Generating potentials via difference equations

The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric functions, energy density and pressure are well behaved which suggests that this model could be used to describe a relativistic sphere. The model admits a barotropic equation of state which approximates a polytrope close to the stellar centre.Comment: 11 pages, To appear in Math. Meth. Appl. Sc

Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity

An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular} solutions governed by a self-bound (that is, the surface density does not vanish together with pressure) equation of state (EOS) or density variation can not exist in the state of hydrostatic equilibrium, because the source mass which belongs to them, does not represent the `actual mass' appears in the exterior Schwarzschild solution. The only configuration which could exist in this regard is governed by the homogeneous density distribution (that is, the interior Schwarzschild solution). Other structures which naturally fulfill the requirement of the source mass, set up by exterior Schwarzschild solution (and, therefore, can exist in hydrostatic equilibrium) are either governed by gravitationally-bound regular solutions (that is, the surface density also vanishes together with pressure), or self-bound singular solutions (that is, the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for publication in Modern Physics Letters

PREPARATION, CHARACTERIZATION AND EVALUATION OF FLOATING MICROPARTICLES OF CIPROFLOXACIN

Objective: The main purpose of this study is to prepare a floating micro articulated drug delivery system of ciprofloxacin by using non-aqueous solvent evaporation technique to increase the bioavailability and therapeutic effectiveness of the drug by prolonging its gastric residence time.Methods: Floating microparticles were prepared by using different low-density polymers such as ethyl cellulose and hydroxypropyl methylcellulose either alone or in combination with the aid of non-aqueous solvent evaporation technique. All the formulated microparticles were subjected to various evaluation parameters such as percentage yield, drug content, drug entrapment, rheological studies, floating characteristics and in vitro drug release studies.Results: Drug-excipient compatibility studies performed with the help of FTIR instrument indicated that there were no interactions. Results revealed that non-aqueous solvent evaporation technique is a suitable technique for the preparation of floating microspheres as most of the formulations were discrete and spherical in shape with a good yield of 65% to 85% and 15 to 22 h of floating duration with 90% of maximum percentage floating capacity shown by formulation FM9. Though, different drug-polymer ratios, as well as a combination of polymers, play a significant role in the variation of overall characteristics of formulations. Based on the data of various evaluation parameters such as particle size analysis, drug content, drug entrapment, rheological studies and in vitro drug release characteristics formulation FM9 was found to fulfil the criteria of ideal floating drug delivery system.Conclusion: Floating microparticles were successfully prepared, and from this study, it can be concluded that the developed floating microspheres of ciprofloxacin can be used for prolonged drug release in the stomach to improve the bioavailability and patient compliance

Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations

We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate solutions were subjected to the following elementary tests: i) isotropy of the pressure, ii) regularity at the origin, iii) positive definiteness of the energy density and pressure at the origin, iv) vanishing of the pressure at some finite radius, v) monotonic decrease of the energy density and pressure with increasing radius, and vi) subluminal sound speed. A total of 127 candidate solutions were found. Only 16 of these passed all the tests. Of these 16, only 9 have a sound speed which monotonically decreases with radius. The analysis was facilitated by use of the computer algebra system GRTensorII.Comment: 25 pages. To appear in Computer Physics Communications Thematic Issue on "Computer Algebra in Physics Research

Mass function and dynamical study of the open clusters Berkeley 24 and Czernik 27

We present a $UBVI$ photometric study of the open clusters Berkeley 24 (Be 24) and Czernik 27 (Cz 27). The radii of the clusters are determined as 2\farcm7 and 2\farcm3 for Be 24 and Cz 27, respectively. We use the Gaia Data Release 2 (GDR2) catalogue to estimate the mean proper motions for the clusters. We found the mean proper motion of Be 24 as $0.35\pm0.06$ mas yr$^{-1}$ and $1.20\pm0.08$ mas yr$^{-1}$ in right ascension and declination for Be 24 and $-0.52\pm0.05$ mas yr$^{-1}$ and $-1.30\pm0.05$ mas yr$^{-1}$ for Cz 27. We used probable cluster members selected from proper motion data for the estimation of fundamental parameters. We infer reddenings $E(B-V)$ = $0.45\pm0.05$ mag and $0.15\pm0.05$ mag for the two clusters. Analysis of extinction curves towards the two clusters show that both have normal interstellar extinction laws in the optical as well as in the near-IR band. From the ultraviolet excess measurement, we derive metallicities of [Fe/H]= $-0.025\pm0.01$ dex and $-0.042\pm0.01$ dex for the clusters Be 24 and Cz 27, respectively. The distances, as determined from main sequence fitting, are $4.4\pm0.5$ kpc and $5.6\pm0.2$ kpc. The comparison of observed CMDs with $Z=0.01$ isochrones, leads to an age of $2.0\pm0.2$ Gyr and $0.6\pm0.1$ Gyr for Be 24 and Cz 27, respectively. In addition to this, we have also studied the mass function and dynamical state of these two clusters for the first time using probable cluster members. The mass function is derived after including the corrections for data incompleteness and field star contamination. Our analysis shows that both clusters are now dynamically relaxedComment: 16 pages including 8 tables. 22 figures. Accepted by MNRA

Arc-heater performance research

The tasks performed can be divided into the following categories: an analysis of the electric arc phenomena, especially near the electrodes; a parametric study of arcjet performance by means of a computer code (ARCFLO) and verification with experimental data where possible; the development of a data acquisition system to collect the above experimental data using Ames arc-jets; and a study of the critical components (electrodes and constrictor disks) and suggestions of how to improve their performance

Evaluation of Daphnia magna as an indicator of Toxicity and Treatment efficacy of Municipal Sewage Treatment Plant

Performance evaluation of wastewater treatment plants (WWTPs) with special reference to toxicity reduction using Daphnia magna straus as test organism is very important to study the likely adverse effects of thetreated wastewater on the aquatic ecosystem of receiving waters and to detect common environmentally realistic concentrations of pollutants at different concentration levels and toxicity discriminatory ability to distinguish different degree of toxicity and toxic specificity of the compounds on target organisms. This test can be considered asuseful analytical tool for screening of chemical analysis and early warning system to monitor the different operational units of wastewater treatment plants. Interrelationship between COD, SS with respect to Daphnia toxicity (Gd) suggests that improvement of the toxicological quality of wastewater could be linked to the removal of both COD and suspended solids. Both the parameters (COD & SS) can serve as a regulatory tool in lieu of an explicit toxicological standard. An important feature of this work was to emphasize the significance of toxicity tests. It could help to reduceinfluent toxicity and thereby avoid impacting microorganisms’ population in activated sludge systems. This study shows the difference between using physico-chemical and biological criteria to define the quality or toxicity ofwastewater, making it clear that both methods are indispensable and complimentary and support the earlier view that Daphnia magna can serve as a valuable model for bio- monitoring of water pollution and for evaluation of the toxicity of an effluent and risk assessment in an aquatic body, as it is highly sensitive to pollutants