27 values, signs

Q Qi lR) when they have different signs. These two expressions can be combined into one by removing the absolute value signs ... 

Removing the absolute value signs from Equation (6.26), we obtain... 

We dropped the absolute-value signs because all quantities involved are real.) Breaking (4.57) up into three sums, we have... 

Note that shear rate y is the magnitude of the tensor y, and therefore it must always be positive. Thus we maintain the absolute-value sign over the term that reflects the shear dependence of the viscosity. 

Absolute-value signs are used with the heat quantities to make the equations independent of the sign convention for Q. We note that for ij to be unity (100 percent thermal efficiency) < c must be zero. No engine has ever been built for which this is true some heat is always rejected to the cold reservoir. This result of engineering experience is the basis for statements 1 and la of the second law. 

If the heat quantities refer to the engine (rather than to the heat reservoirs), the numerical value of Qh is positive and that of Qc is negative. The equivalent equation written without absolute-value signs is therefore... 

The absolute value sign is used, because the spectrum is symmetric and provides no information on whether vA or vB is larger. Note in Eq. 6.36 and Fig. 6.3 that vA — is equal to the geometric average of the spacing of the outer and... 

The absolute value sign about r, ensures that the conductivities are always positive and additive regardless of the sign of the carrier. 

Notice the absolute value signs. It is very important to keep in mind that a square root radical always denotes the positive square root, and to assure the sign is always kept positive. ThusV = x. Failure to observe this is a common cause of errors in integration. 

Now, however, in the range of values chosen for 6, cos0 is always positive. Thus we may remove the absolute value signs from cos 6 in the denominator. (This is one of the reasons that the principal values of the inverse trigonometric functions are defined as they are.) Then the cos0 terms cancel, and the integral becomes... 

Since any permutation may be broken down into a sequence of transpositions the key question is the value (sign) of a (say) in... 

Absolute value sign in the constraint can be handled by replacing it by two constraints. For example, a nonlinear constraint of the type... 

The frontiers are typically 30% and 70% water, with emulsions containing low-viscosity fluids, though they could be quite different in other cases. The formulation effect is rendered through the SAD value sign, i.e (+) for above ofMimum situation and (-) for the opposite case. 

One tensor component, the other two in the 2.015- 2.035 region. °) One tensor component, the other two not resolved. ) Isotropic value. ) Signs obtained from assymetric line widths effects. One tensor component, the other two in the 4 -8 mT region. Temperature dependence investigated. ... 

The value analysis enabled to classify rigorously reactions with participation of TH and intermediates of its transformation both the antioxidant and pro-oxidant temper depending on the value sign. 

Simplification and adding absolute value signs to obtain a geometrically meaningful angle between 0 and 90 degrees then leads to... 

Dropping the absolute value signs gives the signed distance ... 

These equations hold for small introduce absolute value signs [p — pd, ie, in the vicinity of GP. Materials near GP are often called nearly critical gels. The exponents depend not only on the dynamic critical exponent (relaxation exponent Wc) but also on the dynamic exponents s and z for the viscosity (Pc — p) and the equilibrium modulus Ge (p - PcY- If one, in addition, assumes symmetry of the diverging Xmax near the gel point... 

The absolute value sign is required to ensure the positivity of t). Equation 3.35 is equivalent to Equation 2.38. Equation 3.7 then becomes... 

Notice the absolute value signs. It is very important to keep in mind that a square root radical always... 

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