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Trends in Clinical and Medical Sciences

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Latest Published Articles

Topological degrees on unbounded domains

OMA-Vol. 2 (2018), Issue 2, pp. 41–50 | Open Access Full-Text PDF
Dhruba R. Adhikari, Ishwari J. Kunwar
Abstract:Let \(D\) be an open subset of \(\mathbf R^N\) and \(f: \overline D\to \mathbf R^N\) a continuous function. The classical topological degree for \(f\) demands that \(D\) be bounded. The boundedness of domains is also assumed for the topological degrees for compact displacements of the identity and for operators of monotone type in Banach spaces. In this work, we follow the methodology introduced by Nagumo for constructing topological degrees for functions on unbounded domains in finite dimensions and define the degrees for Leray-Schauder operators and \((S_+)\)-operators on unbounded domains in infinite dimensions.
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Analytical Technique for (2+1) Fractional Diffusion Equation with Nonlocal Boundary Conditions

OMS-Vol. 2 (2018), Issue 1, pp. 287–300 Open Access Full-Text PDF
Rahmatullah Ibrahim Nuruddeen, Bashir Danladi Garba
Abstract:In the present article, a time fractional diffusion problem is formulated with special boundary conditions, specifically the nonlocal boundary conditions. This new problem is then solved by utilizing the Laplace transform method coupled to the well-known Adomian decomposition method after employing the modified version of Beilin’s lemma featuring fractional derivative in time. The Caputo fractional derivative is used. Some test problems are included.
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Analytic Functions of Complex Order Defined by New Differential Operator

OMS-Vol. 2 (2018), Issue 1, pp. 266–286 Open Access Full-Text PDF
Abdussalam Eghbiq, Maslina Darus
Abstract:In this paper, we introduce and study the classes \(S_{n,\mu}(\gamma,\alpha,\beta,\) \(\lambda,\nu,\varrho,\mho)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho)\) of functions \(f\in A(n)\) with \((\mu)z(D^{\mho+2}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z))^{‘} \) \(+(1-\mu)z(D^{\mho+1}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z))^{‘}\neq0\), where \(\nu>0,\varrho,\omega,\lambda,\alpha,\mu \geq0, \mho\in N_{0}, z\in U\) and \(D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z):A(n)\longrightarrow A(n),\) is the linear differential operator, newly defined as
\( D^{\mho}_{\lambda,\nu,\varrho}(\alpha,\omega)f(z)=z-\sum_{k=n}^{\infty}\left( \dfrac{\nu+k(\varrho+\lambda)\omega^{\alpha}}{\nu} \right)^{\mho} a_{k+1}z^{k+1}. \)
Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion relation for the functions included in the classes \(S_{n,\mu} (\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) and \(R_{n,\mu}(\gamma,\alpha,\beta,\lambda,\nu,\varrho,\mho,\omega)\) are given.
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Simultaneous Determination of Fexofenadine HCl and Pseudoephedrine HCl in Combined Pharmaceutical Dosage Form

OJC-Vol. 1 (2018), Issue 1, pp. 01–11 | Open Access Full-Text PDF
Sajid Mahmood, Muhammad Arshad, Zaheer Ahmed
Abstract:The objective of the present work was to develop and validate of an analytical method for the quantitative determination of Fexo. HCL and Pseudo. HCL in a combine tablet dosage form by \(UV-V\) is spectrophotometry and TLC. The main problem was to separate the two active ingredient from a single bilayered tablet because both the A.P.I’s were soluble in the same solvents. As media selection, distilled water and ethanol \((1:1)\) were used for Pseudo. HCl and methanol for Fexo. HCl, in which both the drugs were soluble and stable for a sufficient time. Both drugs were measured at \(220\)nm and \(247\)nm, where they showed maximum absorbance. Beer Lambert’s law was obeyed at concentration range \(4-14\) ppm and \(5-30\) ppm for Fexo. HCL and Pseudo HCL respectively. Fexo. HCl \((Y=0.0643x+0.9370)\) was measured with correlation coefficient \(r =0.9574\) and Pseudo. HCl \((Y=0.0843x+0.0219)\) with correlation coefficient \(r =0.9992\). The results of analysis have been validated statistically and recovery studies were carried out as \(99.29\%\pm 0.943\) and \(99.29\%\pm 0.941\) which were close to the assay value \(100.1\% \& 100.6 \%\). Precision of the method was measured which showed results for SD \((99.57 \% \;\;\& \;\;99. 51% )\) and \(\%\) RSD \((99.53 \%\;\; \&\;\; 99.54)\). The proposed method may be suitably applied for the analysis of Fexo. HCL and Pseudo.HCL in tablet pharmaceutical formulation for routine analysis.
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Degree Subtraction Adjacency Eigenvalues and Energy of Graphs Obtained From Regular Graphs

ODAM-Vol. 1 (2018), Issue 1, pp. 08–15 | Open Access Full-Text PDF
Harishchandra S. Ramane, Hemaraddi N. Maraddi
Abstract:Let \(V(G) = \{v_1, v_2, \ldots, v_n\}\) be the vertex set of \(G\) and let \(d_{G}(v_i)\) be the degree of a vertex \(v_i\) in \(G\). The degree subtraction adjacency matrix of \(G\) is a square matrix \(DSA(G)=[d_{ij}]\), in which \(d_{ij}=d_{G}(v_i)-d_{G}(v_j)\), if \(v_i\) is adjacent to \(v_j\) and \(d_{ij}=0\), otherwise. In this paper we express the eigenvalues of the degree subtraction adjacency matrix of subdivision graph, semitotal point graph, semitotal line graph and total graph of a regular graph in terms of the adjacency eigenvalues of \(G\). Further we obtain the degree subtraction adjacency energy of these graphs.
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Some Numerical Invariants Associated with V-phenylenic Nanotube and Nanotori

EASL-Vol. 1 (2018), Issue 1, pp. 01–09 | Open Access Full-Text PDF
Rachanna Kanabur, Sunilkumar Hosamani
Abstract:A carbon nanotube (CNT) is a miniature cylindrical carbon structure that has hexagonal graphite molecules attached at the edges. In this paper, we compute the numerical invariant (Topological indices) of linear [n]-phenylenic, lattice of \(C_{4}C_{6}C_{8}[m, n]\), \(TUC_{4}C_{6}C_{8}[m, n]\) nanotube, \(C_{4}C_{6}C_{8}[m, n]\) nanotori.
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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC