenters will also outline personal examples of collaborations and provide some ideas on how to obtain and maintain collaborators. This, we believe, can help prepare educators and learners for the challenges in life ahead.
On the zero divisor graphs of Galois rings
(Strathmore University, 2015) Oduor, Maurice Owino
Let R be a Galois ring. The subset of zero divisors of R is studied with specific emphasis on the graph theoretical properties. The zero divisor graphs determined by equivalence classes of the zero divisors of the ring are also explored.
Renewable energy biodiesel: a mathematical approach from ecology to production
(Strathmore University, 2015) Roy, Priti Kumar; Chowdhury, Jahangir; Basir, Fahad Al
Biodiesel is one of promising renewable energy source and used as an alternative of conventional hydrocarbon fuels. Jatropha curcas plant oil (JCPO) is the most cost effective sources of biodiesel. The plant can be cultivated in wastelands and grows on almost any type of territory, even on sandy and saline soils. Judicious agricultural practices and effective crop management of Jatropha curcas is preliminary requisite to get maximum yield of oil. Production of biodiesel by transesterification of Jatropha oil significantly depends on four reaction parameters viz., reaction time, temperature, oil to alcohol molar ratio and stirrer speed. In this work, we have formulated a mathematical model of Jatropha curcas plant, which is affected by many type of pest with the aim to control the pest through Nuclear Polyhedrosis Virus (NPV). Here we have also concentrated on insecticide spraying as controlling measure to reduce the pest, to get maximum yield of Jatropha seeds, which gives Jatropha oil. We have also shown the effect of different variants on mass transfer in biodiesel production from JC oil and how the control theoretic approach flags the maximum production of biodiesel under the mathematical paradigm. Our analytical results provide an idea of the cost effective faster rate of biodiesel production, which satisfies our numerical conclusions.
The Science behind a flipped classroom
(Strathmore University, 2015) Olszewski, Peter T.
When first asked to teach a flipped classroom, I was excited and apprehensive at the same time. I knew I always wanted to try it but I wasn’t sure what the best practices were nor which parts of the class should be flipped and which shouldn’t. I soon found out there is a lot more to flipping a classroom, but the results can be rewarding. In this paper, I will describe how I flipped a College Algebra class with a specific focus for nursing students. In addition, valuable ideas and best practices on how to effectively flip a class are presented.

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