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space equations
We present an exact solution of the Einstein empty-space equations referring to four particles in relative motion.
      
A numerical solution of the state-space equations is applied in order to obtain a step response of the transformer winding.
      
Recently an exact solution of Einstein's empty-space equations referring to four uniformly accelerated particles was given.
      
One of the main results of the paper is to show what extra conditions are needed, in addition to those required for input-output-wise linearization, in order to achieve full linearity of both state-space equations and output map.
      
This suggests a danger in the use of 'velocity space' equations to model the effects of evaporation.
      
For such sequences governed by state-space equations, computation of these average values is reduced to solutions of algebraic matrix Riccati and Lyapunov equations.
      
Neural network models are used along with a classical linear servo controller derived from the linear state space equations.
      
The Einstein empty-space equations are also of particular note, and in this case the null datum describes essentially the intrinsic geometry of the null cone.
      
Solutions of Einstein's empty space equations are presented.
      
Yang's pure space equations generalize Einstein's gravitational equations, while coming from gauge theory.
      
The conserved rank four tensor of the spin-2 theory is shown to have the structure of Bel's tensor for a gravitational field satisfying Einstein's empty space equations, in the linearised version of general relativity.
      
Finally the imbedding of Minkowski space equations is studied.SO(4, 2) breaking is seen to enter due to the presence of a non-invariant scalar field, and a non-invariant vector field.
      
The theorem relating invariance of the six-space equations underSO(4, 2) to the invariance of their corresponding four-space equations under the conformal group is carefully stated and proved.
      
On generating state space equations of a linear constant coefficient system
      
The details of the linear algebra which must be performed in order to generate state space equations from primitive equations of the linear constant coefficient ordinary differential mathematical model are presented.
      
We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational.
      
One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.
      
The dynamical equations of motion of a multibody system with closed loops are reduced to state space equations within the framework of the computer-oriented Roberson/Wittenburg multibody formalism.
      
In Part I the state space equations for systems with tree configurations are developed.
      
A more natural approach for complexity reduction would be to start discrete time and space equations.
      
 

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