Number of experiments

Recently a number of experiments have been carried out to clear up the physical nature of the phenomenon [8-11]. A lot of experimental data describing the kinetics of cone s filling with various liquids have been obtained. One of the principal features of the phenomenon is that it takes place only if a gas inside a channel is bounded by liquid surfaces of different curvatures. 

Proposed flux models for porous media invariably contain adjustable parameters whose values must be determined from suitably designed flow or diffusion measurements, and further measurements may be made to test the relative success of different models. This may involve extensive programs of experimentation, and the planning and interpretation of such work forms the topic of Chapter 10, However, there is in addition a relatively small number of experiments of historic importance which establish certain general features of flow and diffusion in porous media. These provide criteria which must be satisfied by any proposed flux model and are therefore of central importance in Che subject. They may be grouped into three classes. 

Giovanni Boocaletti is gratefully acknowledged for the large number of experiments that paved the way to enantioselective Lewis-acid catalysis in water. Furthermore, we kindly thank the Syncom company for the use of the chiral HPLC column. 

Species Number of experiments Rate of gain Eeed/unit gain... 

A considerable number of experiments have shown that symmetrical PMDs in the ground state have an aH-trans configuration and are nearly planar with practically equalized carbon—carbon bonds and slightly alternating valence angles within the polymethine chain (1,3,5,22,23). This is caused by some significant features of the PMD electron stmcture. 

Transport Models. Many mechanistic and mathematical models have been proposed to describe reverse osmosis membranes. Some of these descriptions rely on relatively simple concepts others are far more complex and require sophisticated solution techniques. Models that adequately describe the performance of RO membranes are important to the design of RO processes. Models that predict separation characteristics also minimize the number of experiments that must be performed to describe a particular system. Excellent reviews of membrane transport models and mechanisms are available (9,14,25-29). 

The functional relation ia equation 53 or 54 cannot be determined by dimensional analysis alone it must be suppHed by experiments. The significance is that the mean-free-path problem is reduced from an original relation involving seven variables to an equation involving only three dimensionless products, a considerable saving ia terms of the number of experiments required ia determining the governing equation. 

The number of independent variables is reduced from the original nine to four. This is a great saving in terms of the number of experiments required to determine the desired function. For example, suppose that a decision is made to test only four values for each variable. Then it would require 4 = 262144 experiments to test aU. combinations of these values in the original equation. As a result of equation 59, only 4 = 256 tests are now required for four values each of the four B-numbers. 

The main effects are calculated by calculating the difference between results from all high values of a variable and all low values of a variable the result is divided by the number of experiments at each level. For example, for the first variable ... 

The data in the table were obtained by averaging across the number of experiments shown. 

In frequentist statistics, probability is instead a long-run relative occurrence of some event out of an infinite number of repeated trials, where the event is a possible outcome of the trial. A hypothesis or parameter that expresses a state of nature cannot have a probability in frequentist statistics, because after an infinite number of experiments there can be no uncertainty in the parameter left. A hypothesis or parameter value is either... 

FPEtool is described in Deal (1995). No formal benchmarking has been performed, nor has any source code validation or validation against experimental data but the code is based on a number of experiments Notarianni (1993), Walton (1993), Nelson (1992), Peacock (1993b), Heskestad (1986) and Hinkley (1975). 

Similar compounds to those described above have been prepared by the same group using the bis-cesium salts of pyridine-3,5-dicarboxylic acids. In a number of experiments Piepers and Kellogg showed that Cs plays an irreplacable role as compared with Na", K and Rb for the formation of [the macrocycle shown below] . 

Chen et al. [76C02] and Lawrence and Davison [77L01] have placed the fully coupled nonlinear theory of uniaxial piezoelectric response in a form that is convenient for numerical solution of problems and have simulated a number of experiments in terms of this theory. An example of the results obtained is given below. 

The number of experiments that can be done satisfactorily in a one-semester course varies widely with the physical situation and the individual skills of the student. Therefore, no attempt is made to suggest a schedule. I recommend, however, that a common core of about five experiments be assigned. The remainder of the preparations can then be chosen by individual students as dictated by their interests as well as by the availability of chemicals and special equipment. The common experiments, representing frequently used and important techniques, might be chosen from Chapter 1, Sections I and IV Chapter 2, Section I Chapter 3, Section I Chapter 4, Section I Chapter 5, Section I Chapter 6, Sections III and IV Chapter 7, Sections II and VI Chapter 8, Section II Chapter 9, Sections I and II Chapter 11, Sections I and III or Chapter 13, Section II, Since many of the other experiments draw on the products of this suggested list, the possibility of multistep syntheses also presents itself, and several such sequences are outlined in Appendix 1. Also included, in Appendix 2, are the commercial suppliers of the chemicals required when these chemicals are not routinely available. 

