In 1935, following a controversial debate with Einstein, Silberstein published a solution of Einstein's field equations that appeared to describe a static, axisymmetric Rosen published a Letter to the Editor in which they pointed out a critical flaw in Silberstein's reasoning.
42.
Then from 1992 to 1998 an additional 6 flight tests of the axisymmetric high-speed scramjet-demonstrator were conducted by CIAM together with France and then with NASA, USA . Maximum flight velocity greater than Mach 6.4 was achieved and Scramjet operation during 77 seconds was demonstrated.
43.
We employed the axisymmetric Laplace and gradient operators to write Eqs ( 7 . a-7 . e ) and Eqs ( 8 . a-8 . d ) in a compact way, which is very useful in the derivation of the characteristic relation Eq ( 7 . f ).
44.
These include elaboration of nonlinear numerical methods of solving 3D cavitation problems, refinement of the known plane linear theories, development of asymptotic theories of axisymmetric and nearly axisymmetric flows, etc . As compared to the classical approaches, the new trend is characterized by expansion of the theory into the 3D flows.
45.
These include elaboration of nonlinear numerical methods of solving 3D cavitation problems, refinement of the known plane linear theories, development of asymptotic theories of axisymmetric and nearly axisymmetric flows, etc . As compared to the classical approaches, the new trend is characterized by expansion of the theory into the 3D flows.
46.
The fundamental domain is a half-plane through the axis, and a radial half-line, respectively . "'Axisymmetric "'or "'axisymmetrical "'are adjectives which refer to an object having cylindrical symmetry, or "'axisymmetry " '.
47.
Nonetheless, Einstein was correct and Silberstein was wrong : as we know today, all solutions to Weyl's family of axisymmetric metrics, of which Silberstein's is one example, necessarily contain singular structures ( " struts ", " ropes ", or " membranes " ) that are responsible for holding masses against the attractive force of gravity in a static configuration.
48.
The transformation transforms the equations of axisymmetric boundary layer with external velocity U in terms of original variables x, y, u, v into the equations of plane boundary layer with external velocity \ bar { U } in terms of the new variables \ bar { x }, \ bar { y }, \ bar { u }, \ bar { v }.
49.
Another venue combining the existing exact solutions with approximated and heuristic models was explored in the work " Hydrodynamics of Flows with Free Boundaries " that refined the applied calculation techniques based on the principle of cavity expansion independence, theory of pulsations and stability of elongated axisymmetric cavities, etc . and in " Dimensionality and similarity methods in the problems of the hydromechanics of vessels ".
50.
These functions specify "'initial data "', from which a unique vacuum solution can be " evolved " . ( In contrast, the Ernst vacuums, the family of all stationary axisymmetric vacuum solutions, are specified by giving just two functions of two variables, which are not even arbitrary, but must satisfy a system of two coupled nonlinear partial differential equations.
