We study the effects of oblateness up to J 4 of the primaries and power-law density profile (PDP) on the linear stability of libration location of an infinitesimal mass within the framework of restricted three body problem (R3BP), by using a more realistic model in which a disc with PDP is rotating around the common center of the system mass with perturbed mean motion. The existence and stability of triangular equilibrium points have been explored. It has been shown that triangular equilibrium points are stable for 0 < µ < µ c and unstable for µ c ≤ µ ≤ 1/2, where µ c denotes the critical mass parameter. We find that, the oblateness up to J 2 of the primaries and the radiation reduces the stability range while the oblateness up to J 4 of the primaries increases the size of stability both in the context where PDP is considered and ignored. The PDP has an effect of about ≈ 0.01 reduction on the application of µ c to Earth-Moon and Jupiter-Moons systems. We find that the comprehensive effects of the perturbations have a stabilizing proclivity. However, the oblateness up to J 2 of the primaries and the radiation of the primaries have tendency for instability, while coefficients up to J 4 of the primaries have stability predisposition. In the limiting case c = 0, and also by setting appropriate parameter(s) to zero, our results are in excellent agreement with the ones obtained previously. Libration points play a very important role in space mission and as a consequence, our results have a practical application 1 E-mail: fbjames11@physicist.net; babatunde.falaye@fulafia.edu.ng †Corresponding Author Tel. no: (+52) 1 5521450362 2 E-mail: dongsh2@yahoo.com 3 E-mail: kjoyewumi66@gmail.com 4 E-mail: sesantayo2001@yahoo.com ‡On sabbatical leave from University of Ilorin, Ilorin, Nigeria 5 E-mail: dreamsambo@yahoo.com 6 E-mail: friendsaver1@yahoo.com 7 E-mail: ladiran@gmail.com 8 E-mail: konyekachi@gmail.com 9 E-mail: sameer.ikhdair@najah.edu; sikhdair@gmail.com. 1 in space dynamics and related areas. The model may be applied to study the navigation and stationkeeping operations of spacecraft (infinitesimal mass) around the Jupiter (more massive) -Callisto (less massive) system, where PDP accounts for the circumsolar ring of asteroidal dust, which has a cloud of dust permanently in its wake.

We have investigated the green synthesis and antimicrobial activity of silver nanoparticles using Garcinia kola. Aqueous extract of G. kola was used to reduce AgNO 3 solution to obtain black nanocrystal of silver nanoparticles. Antimicrobial activity of the silver nanoparticles was tested against Escherichia coli, Klebsiella pneumonia, Bacillus subtilis, Staphylococcus aureus, Aspergillus niger, Rhizopus stolonifer and Candida albican. The synthesized silver nanoparticles was characterized using UV-vis spectroscopy, X-ray diffraction (XRD), Transmission electron microscopy (TEM), and Fourier transform infrared (FTIR) spectroscopy. UV-visible exhibits prominently the characteristic surface plasmon resonance at around 427 nm. A remarkable particle growth onset of 10 min was observed while the reaction ended within 30 min. The XRD analysis shows that the synthesized silver nanoparticles are crystalline in nature and well-dispersed silver nanoparticles with an approximate size of 10.4 nm were observed on TEM. The synthesized silver was found to possess good antimicrobial activity against all the tested microbes. The application of the green synthesized nanoparticles can be used in many fields such as foods, beverages, cosmetics and medicine.

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S5 1803+784 is a low synchrotron peaked (LSP) BL Lac object. Recent multiwavelength studies show no clear correlation between the synchrotron emission and the 𝛾-ray emission in this blazar. Unlike most LSP blazars, the spectrum of S5 1803+784 is poorly fitted with a single zone synchrotron self-Compton (SSC) leptonic jet model. We utilize a simple single-zone leptonic jet emission model with external Compton (EC) originating from the dusty torus (DT) to explain the emission and produce the best-fit parameters. The spectral analysis of the blazar in the flaring state reported in Astronomers' Telegram (ATel #13633) is studied using data from Fermi-LAT and NED archival data. We verified that the NED archival data are suitable for the spectral analysis of this blazar both during the flare and in the quiescent state by plotting the available synchrotron simultaneous data of the flare period with the NED archival data. The spectral energy distribution (SED) model of the flare and the quiescent state's best-fit parameters are produced using the JetSeT code. The results constrain the upper limit of the 𝛾-ray emission region length scale, the jet energetics, and the likely acceleration mechanism of the blazar during the flare.