Conditional mean

More correctly, the regression problem involves means instead of averages in (1). Furthermore, when the criterion function is quadratic, the general (usually nonlinear) optimal solution is given by y = [p u ], i.e., the conditional mean of y given the observation u . 

Condition Mean temperature, °C XEPS EPS Polyisocyanurate (PI) Aged Impermeable facing PhenoHc, faced... 

DMS has been observed in the marine atmosphere since the early 1970s, but it was not until the mid-1980s that there was interest in this gas as being a natural source for sulfate CCN. Sulfate aerosols are, in number terms, the dominant source of CCN. The major role clouds play in the climate system leads to possible climatic implications if changes to DMS production occurred. Furthermore, the dependence of this production on environment conditions means that scope for a feedback process arises this feedback is called the Charlson hypothesis. ... 

Reproduction is by binary fission, meaning a cell divides into two new cells, each of which matures and divides again. Fission takes place every 1,530 mill under ideal conditions. Ideal conditions mean that the growth environment has abundant food, oxygen, and essential nutrients. 

When a perturbation is introduced, the stationary condition means that the orbitals must change, which may be described as a mixing of the unperturbed MOs. In other words. 

The ability of a GC column to theoretically separate a multitude of components is normally defined by the capacity of the column. Component boiling point will be an initial property that determines relative component retention. Superimposed on this primary consideration is then the phase selectivity, which allows solutes of similar boiling point or volatility to be differentiated. In GC X GC, capacity is now defined in terms of the separation space available (11). As shown below, this space is an area determined by (a) the time of the modulation period (defined further below), which corresponds to an elution property on the second column, and (b) the elution time on the first column. In the normal experiment, the fast elution on the second column is conducted almost instantaneously, so will be essentially carried out under isothermal conditions, although the oven is temperature programmed. Thus, compounds will have an approximately constant peak width in the first dimension, but their widths in the second dimension will depend on how long they take to elute on the second column (isothermal conditions mean that later-eluting peaks on 2D are broader). In addition, peaks will have a variance (distribution) in each dimension depending on... 

This condition means that for f < 0.63 the disordered arrangement of molecules is thermodynamically unstable and the system is spontaneously reorganized into an ordered liquid crystalline phase of a nematic type (Flory called this state crystalline ). This result has been obtained only as a consequence of limited chain flexibility without taking into account intermolecular interactions. 

In some cases there also occur semistable limit cycles (in this discussion the single term cycle is used wherever it is unambiguous or if no confusion is to be feared) characterized by stability on one side and instability on the other side. Figure 6-5(a), (b), and (c) illustrate these definitions. Physically, only stable cycles are of interest the unstable cycles play the role of separating the zones of attraction of stable cycles in the case when there are several cycles. It is seen from this definition that, instead of an infinity of closed trajectories, we have now only one such trajectory determined by the differential equation itself and the initial conditions do not play any part. In fact, the term initial conditions means just one point (x0,y0) of the phase plane as a spiral trajectory O passes through that point and ultimately winds itself onto the cycle 0, it is clear that the initial conditions have nothing to do with this ultimate closed trajectory C—the stable [Pg.329]

In this expression, E° is the standard emf of the cell, the emf measured when all the species taking part are in their standard states. In practice, this condition means that all gases are at 1 bar, all participating solutes are at 1 molT-1, and all liquids and solids are pure. For example, to measure the standard emf of the Daniell cell, we use 1 M CuS04(aq) and a pure copper electrode in one electrode compartment and 1 M ZnS04(aq) and a pure zinc electrode in the other. 

Throughout this book, an indication such as 0°C 70°C (within parenthesized reaction conditions) means that the reaction was commenced at the first temperature and completed at the second in contrast, an indication such as 20-30°C means that the reaction was conducted somewhere within that range. Terms such as recent literature invariably refer to publications within the period 1975 to 2003. 

Table 12,2. Experimental conditions, mean 5 N values and diet-tissue and tissue-tissue dilTerence values (A N) of rats not subjected to water stress and/or heat stress, Diet 8 N values are those of the protein source rather than the whole diet pellets. SD = standard deviation, co-d = collagen-diet, h-d = hair-dici, f-d = flesh-diet, co-f = collagen-flesh. 

The reader is invited to prove this assertion on his/her own. The summarized approximation condition means that... 

Arctic Conditions. The effectiveness of relevant dispersants for use under arctic conditions has been tested with a dilution test [235,236]. Arctic conditions mean a low temperature of 0° C and water salinities of 0.5% to... 

There are many specific ways to generate equally spaced tags but they are all based on the same principle of manipulating the rf pulses to generate equally spaced bands of rf radiation in the frequency domain. It is well known that under ordinary conditions, meaning normal levels of nuclear spin excitation, the frequency spectrum of the rf excitation pulse(s) is approximately the Fourier transform of the pulses in the time domain. Thus, a single slice can be generated in the... 

When we change a specific operating condition, meaning the set point, we would like, for example, the pH of the bioreactor to follow our command. This is what we call servo control. 

Normal conditions mean that only minor amounts of overtime are involved, that an adequate number of competent tradesmen can be found, and that scheduled delivery times for equipment and supplies will be met. No provisions are made for work stoppages or slowdowns due to labor unrest. 

As the pressure is lowered, slip occurs, and the flow mechanism is referred to as transition flow. At pressures so low that collisions between gas molecules are rare compared to the collisions between the gas and the tube wall, the flow is said to be Knudsen flow or free molecular flow. Free molecular flow prevails when Lla > 1. For air at 25°C, this condition means that we have free molecular flow when aPm on < 5. We now consider an intuitive derivation of the result for Fc in the free molecular flow region. 

Thus, the input message 01101 matches each of the conditions 01101 oi i and but does not match mo. Note that the presence of the identifier tag at the start of a message and the requirement that this must match the corresponding digits in the classifier conditions means that some classifiers will match and, therefore, deal with only messages from a particular probe. 

Based on the same underlying principles as the molecular-based quantum methods, solid-state DFT represents the bulk material using periodic boundary conditions. The imposition of these boundary conditions means that it becomes more efficient to expand the electron density in periodic functions such as plane waves, rather than atom-based functions as in the molecular case. The efficiency of the calculations is further enhanced by the use of pseudo-potentials to represent the core electrons and to make the changes in the electron density... 

Garcia-Fontes and Motta57 study the regulation of freedom of establishment or entry and the prices of these distribution services. They use a variant of Hotelling s model (horizontal differentiation by location throughout a linear city ). The originality here lies in the fact that the consumers have a high but finite reserve price. This condition means that the market may not be covered, and hence the positive effects of perfect competition may not occur. 

Fig. 5.3. Relationship between the oral fraction basolateral Papp values were determined at absorbed in humans and apparent permeability drug concentrations of 10-500 pM at pH 6.5/ coefficients obtained in Caco-2 cell monoalyers 7.4 or 7.4/7.4 on the apical/basolateral sides of at two different pH conditions. Mean apical to the cell monolayers.

Operation in extreme conditions has its own problems and hazards. Extreme conditions mean usually either very low or high temperatures or pressures. 

We say the gas discharges under these conditions, meaning that it can conduct, i.e. an electric current can flow through it. 

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