Solutions of the einstein equations with zero coupling. III

1971 ◽  
Vol 14 (11) ◽  
pp. 1521-1524
Author(s):  
I. M. Do zmorov
Keyword(s):  
Einstein Equations ◽  
Zero Coupling

Solutions of the einstein equations with zero coupling. II

1971 ◽  
Vol 14 (11) ◽  
pp. 1514-1520
Author(s):  
I. M. Dozmorov
Keyword(s):  
Einstein Equations ◽  
Zero Coupling

Solutions of the Einstein equations with zero coupling

1970 ◽  
Vol 13 (10) ◽  
pp. 1284-1288
Author(s):  
I. M. Dozmorov
Keyword(s):  
Einstein Equations ◽  
Zero Coupling

Einstein equations for a Finsler-Larange space with canonical N-linear connections

2020 ◽  
Vol 4 (1) ◽  
pp. 240-247
Author(s):  
Roopa M. K ◽  
◽  
Narasimhamurthy S. K ◽  
Keyword(s):  
Einstein Equations ◽  
Linear Connections

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

scholarly journals The Influence of Temperature and Viscosity of Polyethylene Glycol on the Rate of Microwave-Induced In Situ Amorphization of Celecoxib

Molecules ◽  
2020 ◽  
Vol 26 (1) ◽  
pp. 110
Author(s):  
Nele-Johanna Hempel ◽  
Tra Dao ◽  
Matthias M. Knopp ◽  
Ragna Berthelsen ◽  
Korbinian Löbmann
Keyword(s):  
Polyethylene Glycol ◽  
Microwave Radiation ◽  
Magnesium Stearate ◽  
Einstein Equations ◽  
Dissolution Process ◽  
Target Temperature ◽  
Peg 4000 ◽  
Lower Viscosity ◽  
Model Drug

Microwaved-induced in situ amorphization of a drug in a polymer has been suggested to follow a dissolution process, with the drug dissolving into the mobile polymer at temperatures above the glass transition temperature (Tg) of the polymer. Thus, based on the Noyes–Whitney and the Stoke–Einstein equations, the temperature and the viscosity are expected to directly impact the rate and degree of drug amorphization. By investigating two different viscosity grades of polyethylene glycol (PEG), i.e., PEG 3000 and PEG 4000, and controlling the temperature of the microwave oven, it was possible to study the influence of both, temperature and viscosity, on the in situ amorphization of the model drug celecoxib (CCX) during exposure to microwave radiation. In this study, compacts containing 30 wt% CCX, 69 wt% PEG 3000 or PEG 4000 and 1 wt% lubricant (magnesium stearate) were exposed to microwave radiation at (i) a target temperature, or (ii) a target viscosity. It was found that at the target temperature, compacts containing PEG 3000 displayed a faster rate of amorphization as compared to compacts containing PEG 4000, due to the lower viscosity of PEG 3000 compared to PEG 4000. Furthermore, at the target viscosity, which was achieved by setting different temperatures for compacts containing PEG 3000 and PEG 4000, respectively, the compacts containing PEG 3000 displayed a slower rate of amorphization, due to a lower target temperature, than compacts containing PEG 4000. In conclusion, with lower viscosity of the polymer, at temperatures above its Tg, and with higher temperatures, both increasing the diffusion coefficient of the drug into the polymer, the rate of amorphization was increased allowing a faster in situ amorphization during exposure to microwave radiation. Hereby, the theory that the microwave-induced in situ amorphization process can be described as a dissolution process of the drug into the polymer, at temperatures above the Tg, is further strengthened.

Einstein Equations and Alternative Lagrangians

1995 ◽  
Vol 32 (2) ◽  
pp. 185-190 ◽  
Author(s):  
R. de Ritis ◽  
C Rubano ◽  
P Scudellaro
Keyword(s):  
Einstein Equations
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