A large number of experiments [22,68-71] have shown that the specific volume, vi, and specific entropy, Sh, of the high-pressure hexagonal phase of PE are closer to the corresponding values v , and s , of the melt than they are to those of the orthorhombic phase, and s. For instance, at 500 MPa, the ratio of entropies of the orthorhombic-hexagonal and hexagonal-melt transi-... 

Now we are going to review the types of evidence that form the basis for belief in the atomic theory. We shall include a number of experiments that are close, in concept, to the direct vision type. These are particularly convincing and they provide detailed information that is less readily obtained in other ways. 

Direct measurements of equilibrium stress-strain isotherms of SAH are complicated by the gel softness. Nevertheless, a number of experiments on compression and tension of the gels has been reported (see, for example, Refs. [18, 21, 42]). The method of dynamic light scattering is free from such inconveniences... 

No. Polymers Blowing agent concentration, % mass Number of experiments on various channels and various volum. flow rates Pcr (bar) in accordance with Eq. (5) APexp (mean) bar APcalcd Eq (15), bar AP AP 0/ calc exp tnri... 

Charles and Gay-Lussac carried out a number of experiments with the hope of improving the performance of their balloons. They found that, provided the pressure is kept constant, the volume of a gas increases as its temperature is raised. In this case, a straight-line graph is obtained when the volume is plotted against the temperature (Fig. 4.10). This result implies... 

There are a number of experiments directed at studying the incipience of nucleate boiling in heated channels of hydraulic diameter db = 0.04-20 mm. The overall... 

A number of experiments performed since the late 1970s [11-13, 301 found a variety of smectic phases with a broken head-to-tail symmetry among mesogens possessing strongly polar cyano or nitro terminal groups (Fig. 6). 

What strategy should one follow In the classical experiment, one factor is varied at a time, usually over several levels, and a functional relationship between experimental response and factor level is established. The data analysis is carried out after the experiment(s). If several factors are at work, this approach is successful only if they are more or less independent, that is, do not strongly interact. The number of experiments can be sharply increased as in the brute-force approach, but this might be prohibitively expensive if a single production-scale experiment costs five- or six-digit dollar sums. Figure 3.4 explains the problem for the two-factor case. 

Because of the relatively small number of experiments done on commercial-scale equipment before submission, and the often very narrow factor ranges (Hi/Lo might differ by only 5-10%), if conditions are not truly under control, high-level models (multi-variate regressions, principal components analysis, etc.) will pick up spurious signals due to noise and unrecognized drift. For example, Fig. 4.43 summarizes the yields achieved for... 

As yet, a number of experiments have failed to convert ureas 205 such as N-phenylurea or imidazolin-2-one by silylation amination with excess amines R3NHR4 such as benzylamine or morpholine and excess HMDS 2 as well as equivalent amounts of NH4X (for X=C1, I) via the silylated intermediates 206 and 207 in one reaction step at 110-150°C into their corresponding guanidines 208 with formation of NH3 and HMDSO 7 [35] (Scheme 4.13). This failure is possibly due to the steric repulsion of the two neighbouring bulky trimethylsilyl groups in the assumed activated intermediate 207, which prevents the formation of 207 in the equilibrium with 206. Thus the two step Rathke-method, which demands the prior S-alkylation of 2-thioureas followed by amination with liberation of alkyl-mercaptans, will remain one of the standard syntheses of guanidines [21, 35a,b,c]. 

Exchange correlation spectroscopy (E. COSY), a modified form of COSY, is useful for measuring coupling constants. The pulse sequence of the E. COSY experiment has a mixing pulse )3 of variable angle. A number of experiments with different values of /3 are recorded that eliminate the multiplet components of unconnected transitions and leave only the multiplet components for connected transitions. This simplified 2D plot can then be used to measure coupling constants. 

A number of experiments and flnite-element simulations were done to confirm even flow distribution, uniform pressure drop and isobaric properties and also to analyse quantitatively mass and thermal transfer for the wide packed-bed reactor [78]. 

GP 11] [R 5] A judgement on mass-transfer limitations on the reaction rate according to the Mears criterion was made [121], This inequality predicts no such limitations in the boundary layer when the Mears criterion is smaller than 0.15. Using process parameter data applied in a number of experiments, the highest... 

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