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By Assumption 2, the Jacobian of the dual control system at ((a^, b^)) has negative trace.
A matrix has two negative eigenvalues if it has a negative trace and positive determinant.
Under these conditions, the Jacobian matrix at any fixed point has a negative trace and positive determinant, therefore, the fixed point must be stable.
In this section we apply our sharp interpolation inequalities with the method of [7] for estimates of the negative trace of the discrete operators [16].
For σ > 1, the wrinkles actually have a positive roll-off character for the phase with axial downstream distance, indicating a flame wrinkle with a negative trace velocity, but whose actual propagation velocity is positive.
The original fruitful idea in [7] has been generalized in [6] to give best-known estimates for the Lieb Thirring constants in estimates for the negative trace of Schrödinger operators.
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Only the most negative traces are shown to emphasize the negatively activating component of the linopirdine-sensitive current.
Embroidery was limited to a negative tracing of roses — white on sheer black silk, say — or several lines of script.
The CCA dipstick is scored according to test band reaction intensity as negative, trace-positive (tr), single-positive, double-positive, and triple-positive (Stothard 2006).
The results of urine reagent tests used to measure haematuria are scored as 0 (negative), trace-positive (tr), 1+ (5 to 10 erythrocytes/μL), 2++ (10 to 50 erythrocytes/μL), or 3+++ (50 to 250 erythrocytes/μL).
For proteinuria, results are scored as 0 (negative), trace-positive (tr), 1+ (30 mg protein/dL), 2++ (100 mg protein/dL), or 3+++ (500 mg protein/dL) (Murare 1987).
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