The Independent

The off-diagonal elements of the variance-covariance matrix represent the covariances between different parameters. From the covariances and variances, correlation coefficients between parameters can be calculated. When the parameters are completely independent, the correlation coefficient is zero. As the parameters become more correlated, the correlation coefficient approaches a value of +1 or -1. 

This type of contract requires the operator to pay a fixed amount to the contractor upon completion of the well, while the contractor furnishes all the material and labour and handles the drilling operations independently. The difficulty with this approach Is to ensure that a quality well Is delivered to the company since the drilling contractor will want to drill as quickly and cheaply as possible. The contractor therefore should guarantee an agreed measurable quality standard for each well. The guarantee should specify remedial actions which will be implemented should a substandard well be delivered. 

The Channel area contains controls which affect each of the channels (detection and coupling) independently. The parameter values displayed refer to the channel currently selected for dis-play-... 

Since translational and internal energy (of rotation and vibration) are independent, the partition function for the gas can be written... 

Since in this case the Flamiltonian is time independent, the general solution can be written as... 

For hard spheres, the coefficients are independent of temperature because the Mayer/-fiinctions, in tenns of which they can be expressed, are temperature independent. The calculation of the leading temiy fy) is simple, but the detennination of the remaining tenns increases in complexify for larger n. Recalling that the Mayer /-fiinction for hard spheres of diameter a is -1 when r < a, and zero otherwise, it follows thaty/r, 7) is zero for r > 2a. For r < 2a, it is just the overlap volume of two spheres of radii 2a and a sunple calculation shows tliat... 

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

The magnitudes of e i =1, )contam the Fresnel factors from equation Bl.5,34. equation B1,5,35 and equation B 1,5.36. which depend on the incident, reflected and polarization angles. Experimentally, one approach is to fix the input polarization and adjust the analyser to obtain a null in the SFl signal [ ]. By choosing distinct configurations such that the corresponding tliree equations from equation B 1.5.40 are linearly independent, the relative values of Xs lim = inferred. This method has... 

Within the approximation that the eleetronie, vibrational, and rotational states of a moleeule ean be treated as independent, the total moleeular wavefunetion of the "initial" state is a produet... 

It has not been found possible to reconcile all these observations with a simple kinetic scheme. A major difficulty is that whilst the stoichiometric concentrations of nitric acid and of acetic acid can be varied independently, the actual concentrations of these species cannot, because of the existence of the equilibrium ... 

The reason for this relative lack of reactivity of 2-methylthiazoIium is probably due to the too-weak nucleophilic character of its carbon-2. For example, any /S-alkoxyalcene (29) derivatives resulting from the condensation of o-ester could never have been isolated, whereas they constitute the essential intermediate step in trimethine syntheses for rings of acidic character (64). However, even if a negative 5-substituent such as ethoxy-carbonyl increases the yield (61) by promoting independently the possible formation of the methylene base, it may be stressed that the presence of this base is not the essential condition of the reaction, since the isolated anhydrobase itself is not reactive toward the o-ester (Scheme 41). 

Two views of a two-factor response surface for which the factors are independent. The optimum response in (b) is indicated by the at (2, 8). Contour lines are shown for intervals of 0.5 response units. 

If the rate of initiation is investigated independently, the rate of polymeri-... 

Truck scales weigh highway vehicles they may be installed in a pit or above-ground with inclined approach ramps. A capacity of 100-t is typical. For monitoring axle weights, the scale deck can be broken into three scales, which are monitored independently the individual axle weights or total vehicle weight can be displayed by the indicator. 

CMC hydrates rapidly and forms clear solutions. Viscosity buUding is the single most important property of CMC. DUute solutions of CMC exhibit stable viscosity because each polymer chain is hydrated, extended, and independent. The sodium carboxylate groups are highly hydrated, and the ceUulose molecule itself is hydrated. The ceUulose molecule is linear, and conversion of it into a polyanion (polycarboxylate) tends to keep it in an extended form by reason of coulombic repulsion. This same coulombic repulsion between the carboxylate anions prevents aggregation of the polymer chains. Solutions of CMC are either pseudoplastic or thixotropic, depending on the type. 

Figure 5 Schematic representation of a Cartesian dynamics protocol starting from random torsion angles. The weights for non bonded (i.e., van der Waals) interactions, unambiguous distance restraints, and ambiguous distance restraints are varied independently. The covalent interactions are maintained with full weight, co.aie - for the entire protocol. Weights for other experimental terms may be varied in an analogous way. Coupling constant restraints and anisotropy restraints are usually used only in a refinement stage.

Normal distribution and that they are statistieally independent. The problem is governed, in faet, by the amount of negative elearanee. This translates into a differenee between the mean of the two random variables, /i, and i, (see Figure 4). The mean of this differenee distribution, /i, is given by ... 

Lubrication skid. The gas turbine lubrication skid is usually independent of the steam turbine skid as the lubrication oil is usually synthetic due to the high temperatures in the gas turbine. Another reason is due to water contamination of the lubrication oil from the steam turbine. It is advisable to have the lubrication system be totally independent. The gas turbine lubrication skid would report to the gas turbine controller. Since the lubrication system is also used for providing cooling, it is usually operated for about 20 minutes after the gas turbine is shutdown. The lubrication skid contains at least three pumps, two pumps in which each can provide the head required and a third pump, which is usually recommended to be a DC drive for emergency use. These pumps and their control fall under the drive level hierarchy. 

In a combination of two immiscible liquids, each exerts its own vapour pressure independently. The total pressure is then the sum of the vapour pressures,... 

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