pisrt – Page 71

Isolation, Purification and Complex Formation of Nicotine Alkaloid

EASL-Vol. 1 (2018), Issue 2, pp. 30–36 | Open Access Full-Text PDF

Sajid Mahmood, Saiqa Jameel, Zaheer Ahmad

Abstract:Nicotiana tabacum is rich with medicinal importance. The aim of the study is to isolate, purify and compare nicotine (3-[1-Methylpyrolidine-2 yl] pyridine) from different brands of cigarettes. Isolation is carried out by liquid-liquid extraction using ether as solvent. Crude nicotine samples are further purified with SPE (solid phase extraction) method. Nicotine crystals are complexed with zinc chloride (\(ZnCl_{2}\)). Fine and pure crystals of metal complexes are obtained with Nic-C and Nic-D. However, no complex formation is synthesized with Nic A and Nic-B due to impurities in the sample which is confirmed by thin layer chromatography. Antibacterial activity of the samples is carried out against different strains of bacteria which showed positive results for Nic-C and Nic-D. The outcomes of the study reveal that Zinc-Nicotine complexes can be used as therapeutic agents and anti-sickness agents in sickle cell disease.

Biological Synthesis and Characterization of Chromium (iii) Oxide Nanoparticles

EASL-Vol. 1 (2018), Issue 2, pp. 23–29 | Open Access Full-Text PDF

Zaheer Ahmad, Aisha Shamim, Sajid Mahmood, Tariq Mahmood, Farman Ullah Khan

Abstract:Nanoparticles are nanosized clusters with dimensions less than 100nm. Nanoparticles are fabricated by physical, chemical, and biological methods. Physical and chemical methods are energy intensive and involve hazards of contaminations. Biological synthesis of nanoparticles is environment friendly, less toxic and cost effective process. Plants, microorganisms, and biomolecules are commonly exploited species for merging of nanoparticles in this method. In present work we synthesize Chromium oxide nanoparticles by biological method using fungal extract of Aspargillus Niger. The synthesized nanoparticles are characterized by XRD (X-Ray Diffraction), SEM (Scanning Electron Microscopy) and UV-Vis (Ultraviolet Visible) techniques.

Boundedness of Littlewood-Paley Operators with Variable Kernel on Weighted Herz Spaces with Variable Exponent

EASL-Vol. 1 (2018), Issue 2, pp. 10–22 | Open Access Full-Text PDF

Afif Abdalmonem, Omer Abdalrhman, Shuangping Tao

Abstract:Let \(\Omega\in{L}^{\infty}(\mathbb{R}^{n})\times{L^{2}(S^{n-1})}\) be a homogeneous function of degree zero. In this article, we obtain some boundedness of the parameterized Littlewood-Paley operators with variable kernels on weighted Herz spaces with variable exponent.

Global solution and asymptotic behaviour for a wave equation type \(p\)-laplacian with memory

OMA-Vol. 2 (2018), Issue 2, pp. 156–171 | Open Access Full-Text PDF

Carlos Alberto Raposo, Adriano Pedreira Cattai, Joilson Oliveira Ribeiro

Abstract:In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation
\begin{eqnarray*}
u_{tt} – \Delta_{p} u = \Delta u – g*\Delta u
\end{eqnarray*}
where \(\Delta_{p} u\) is the nonlinear \(p\)-Laplacian operator, \(p \geq 2\) and \(g*\Delta u\) is a memory damping. The global solution is constructed by means of the Faedo-Galerkin approximations taking into account that the initial data is in appropriated set of stability created from the Nehari manifold and the asymptotic behavior is obtained by using a result of P. Martinez based on new inequality that generalizes the results of Haraux and Nakao.

Identification of a diffusion coefficient in degenerate/singular parabolic equations from final observation by hybrid method

OMA-Vol. 2 (2018), Issue 2, pp. 142–155 | Open Access Full-Text PDF

Khalid Atifi, El-Hassan Essoufi, Hamed Ould Sidi

Abstract:This paper deals with the determination of a coefficient in the diffusion term of some degenerate /singular one-dimensional linear parabolic equation from final data observations. The mathematical model leads to a non convex minimization problem. To solve it, we propose a new approach based on a hybrid genetic algorithm (married genetic with descent method type gradient). Firstly, with the aim of showing that the minimization problem and the direct problem are well posed, we prove that the solution’s behavior changes continuously with respect to the initial conditions. Secondly, we chow that the minimization problem has at least one minimum. Finally, the gradient of the cost function is computed using the adjoint state method. Also we present some numerical experiments to show the performance of this approach.

