Hypothesis forming

On the hypothesis developed by Derjaguin, Landau, Verwey, and Overbeek (DLVO), a colloidal suspension becomes rapidly unstable if the maximum value of random thermal energy of the colloidal particles. This hypothesis forms the basis of the DLVO theory of colloidal stability. With the approximate expression for

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The capture hypothesis forms the basis for the LGS model for ion-neutral reactions and many exothermic reactions appear to proceed at the collision frequency. Despite the appeal and widespread validity of the LGS model, a number of ion-neutral reactions have rates significantly... 

The quantity coming from air is practically invariant and corresponds to a level approaching 130 mg/Nm. Nitrogen present in the fuel is distributed as about 40% in the form of NO and 60% as N2. With 0.3% total nitrogen in the fuel, one would have, according to stoichiometry, 850 mg/Nm of NO in the exhaust vapors. Using the above hypothesis, the quantity of NO produced would be (//-U... 

Contrary to the impression that one might have from a traditional course in introductory calculus, well-behaved functions that cannot be integrated in closed form are not rare mathematical curiosities. Examples are the Gaussian or standard error function and the related function that gives the distribution of molecular or atomic speeds in spherical polar coordinates. The famous blackbody radiation cuiwe, which inspired Planck s quantum hypothesis, is not integrable in closed form over an arbitiar y inteiwal. 

The scientific method is taught starting in elementary school. The first step in the scientific method is to form a hypothesis. A hypothesis is just an educated guess or logical conclusion from known facts. It is then compared against all available data and its details developed. If the hypothesis is found to be consistent with known facts, it is called a theory and usually published. The characteristics most theories have in common are that they explain observed phenomena, predict the results of future experiments, and can be presented in mathematical form. When a theory is found to be always correct for many years, it is eventually referred to as a scientific law. However useful this process is, we often use constructs that do not fit in the scientific method scheme as it is typically described. 

The physical stmcture of mixed-layer minerals is open to question. In the traditional view, the MacEwan crystallite is a combination of 1.0 nm (10 E) non-expandable units (iUite) that forms as an epitaxial growth on 1.7 nm expandable units (smectite) that yield a coherent diffraction pattern (37). This view is challenged by the fundamental particle hypothesis which is based on the existence of fundamental particles of different thickness (160—162). 

Jui y trials represent a form of decision making. In statistics, an analogous procedure for making decisions falls into an area of statistical inference called hypothesis testing. 

Under the null hypothesis, it is assumed that the sample came from a population whose mean [L is equivalent to some base or reference designated by lo. This can take one of three forms ... 

If the null hypothesis is assumed to be true, say, in the case of a two-sided test, form 1, then the distribution of the test statistic t is known. Given a random sample, one can predict how far its sample value of t might be expected to deviate from zero (the midvalue of t) by chance alone. If the sample value oft does, in fact, deviate too far from zero, then this is defined to be sufficient evidence to refute the assumption of the null hypothesis. It is consequently rejected, and the converse or alternative hypothesis is accepted. 

The decision rule for each of the three forms would be to reject the null hypothesis if the sample value oft fell in that area of the t distribution defined by Ot, which is called the critical region. Other wise, the alternative hypothesis would be accepted for lack of contrary evidence. 

Under the null hypothesis, it is assumed that the sample came from a population with a proportion po of items having the specified attribute. For example, in tossing a coin the population could be thought of as having an unbounded number of potential tosses. If it is assumed that the coin is fair, this would dictate po = 1/2 for the proportional number of heads in the population. The null hypothesis can take one of three forms ... 

During the early years of physieal ehemistry, Ostwald did not believe in the existence of atoms... and yet he was somehow ineluded in the wild army of ionists. He was resolute in his scepticism and in the 1890s he sustained an obscure theory of energetics to take the place of the atomic hypothesis. How ions could be formed in a solution containing no atoms was not altogether clear. Finally, in 1905, when Einstein had shown in rigorous detail how the Brownian motion studied by Perrin could be interpreted in terms of the collision of dust motes with moving molecules (Chapter 3, Section 3.1.1), Ostwald relented and publicly embraced the existence of atoms. 

A striking example of the importance of narrowing the focus in research, which is what the concept of the parepisteme really implies, is the episode (retailed in Chapter 3, Section 3.1.1) of Eilhard Mitscherlich s research, in 1818, on the crystal forms of potassium phosphate and potassium arsenate, which led him, quite unexpectedly, to the discovery of isomorphism in crystal species and that, in turn, provided heavyweight evidence in favour of the then disputed atomic hypothesis. As so often happens, the general insight comes from the highly specific observation. 

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