Cyclic Kite Configuration with Variable Mass of the Fifth Body in R5BP

This paper presents a numerical investigation on some characteristics and parameters related to the motion of an infinitesimal body with variable mass in five-body problem. The other four bodies are considered as primaries. The whole system forms a cyclic kite configuration and moves on a circle, the center of which is taken as the origin.We assume that the motion of the fifth infinitesimal body is affected by the other components of the system but it has no effect on their behavior. We started by setting the equations of motion of the fifth body by using Jeans’ law and Meshcherskii’s space-time transformations. Further, we determined numerically, using Mathematica software, the positions of Lagrangian points and basins of attraction in various planes. Finally, we investigated the linear stability of the Lagrangian points and noticed that all the Lagrangian points are unstable

Complex Pyogenic Liver Abscess: Outcome of Open vs Laparoscopic Drainage

OBJECTIVES Our study aimed to evaluate the safety and efficacy of laparoscopic drainage as a management of complex pyogenic liver abscesses in comparison to open surgical drainage. METHODOLOGY The comparative research design was used to compare the outcomes, complications, perioperative morbidity, mortality, and potential recurrence of 60 patients with a complex pyogenic liver abscess who were hospitalized at the General Surgery Department of Hayatabad Medical Complex Peshawar and treated either laparoscopically or openly from January 2019 to December 2020. 30 patients had open drainage management, while 30 patients received laparoscopic drainage management. For all patients, pus was examined for culture sensitivity. Patients with a small, solitary and unilocular pyogenic liver abscess that improved with antibiotic therapy and or/and percutaneous drainage were excluded. Each patient had a thorough clinical evaluation, lab tests, ultrasound, computed tomography, or magnetic resonance imaging of the pelvis and abdomen. RESULTS All patients underwent abdominal ultrasonography & sonographic diagnosis was made in 43(71.7%), followed by a computed tomography scan (CT) in 12(20%) & magnetic resonance imaging (MRI) diagnosis was made in 5(8.3%) patients respectively. Diabetes mellitus was present in 15(25%) patients, severe chronic obstructive pulmonary disease in 10(16.7%) and severe anemia in 9(15%) patients. All individuals associated with co-morbidity were considered high-risk patients. CONCLUSION Laparoscopic drainage of liver abscess has a shorter surgical time, lower morbidity rate, and shorter hospital stay as compared to open surgical drainage

Existence and Stability of the Libration Points in the Circular Restricted Three Body Problem with Variable Masses

We have investigated the existence and stability of the libration points in the circular restricted three body problem with the variation of all the masses (primaries and infinitesimal body) with time. We have used the Meshcherskii transformation for finding the autonomized equations of motion and found at most nine libration points. We have drawn the zero velocity curves and Poincare surface of sections for the different values of parameter k. Finally, we have checked the stability and found that all the libration points are unstable

Properties of Motion of the Infinitesimal Variable Mass Body in the Well Known Circular Restricted Three-Body Problem with Newtonian and Yukawa Potential

The effects of Newtonian and Yukawa gravitational potentials are studied on the circular restricted three-body system under the assumption that infinitesimal body varies its mass according to Jeans law. The equations of motion are determined under these perturbations. The numerical studies are conducted where locations of equilibrium points, regions of motion, trajectories with Poincare ́ surfaces of section and the basins of attraction have been investigated by well known software Mathematica. Moreover, the stability of the locations of equilibrium points are determined and it was found that all these points are unstable