As J is anti-symmetric
and R is symmetric positive definite, substitute the controller of (8) into (9) yields
2] representing the symmetric, anti-symmetric
, and two degenerate bending modes.
That means that when the unsymmetrical vibration mode shape of the object has been received as the result of the test, both symmetrical and anti-symmetric
parts may be isolated on its basis.
LMS algorithm with LUT based multiplier optimization techniques Anti-symmetric
In my past works (with each of my theories being independent and self-contained; and I do not repeat myself ever), I have shown how all this can be accomplished: one is with the construction of an asymmetric metric tensor whose anti-symmetric
part gives pure spin and electromagnetism, and whose differential structure gives an anholonomic, asymmetric connection uniquely dependent on x and dx (and hence x and the world-velocity u, giving a new kind of Finslerian space), which ultimately constructs matter (and motion) from pure kinemetric scratch.
nxn] denote the set of all n x m real matrices, the set of all n x n orthogonal matrices, the set of all n x n real symmetric matrices, the set of all n x n real anti-symmetric
matrices, respectively; The symbols, [A.
can be replaced by symmetric (or anti-symmetric
if sums of signal values will be replaced by differences) version (which requires m + 1 multiplications and M additions):
Using this transducer configuration, along with accurate synchronization of oscilloscope channels enables symmetric or anti-symmetric
guided waves modes emphasis in recorded signals.
Another result is that the anti-symmetric
state of the [[DELTA].
If we define a second-rank anti-symmetric
tensor B by
As in , for reasons that will be clear later, we define the electromagnetic field tensor F via the torsion tensor of spacetime (the anti-symmetric
part of the connection [GAMMA]) as follows:
In this framework, we produce the microspin tensor and the anti-symmetric
part of the stress tensor as intrinsic geometric objects rather than alien additions to the framework of classical elasticity theory.