The Gram determinant  (composed from pairwise scalar products
of the current and voltage IV vectors) equals to square of the vectorial IP (8)
j] (j = 1,2) be separable Hilbert spaces with scalar products
According to , CTC, describing the evolution of the trains of Manakov solitons must be modified by attaching the scalar products
of the relevant polarization vectors to the exponential factors.
Also recently in , appropriate scalar products
are studied, which can guide the choice of block-diagonal preconditioners for self-adjoint saddle-point problems.
He then moves to interval arithmetic, floating point arithmetic, implementation, hardware sorting for interval arithmetic, scalar products
and complete arithmetic, principals of verified computing, and sample applications.
These scalar products
are defined as in the complex case, but for some automatic restrictions imposed by the non commutativity of H: see the Appendix B for more details.
He covers implementations of arithmetic on computers (floating-point arithmetic and its implementation on a computer, hardware support for interval arithmetic and scalar products
and complete arithmetic) and principles of verified computing including sample applications, including the extended interval Newton methods, verified solutions of systems of linear equations and multiple precision arithmetics.
The first one uses an index of confidence of the estimated orientation, and the second one the detection of minima of scalar products
in a neighbourhood.
In this case [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], because according to the above, this inequality between the scalar products
is valid and the coefficient -[epsilon] is positive.
y]], respectively, but are equipped with scalar products
The directional theory predicts that they will instead be based on the respective scalar products
minus any penalty for parties outside the region of acceptability.
The configuration flexibility built into the Scalar products
allows for optimized control of library functions by allocating separate SCSI-2 addresses for the robotic control interface and the DLT drives.