A fundamental fact

The most stable state of the atom would be expected to be the one in which the atom has the lowest energy. Bohr reasoned that since we observe that the nuclear atom does exist then it must be a fundamental fact of nature that an atom can exist in its most stable state indefinitely. Even though this fact could not be rationalized (remember, the earlier laws of physics predicted the atom should collapse) it had to be accepted because it was a result of experiments. 

It is a fundamental fact that in steady state nothing is accumulating acywhere around the catalyst and therefore these rates must be exactly equal. 

In the case of coneentrated solutions of defects, i.e. large departures from stoichiometry, a fundamental fact in encountered AHimer and ASconf are strongly correlated, i.e. 

Itis important to note that the uncertainty in measurement Tm talking about is not due to scientists just not having sensitive enough equipment. No matter how sensitive the equipment, it is a fundamental fact of nature that we cannot get exact information about what small-scale systems are doing and where they are. In other words, nature will always keep us somewhat in the dark about these measurements. This limitation has bothered many scientists for many years. Even Albert Einstein didn t accept it at first. In referring to the probabilistic nature of the atomic world, in a letter to fellow physicist Max Born, Einstein stated, "I, at any rate, am convinced that He [meaning God] does not throw dice." ... 

Marx, it is usually said, believed the uninterrupted progress of the productive forces to be a fundamental fact about history. There is no doubt that he often expressed himself in a way that supports this view, notably in The German Ideology. The acknowledgment of local or... 

It is a fundamental fact of quantum mechanics, that a spin-independent Hamiltonian will have pure spin eigenstates. For approximate wave functions that do not fulfill this criterion, e.g. those obtained with various unrestricted methods, the expectation value of the square of the total spin angular momentum operator, (5 ), has been used as a measure of the degree of spin contamination. is obviously a two-electron operator and the evaluation of its expectation value thus requires knowledge of the two-electron density matrix. 

A fundamental fact that has been found is that oscillation amplitudes are larger in the low-frequency range than those measured at the rotary tone frequency of the HP turbine. 

The concept of microemulsions now holds a central role within the field of surfactant technology. Perhaps the most fundamental fact captured by the term is that, contrary to a popular saying, oil and water can mix. 

The defect question delineates solid behavior from liquid behavior. In liquid deformation, there is no fundamental need for an unusual deformation mechanism to explain the observed shock deformation. There may be superficial, macroscopic similarities between the shock deformation of solids and fluids, but the fundamental deformation questions differ in the two cases. Fluids may, in fact, be subjected to intense transient viscous shear stresses that can cause mechanically induced defects, but first-order behaviors do not require defects to provide a fundamental basis for interpretation of mechanical response data. 

A determination of the dissociation constants of the compounds reveals that 5-azauracil (pi a = 6.73) is practically of the same acidity as 6-azauracil and considerably more acidic than uracil, A fundamental difference between 5-azauracil, on the one hand, and 6-azauracil and uracil, on the other, lies in the low stability of 5-azauracil toward acid and especially to alkaline hydrolysis. This fact appears to be in agreement with the differences in electron densities of these substances computed by the simple MO-LCAO method. ... 

The last of the procedures of preparation of A -alkyl derivatives of dioxotriazines is the cyclization of A-alkylated semicarbazones of a-keto acids. It was employed only in a few cases and it appears that its yields are very low. Despite the fact that even here a fundamental effect of substitution on the yield of cyclization can be expected, as the case is with analogous thiosemicarbazones (e.g., Section II,B,4,b), the method is of no particular preparative value. 

Accelerators are responsible for many fundamental discoveries as well as many practical applications. An example of a fundamental discovery was the observation of the W and Z particles that carry the weak force that is responsible, along with the strong and electromagnetic forces, for the fact that the sun shines. An example of a practical application is the use of accelerator beams to kill cancerous tumors in patients. 

Review of Solutions in General. In the discussion of these various examples we have noticed at extreme dilution the prevalence of the term — In Xb, or alternatively — In yB. The origin of this common factor in many different types of solutions can be shown, as we might suspect, to be of a fundamental nature. For this purpose let us make the familiar comparison between a dilute solution and a gas. Since the nineteenth century it has been recognized that the behavior of any solute in extremely dilute solution is, in some ways, similar to that of a gas at low pressure. Now when a vessel of volume v contains n particles of a perfect gas at a lixed temperature, the value of the entropy depends on the number of particles per unit volume, n/v. In fact, when an additional number of particles is introduced into the vessel, the increment in the entropy, per particle added, is of the form... 

Quantum Mechanics offers the most comprehensive and most successful explanation of many chemical phenomena such as the nature of valency and bonding as well as chemical reactivity. It has also provided a fundamental explanation of the periodic system of the elements which summarizes a vast amount of empirical chemical knowledge. Quantum Mechanics has become increasingly important in the education of chemistry students. The general principles provided by the theory mean that students can now spend less time memorizing chemical facts and more time in actually thinking about chemistry. 

Since non-Newtonian flow is typical for polymer melts, the discussion of a filler s role must explicitly take into account this fundamental fact. Here, spoken above, the total flow curve includes the field of yield stress (the field of creeping flow at x < Y may not be taken into account in the majority of applications). Therefore the total equation for the dependence of efficient viscosity on concentration must take into account the indicated effects. 

The most important characteristic of self information is that it is a discrete random variable that is, it is a real valued function of a symbol in a discrete ensemble. As a result, it has a distribution function, an average, a variance, and in fact moments of all orders. The average value of self information has such a fundamental importance in information theory that it is given a special symbol, H, and the name entropy. Thus... 

We refer to footnotes 6 and 8 for the details of this problem, but mention only one conclusion the fact that Li6nard s argument was purely geometrical enabled him to make a fundamental discovery, the significance of which was fully understood only at a later date. 

From a water treatment technical and marketing viewpoint, there is, in fact, a fundamental distinction between these two groups, as discussed below. 

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