Sense belonging

Self-assembled monolayers (SAMs) are molecular layers tliat fonn spontaneously upon adsorjDtion by immersing a substrate into a dilute solution of tire surface-active material in an organic solvent [115]. This is probably tire most comprehensive definition and includes compounds tliat adsorb spontaneously but are neither specifically bonded to tire substrate nor have intennolecular interactions which force tire molecules to organize tliemselves in tire sense tliat a defined orientation is adopted. Some polymers, for example, belong to tliis class. They might be attached to tire substrate via weak van der Waals interactions only. 

All Np states belonging to the Pth sub-space interact strongly with each other in the sense that each pair of consecutive states have at least one point where they form a Landau-Zener type interaction. In other words, all j = I,... At/> — I form at least at one point in configuration space, a conical (parabolical) intersection. 

These permutational symmetries are not only eharaeteristies of the exaet eigenfunetions of H belonging to any atom or moleeule eontaining more than a single eleetron but they are also eonditions whieh must be plaeed on any aeeeptable model or trial wavefunetion (e.g., in a variational sense) whieh one eonstruets. 

Whereas pattern (b) is intuitively the most complex of the three patterns, it has neither the highest entropy (which belongs to pattern (c)) or the lowest (which belongs to pattern (a)). Indeed, were we to plot our intuitive sense of complexity as a function of the amount of order or disorder in a system, it would probably look something like that shown in figure 12.2. The problem is to find an objective measure of the complexity of a system that matches this intuition. 

Two planted trees whose principal branches form the same configuration are certainly congruent in the sense of Sec. 34. Is it possible that different configurations of the principal branches belong to congruent planted trees ... 

One further point needs to be mentioned—the matter of absolute configuration. How do we know that our assignments of R,S configuration are correct in an absolute, rather than a relative, sense Since we can t see the molecules themselves, how do we know that the R configuration belongs to the dextrorotatory enantiomer of lactic acid This difficult question was finally solved in 1951, when J. M. Bijvoet of the University of Utrecht reported an X-ray spectroscopic method for determining the absolute spatial arrangement of atoms in a molecule. Based on his results, we can say with certainty that the R,S conventions are correct. 

It is hardly possible in chemistry to introduce a contrast between elements and simple bodies, as the definition of element since Lavoisier is based on the simple body. It seems to me to be even less apt simply to equate the terms element/atom and simple body/molecule, respectively for apart from the fact that there are simple bodies whose molecules are single atoms, molecules and atoms belong indubitably to one and the same group of scientific concepts, while the essential difference between element and simple body in the Men-deleeffian sense of the words, lies in their belonging to quite different spheres in epistemology ([33], p 57). 

Sensory receptors that structurally and functionally belong to the G protein coupled receptor superfamily. Olfactory receptors are a large GPCR family with >300 members in human that are expressed in neurons of the nasal olfactory epithelium where they sense mostly volatile olfactory molecule. The overall number of olfactory receptors differs widely between species and an expansion of different recqrtors is in particular obvious in species that depend on their olfactory sense for survival. 

If 0.6 N lithium bromide is added to the solution of the polyelectrolyte and also to the solvent on the opposite side of the osmometer membrane, the lowermost set of points in Fig. 145 (lower and left scales) is observed. The anion concentration inside and outside the coil is now so similar that there is little tendency for the bromide ions belonging to the polymer to migrate outside the coil. Hence the osmotic pressure behaves normally in the sense that each poly electrolyte molecule contributes essentially only one osmotic unit. The izjc intercept is lower than that for the parent poly-(vinylpyridine) owing to the increase in molecular weight through addition of a molecule of butyl bromide to each unit. 

The problem is to "translate" the fact that certain terms are absent in the expansion (IV.3) to symmetry properties of the density in the sense of transformation properties under certain operations. We have a density with non vanishing Fourier components only for such wave vectors k which belong to the lattice L ... 

The simultaneous test given by Equations 6 and 7 leads to a test appropriate for (X,t) unknown. The (X,T)-unknown test rejects the null hypothesis that xgj belongs to the background population if tj > c(r) for all (X,t). Since this test rejects the null hypothesis only if Equation 6 is satisfied for the true value of (X,t), this test has no greater probability of false detection than the simultaneous test. Thus, the (X,r)-unknown test is conservative in the sense that the probability of a false detection is less than a if the probability of false detection for the simultaneous test is a. 

A classification of electrodes has already been given in Section 1.3.1. The function of the indicator electrode is to indicate by means of its potential the concentration of an ion or the ratio of the concentrations of two ions belonging to the same redox system. Under non-faradaic conditions, the relationship between the potential and these concentrations is given by the Nemst or the more extended Nernst-Van t Hoff equation, as explained below. As a single potential between an electrode and a solution cannot be measured in the absolute sense but only in a relative manner, a reference electrode is needed its function is merely to possess preferably a constant potential or at any rate a known potential under the prevailing experimental conditions. Often both electrodes cannot be placed in the same solution, so that a second solution... 

In a scientific application, the sets to which an object might belong may describe physical or chemical observables that are in some sense continuously variable, such as "volatile," "acidic," or "green," but not all sets are so tangible, nor does the description of a set itself need to be inherently vague. We could create the sets "True" and "False" and, thus, define degrees of truth. 

---