The valence vector hypothesis, eq 44, provides three further constraints on the geometry of each atom in addition to the valence sum rule, suggesting that the four constraints together could be used in structure modeling as described in section 12, at least in cases where the ions were expected to be spherically symmetric.
First and foremost is the fact that the systems and networks one infers often have so many units/nodes that the problem is not well-posed, for any mathematical model, due to lack of data [6], [7] (unless one introduces further constraints, such as sparseness).
Accelerating quadrupeds may, by analogy with accelerating motorcycles, be limited by two further, inter-related physical constraints: pitch avoidance and traction.
For both models, we examined two further submodels with or without constraints, whereby coefficients for the corresponding correlations were held constant across sessions (It was hypothesized that paths a2 = a3, b2 = b3 = b4, c2 = c3, and d2 = d3 in the constrained model, but not in the unconstrained model).
"The new policy measures announced... will involve the period of tough spending constraint being extended for two further years.
For example [28 30] find robust cycles in systems of four or more identical, globally coupled phase oscillators with no further constraints.
It is clear that a minimization approach without further constraints on the X i would drive all diagonalizers to zero.
In impermissive forms of Bayesianism (often otherwise called "objective"), further constraints are put forward that significantly restrict the range of rational credences, possibly up to one single "right" probability function in any given setting.
Specific designs are subject to further constraints.
which imply the following further constraints: (2.2).
