Evaluation of Markov chains to describe movements on tiling

OMS-Vol. 3 (2019), Issue 1, pp. 358 – 381 Open Access Full-Text PDF
Meseyeki Saiguran, Arne Ring, Abdullahi Ibrahim
Abstract: This study investigate movements of molecule on the biological cell via the cell walls at any given time. Specifically, we examined the movement of a particle in tiling, i.e. in hexagonal and square tiling. The specific questions we posed includes (i) whether particles moves faster in hexagonal tiling or in square tiling (ii) whether the starting point of particles affect the movement toward attainment of stationary distribution. We employed the transitional probabilities and stationary distribution to derive expected passage time to state \(j\) from state \(i\), and the expected recurrence time to state \(i\) in both hexagonal and square tiling. We also employed aggregation of state symmetries to reduce the number of state spaces to overcome the problems (i.e. the difficulty to perform algebraic computation) associated with large transition matrix. This approach leads to formation of a new Markov chain \(X_t\) that retains the original Markov chains properties, i.e. by aggregation of states with the same stochastic behavior to the process. Graphical visualization for how fast the equilibrium is attained with different values of the probability parameter \(p\) in both tilings is also provided. Due to difficulties in obtaining some analytical results, numerical simulation were performed to obtains useful results like expected passage time and recurrence time.
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On graceful difference labelings of disjoint unions of circuits

ODAM-Vol. 2 (2019), Issue 3, pp. 38 – 55 Open Access Full-Text PDF
Alain Hertz, Christophe Picouleau
Abstract: A graceful difference labeling (gdl for short) of a directed graph \(G\) with vertex set \(V\) is a bijection \(f:V\rightarrow\{1,\ldots,\vert V\vert\}\) such that, when each arc \(uv\) is assigned the difference label \(f(v)-f(u)\), the resulting arc labels are distinct. We conjecture that all disjoint unions of circuits have a gdl, except in two particular cases. We prove partial results which support this conjecture.
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Optimal control analysis of combined anti-angiogenic and tumor immunotherapy

OMS-Vol. 3 (2019), Issue 1, pp. 349 – 357 Open Access Full-Text PDF
Anuraag Bukkuri
Abstract: The author considers a mathematical model of immunotherapy and anti-angiogenesis inhibitor therapy for cancer patients over a fixed time horizon. Disease dynamics are captured by a system of ODEs developed in [1], describing dynamics among host cells, cancer cells, endothelial cells, effector cells, and anti-angiogenesis. Existence, uniqueness, and characterization of optimal treatment profiles that minimize the tumor and drug usage, while maintaining healthy levels of effector and host cells are determined. A theoretical analysis is performed to characterize the optimal control. Numerical simulations are performed to illustrate optimal control profiles for a variety of different patients, each leading to different treatment protocols.
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Existence and uniqueness of mild solution for stochastic partial differential equation with poisson jumps and delays

OMS-Vol. 3 (2019), Issue 1, pp. 343 – 348 Open Access Full-Text PDF
Annamalai Anguraj, Ravi kumar
Abstract: The objective of this paper is to investigate the existence and uniqueness theorem for stochastic partial differential equations with poisson jumps and delays. The existence of mild solutions of the problem is studied by using a different resolvent operator defined in [1] and fixed point theorem.
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Investigation of nanostructured iron oxides as anodic material for water splitting

OJC-Vol. 2 (2019), Issue 2, pp. 15 – 21 Open Access Full-Text PDF
Masood Rauf Khan, Zahid Sarfraz, Hafiz Sami ur Rehman
Abstract: We explore the possibility of using an iron-based anodic material (\(\alpha\)-hematite) synthesized with a hierarchical 3D urchin-like morphology, as an OER catalyst. The electrodes are prepared by pulsed laser deposition followed by thermal annealing leading to the hierarchical 3D urchin-like morphology. The effect of the deposition parameter on the catalyst phase and morphology are investigated by microRaman spectroscopy and scanning electron microscopy, while the electrode metrics are determined by voltammetric methods and Tafel analysis. We observe that the material is highly electroactive towards the OER, with performance in-line with that of noble-metal based state-of-the-art catalysts.
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Analysis of the small oscillations of a heavy barotropic gas filling an elastic body with negligible density

OMS-Vol. 3 (2019), Issue 1, pp. 331 – 342 Open Access Full-Text PDF
Hilal Essaouini, Pierre Capodanno
Abstract: In this work, we study the small oscillations of a system formed by an elastic container with negligible density and a heavy barotropic gas (or a compressible fluid) filling the container. By means of an auxiliary problem, that requires a careful mathematical study, we deduce the problem to a problem for a gas only. From its variational formulation, we prove that is a classical vibration problem.
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A new modified Adomian decomposition method for nonlinear partial differential equations

OMA-Vol. 3 (2019), Issue 2, pp. 81 – 90 Open Access Full-Text PDF
Djelloul Ziane, Rachid Belgacem, Ahmed Bokhari
Abstract: In literature, there are many methods for solving nonlinear partial differential equations. In this paper, we develop a new method by combining Adomian decomposition method and Shehu transform method for solving nonlinear partial differential equations. This method can be named as Shehu transform decomposition method (STDM). Some examples are solved to show that the STDM is easy to apply.
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Analytical solution of isotropic rectangular plates resting on Winkler and Pasternak foundations using Laplace transform and variation of iteration method

EASL-Vol. 2 (2019), Issue 4, pp. 6 – 20 Open Access Full-Text PDF
M. G. Sobamowo, O. M. Sadiq, S. A. Salawu
Abstract: Dynamic analysis of isotropic thin rectangular plate resting on two-parameter elastic foundations is investigated. The governing system is converted to system of nonlinear ordinary differential equation using Galerkin method of separation. The Ordinary differential equation is analyzed using hybrid method of Laplace transform and Variation of iteration Method. The accuracies of the analytical solutions obtained are verified with existing literature and confirmed in good agreement. Thereafter, the analytical solutions are used for parametric studies. From the results, it is observed that, increase in elastic foundation parameters increases the natural frequency. Increase in aspect ratios increases the natural frequency. It is expected that the present study will add value to the existing knowledge in the field of vibration.
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A comparative analysis of the travelling salesman problem: Exact and machine learning techniques

ODAM-Vol. 2 (2019), Issue 3, pp. 23 – 37 Open Access Full-Text PDF
Jeremiah Ishaya, Abdullahi Ibrahim, Nassirou Lo
Abstract: Given a set of locations or cities and the cost of travel between each location, the task is to find the optimal tour that will visit each locations exactly once and return to the starting location. We solved a routing problem with focus on Traveling Salesman Problem using two algorithms. The task of choosing the algorithm that gives optimal result is difficult to accomplish in practice. However, most of the traditional methods are computationally bulky and with the rise of machine learning algorithms, which gives a near optimal solution. This paper studied two methods: branch-and-cut and machine learning methods. In the machine learning method, we used neural networks and reinforcement learning with 2-opt to train a recurrent network that predict a distribution of different location permutations using the negative tour-length as the reward signal and policy gradient to optimize the parameters of recurrent network. The improved machine learning with 2-opt give near-optimal results on 2D Euclidean with upto 200 nodes.
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Software quality assurance of cryocooler drive electronics software used in spacecraft

EASL-Vol. 2 (2019), Issue 4, pp. 1 – 5 Open Access Full-Text PDF
Savitha A, Sudeesh B, PrakashaRao P J V K S
Abstract: Software plays an important role in the ISRO space mission. Reliability of this software is vital to achieve zero defects in space systems and services. There are varieties of software used in realization of spacecraft. Mainly it is categorized into onboard, mission and ground software. Evaluation of this software is the major activity for a software quality assurance person. Software quality engineer has to certify the software based on system level requirements, mission requirements and functional requirements. All the hardware and software interactions also have to be verified. Risk management is the key factor for effective software management. Software life cycle activities are carried out based on ISRO software process document. Following these standards and guidelines helps to find the defects in the earlier phase of software development life cycle. This paper mainly describes the software quality assurance activities carried out for control drive electronics unit used in GSAT spacecraft. SQA activities complied against the IEEE12207 standards (ISPD-2) at ISRO level. Pulse Tube Cryocoolers are active cryogenic devices used to generate cryogenic temperatures in the 50K-80K range in a single stage. Cryocooler drive electronics unit generates identical drive to both the compressors of pulse tube cryocooler.
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