Analytic study on hilfer fractional langevin equations with impulses

OMA-Vol. 2 (2018), Issue 2, pp. 129–141 | Open Access Full-Text PDF

S. Harikrishnan, E. M. Elsayed, K. Kanagarajan

Abstract: In this paper, we find a solution of a new type of Langevin equation involving Hilfer fractional derivatives with impulsive effect. We formulate sufficient conditions for the existence and uniqueness of solutions. Moreover, we present Hyers-Ulam stability results.

Coefficient estimates of some classes of rational functions

OMA-Vol. 2 (2018), Issue 2, pp. 114–128 | Open Access Full-Text PDF

Hanan Darwish, Suliman Sowileh, Abd AL-Monem Lashin

Abstract:Let \(\mathcal{A}\) be the class of analytic and univalent functions in the open unit disc \(\Delta\) normalized such that \(f(0)=0=f^{\prime }(0)-1.\) In this paper, for \(\psi \in \mathcal{A}\) of the form \(\frac{z}{f(z)}, f(z)=1+\sum\limits_{n=1}^{\infty }a_{_{n}}z^{n}\) and \(0\leq \alpha \leq 1,\) we introduce and investigate interesting subclasses \(\mathcal{H}_{\sigma }(\phi ), \;S_{\sigma }(\alpha ,\phi ), \; M_{\sigma }(\alpha ,\phi ),\) \( \Im _{\alpha} (\alpha ,\phi )\) and \(\beta _{\alpha}(\lambda ,\phi ) \left( \lambda \geq 0 \right)\) of analytic and bi-univalent Ma-Minda starlike and convex functions. Furthermore, we find estimates on the coefficients \(\left\vert a_{1}\right\vert\) and \(\left\vert a_{2}\right\vert\) for functions in these classess. Several related classes of functions are also considered.

Asymptotic stability and blow-up of solutions for the generalized boussinesq equation with nonlinear boundary condition

OMA-Vol. 2 (2018), Issue 2, pp. 93–113 | Open Access Full-Text PDF

Jian Dang, Qingying Hu, Hongwei Zhang

Abstract:In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish both the existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow-up result for solutions with positive and negative initial energy respectively.

Super \((a,d)\)-\(C_3\)-antimagicness of a Corona Graph

OMS-Vol. 2 (2018), Issue 1, pp. 371–378 Open Access Full-Text PDF

Noshad Ali, Muhammad Awais Umar, Afshan Tabassum, Abdul Raheem

Abstract:A simple graph \(G=(V(G),E(G))\) admits an \(H\)-covering if \(\forall \ e \in E(G)\ \Rightarrow\ e \in E(H’)\) for some \((H’ \cong H )\subseteq G\). A graph \(G\) with \(H\) covering is an \((a,d)\)-\(H\)-antimagic if for bijection \(f:V\cup E \to \{1,2,\dots, |V(G)|+|E(G)| \}\), the sum of labels of all the edges and vertices belong to \(H’\) constitute an arithmetic progression \(\{a, a+d, \dots, a+(t-1)d\}\), where \(t\) is the number of subgraphs \(H’\). For \(f(V)= \{ 1,2,3,\dots,|V(G)|\}\), the graph \(G\) is said to be super \((a,d)\)-\(H\)-antimagic and for \(d=0\) it is called \(H\)-supermagic. In this paper, we investigate the existence of super \((a,d)\)-\(C_3\)-antimagic labeling of a corona graph, for differences \(d=0,1,\dots, 5\).

Fractional Integral Inequalities on Time Scales

OMS-Vol. 2 (2018), Issue 1, pp. 361–370 Open Access Full-Text PDF

Deniz Uçar, Veysel F. Hatipo\(\breve{\text{g}}\)lu, Aysegűl Akincali

Abstract:In this paper, we use the Delta Riemann-Liouville fractional integrals to establish some new integral inequalities for the Chebyshev functional in the case of two synchronous functions on time scales. Our results improve the inequalities for the discrete and continuous cases.

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