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Latest Published Articles

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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BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC