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Latest Published Articles

Bounds on the covering radius of some classes of codes over \(\mathbb R\)

ODAM-Vol. 2 (2019), Issue 1, pp. 14–23 Open Access Full-Text PDF
P. Chella Pandian
Abstract: In this paper, the covering radius of codes over \(\mathbb R ={\mathbb Z_2}{R^{*}},\) where \(R^{*}={\mathbb Z_2}+v{\mathbb Z_2},v^{2}=v\) with different weight are discussed. The block repetition codes over \(\mathbb R\) is defined and the covering radius for block repetition codes, simplex code of \(\alpha\)-type and \(\beta\)-type in \(\mathbb R\) are obtained.
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Existence and uniqueness results for Navier problems with degenerated operators

OMA-Vol. 3 (2019), Issue 1, pp. 07–18 Open Access Full-Text PDF
Albo Carlos Cavalheiro
Abstract: In this article, we prove the existence and uniqueness of solutions for the Navier problem \( \Delta\big[\omega_1(x)\vert\Delta u\vert^{p-2}\Delta u+ \nu_1(x)\vert\Delta u\vert^{q-2}\Delta u\big] -{div}\big[\omega_2(x)\vert\nabla u\vert^{p-2}\nabla u +\nu_2(x)\vert\nabla u\vert^{s-2}\nabla u\big] = f(x) – { div}(G(x)),\) in \({\Omega},\) with
\(u(x) = {\Delta}u= 0,\) in \({\partial\Omega},\) where \(\Omega\) is a bounded open set of \(\mathbb{R}^N\) for \(N\geq 2\), \(\frac{f}{\omega_2}\in L^{p’}(\Omega , {\omega}_2)\) and \(\frac{G}{{\nu}_2}\in \left[L^{s’}(\Omega ,{\nu}_2)\right]^N\).
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Degree based graph invariants for the molecular graph of Bismuth Tri-Iodide

EASL-Vol. 2 (2019), Issue 1, pp. 01–11 Open Access Full-Text PDF
Zehui Shao, Abaid ur Rehman Virk, Muhammad Samar Javed, M. A. Rehman, Mohammad Reza Farahani
Abstract:In the fields of chemical graph theory (CGT), mathematical chemistry and molecular topology, a~topological index (TI) also known as a connectivity~index~is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. \(BiI_{3}\) is an excellent inorganic compound and is very useful in qualitative inorganic analysis and topological indices of \(BiI_{3}\) help to predict many properties like boiling point, heat of formation, strain energy, rigidity and fracture toughness and correlate the structure with various physical properties, chemical reactivity and biological activities. This paper computes several degree-based topological indices like multiplicative first Zagreb index, multiplicative second Zagreb index, multiplicative atomic bond connectivity index, multiplicative first and second hyper Zagreb index and multiplicative geometric arithmetic index for Bismuth Tri-Iodide chains and sheets.
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Study on data transmission problem from the existence of Hamiltonian fractional factor

OMS-Vol. 3 (2019), Issue 1, pp. 49–58 Open Access Full-Text PDF
Jianzhang Wu, Jiabin Yuan, Wei Gao
Abstract:In the field of computer networks, the performance of data transmission is usually characterized by the fractional factor. Some sufficient conditions for the existence of Hamilton fractional factors are obtained in this paper, and they extend the original theory presented in Gao et al. [1].
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC