The problem with

A further aspect of the p-value that causes some problems of interpretation is the cut-off for significance at 0.05. This issue was briefly raised in Section 3.3.5 where it was pointed out that 0.05 is a completely arbitrary cut-off for statistical significance and that p-values close to 0.05, but sitting on either side of 0.05 should not really lead to different conclusions. 

Too often a p-value less than 0.05 is seen as definitive proof that the treatments are different while a p-value above 0.05 is seen as no proof at all. The p-value is a measure of the compatibility of the data with equal treatments, the smaller the p-value the stronger the evidence against the null hypothesis. The p-value is a measure of evidence in relation to the null hypothesis treating p 0.05, p 0.05 in a binary way as proof/no proof is a gross over-simplification and we must never lose sight of that. 

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The problem with using a pressure change is that the smaller the change in azeotropic composition, the larger is the recycle in Figs. 3.86 and 3.96. If the azeotrope is not sensitive to changes in pressure, then an extraneous material can be added to the distilla-... 

The problem with this approach is obvious. It involves a considerable amount of work to generate a measure of the quality of the sequence, the total vapor load, which is only a guideline. There are many other factors to be considered. Indeed, as we shall see later, when variables such as reactor conversion are optimized, the sequence might well need readdressing. 

Most constraints can be evaluated by scoping the problem with different boundaries, as illustrated in Example 6.2. If this approach cannot be applied, then mathematical programming must be used to obtain the energy target. ... 

The problem with Eq. (7.5) is that the overall heat transfer coefficient is not constant throughout the process. Is there some way to extend this model to deal with the individual heat transfer coefficients ... 

The problem with relying on end-of-pipe treatment is that once waste has been created, it cannot be destroyed. The waste can be... 

The problem with the fiowsheet shown in Fig. 10.5 is that the ferric chloride catalyst is carried from the reactor with the product. This is separated by washing. If a reactor design can be found that prevents the ferric chloride leaving the reactor, the effluent problems created by the washing and neutralization are avoided. Because the ferric chloride is nonvolatile, one way to do this would be to allow the heat of reaction to raise the reaction mixture to the boiling point and remove the product as a vapor, leaving the ferric chloride in the reactor. Unfortunately, if the reaction mixture is allowed to boil, there are two problems ... 

The problem with this approach is that if the steam generated in the boilers is at a very high pressure and/or the ratio of power to fuel costs is high, then the value of low-pressure steam can be extremely low or even negative. This is not sensible and discourages efficient use of low-pressure steam, since it leads to low-pressure steam with a value considerably less than its fuel value. 

In this paper we propose a multivariable regression approach for estimating ultrasound attenuation in composite materials by means of pulse-echo measurements, thus overcoming the problems with limited access that is the main drawback of through-transmission testing. 

The problem with figure A2.5.6 and figure A2.5.7 is that, because it extends to infinity, volume is not a convenient variable for a graph. A more usefiil variable is the molar density p = 1 / V or the reduced density p. = 1 / Fj. which have finite ranges, and the familiar van der Waals equation can be transfonned into an alternative although relatively unfamiliar fonn by choosing as independent variables the chemical potential p and the density p. 

Time-resolved fluorescence is perhaps the most direct experunent in the ultrafast spectroscopist s palette. Because only one laser pulse interacts with the sample, the mediod is essentially free of the problems with field-matter time orderings that arise in all of the subsequently discussed multipulse methods. The signal... 

In (10), both 5i and 52 appear as independent constants. If, in addition, the dynamical system possesses some symmetry, then these numbers may satisfy a further relation. To illustrate this fact, let us consider the simplest case where we have a symmetry transformation k in the problem with k = id. Then one can show (see again [6]) ... 

The problem with most quantum mechanical methods is that they scale badly. This means that, for instance, a calculation for twice as large a molecule does not require twice as much computer time and resources (this would be linear scaling), but rather 2" times as much, where n varies between about 3 for DFT calculations to 4 for Hartree-Fock and very large numbers for ab-initio techniques with explicit treatment of electron correlation. Thus, the size of the molecules that we can treat with conventional methods is limited. Linear scaling methods have been developed for ab-initio, DFT and semi-empirical methods, but only the latter are currently able to treat complete enzymes. There are two different approaches available. 

The problem with removing large amounts of formic acid by distillation is that it takes a long time to do so. Really big batches can take an entire day to distill. So a second option [10] after removal of the acetone would be to cool the formic acid solution then extract the whole thing with ether. The black ether layer is then washed with an ice cold 5% sodium carbonate (Na2C03) solution to neutralize any formic acid that was carried over, then washed... 

Nitroethane and 1-(3,4 methylenedioxy) 2- nitropropane This method of producing the above mentioned nitro compounds is by far the best Ritter has come across yet The problem with standard nitroethane synthesis is that the -NO2 source most commonly used is silver nitrite (a la Merck Index citing). Needless to say, this is going to be an expensive compound to make as it is not available commercially but must be synthesized from costly silver nitrate. The other methods mentioned in Vogels 5th masterpiece... 

One of the problems with all the current phenol conversions is that a certain amount of other phenols, such as resorcinol and hydro-quinone, will be formed along with the catechol (don t ask). These species are very hard to separate from the catechol because they are all so similar. Aside of carefully monitored fractional distillation there are some vague strategies which can be found in the Chemical Abstract references 116-118. 

The problem with a simple extraction is that the separation only occurs in one direction. In a liquid-liquid extraction, for example, we extract a solute from its initial phase into the extracting phase. Consider, again, the separation of an analyte and a matrix interferent with distribution ratios of 5 and 0.5, respectively. A single liquid-liquid extraction transfers 83% of the analyte and 33% of the interferent to the extracting phase (Figure 12.1). If the concentrations of A and I in the sample were identical, then their concentration ratio in the extracting phase after one extraction is... 

This is entirely analogous to the problem with simple chemical ionization, and the solution to it is similar. To give the quasi-molecular ions the extra energy needed for them to fragment, they can be passed through a collision gas and the resulting spectra analyzed for metastable ions or by MS/MS methods (see Chapters 20 through 23). 

A detailed examination of the correlation between Vj and M is discussed in references on analytical chemistry such as Ref. 6. We shall only outline the problem, with particular emphasis on those aspects which overlap other topics in this book. To consider the origin of the calibration curve, we begin by picturing a narrow band of polymer solution being introduced at the top of a solvent-filled column. The volume of this solvent can be subdivided into two categories the stagnant solvent in the pores (subscript i for internal) and the interstitial liquid in the voids (subscript v) between the packing particles ... 

The problem with all the mirror approaches is that none has achieved the degree of confinement quaUty that the closed systems have. Closed systems ate characterized by magnetic field lines that close on themselves so that charged particles following the field lines remain confined within the system. 

One of the problems with early hydride systems was decrepitation of the alloy. Each time the metal hydride storage tank was recharged the particles would break down and eventually the particles became so small that they began to pass through the 5-p.m sintered metal filter which kept the hydride inside the tank. Addition of 0.5% manganese, which caused the decrepitation process to cease once the particles reached a size of about 10 p.m, solved this problem. 

Divalent europium-activated BaECl was the first rare-earth-activated x-ray phosphor (24). The advantage of BaECLEu " over the conventional CaWO material is in the higher x-ray absorption and better x-ray-to-visible light conversion. The problem with BaECl for x-ray appHcation is in the lower density (4.56 g/cm vs 6 g/cm for CaWO and plate-like morphology. 

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