In the absence of any synaptic input from the inhibitory neuron, we restate system (1) to reduce the complexity of notation: d x d t = φ ( x, y ) ≡ ( 1 − cos ( x ) ) + ( I E + λ ( 1 + cos ( y ) ) ) ( 1 + cos ( y ) ), d y d t = ε ψ ( x, y ) ≡ ε ω. (40).
Notice that to reduce the overuse of notations, we distinguish between central and noncentral chi-square by the symbol.
Using this kernel language as a bridge between design-oriented and analysis-oriented notations we reduce the burden of defining a variety of direct transformations from the former to the latter to the less complex problem of defining transformations to/from the kernel language.
However, compared to the first scheme, it requires some changes in the hardware of the data acquisition of the imaging system and a different notation for reducing the measurements than by basic matrix multiplication.
The ROS measure was designed for cases in which the two ranges overlapped and neither was contained in the other; if one was contained in the other, then ROS reduces to 1 (the notation ||[ m, M]|| for a closed interval refers to the length of the interval, M - m).
All wall stress values were multiplied by 105 to reduce scientific notation.
To simplify the notation and reduce bandwidth, a simple modification can be made to the current method by computing all subformulæ of φ in advance and later on designate them with a single digit, as shown in Table 5 for the formula used as an example throughout the paper.
Solving the resultant Lagrangian problem, it can be shown that the regression problem reduces to the following: Here, the notation 〈.,.〉 denotes the inner product of the vectors.
He stands close to ruin's precipice, this tireless crusader and once-charmed politician reduced to a notation on a federal affidavit: Client 9.
However, we suppress the additional parameter to reduce clutter in our notation.
