Facts, simplified

Each stream has a constant specific heat. Isothermal phase transitions (corresponding to an effective specific heat of infinity) satisfy this requirement and, in fact, simplify the solution. 

In Section II we have seen that although the nucleus in a molecule has an NMR spectrum that is a reflection of the entire molecular framework and the anistropy of this framework about the resonating nucleus, in the liquid state the resonance frequencies are simply a reflection of isotropic shielding and scalar coupling. This fact simplifies the observed spectra of liquids relative to those of solids. In addition, NMR has the capability of yielding both a quantitative and a qualitative analysis simultaneously. The reason for this remarkable fact is that it is... 

If we can get by with using only the zero-order tenn of (B 1.1.7 ). we can take out of the integral and use the fact that ( ) q is nonnalized. The last equation then simplifies fiirther to... 

The only tenn in this expression that we have not already seen is a, the vibration-rotation coupling constant. It accounts for the fact that as the molecule vibrates, its bond length changes which in turn changes the moment of inertia. Equation B1.2.2 can be simplified by combming the vibration-rotation constant with the rotational constant, yielding a vibrational-level-dependent rotational constant. 

If there is only significant overlap with one excited vibrational state, equation (Bl.2.11) simplifies fiirther. In fact, if the mitial vibrational state is v. = 0, which is usually the case, and there is not significant distortion of the molecule in the excited electronic state, which may or may not hold true, then tire intensity is given by... 

The principal idea behind the CSP approach is to use input from Classical Molecular Dynamics simulations, carried out for the process of interest as a first preliminary step, in order to simplify a quantum mechanical calculation, implemented in a subsequent, second step. This takes advantage of the fact that classical dynamics offers a reasonable description of many properties of molecular systems, in particular of average quantities. More specifically, the method uses classical MD simulations in order to determine effective... 

The course instructors or professors have not tried to intentionally deceive their students. Most individuals cannot grasp the full depth and detail of any chemical concept the first time that it is presented to them. It has been found that most people learn complex subjects best when first given a basic description of the concepts and then left to develop a more detailed understanding over time. Despite the best elforts of educators, a few misconceptions are at times possibly introduced in the attempt to simplify complex material for freshmen students. The part of this process that perpetuates any confusion is the fact that texts and instructors alike often do not acknowledge the simplifications being presented. 

Another troublesome aspect of the reactivity ratios is the fact that they must be determined and reported as a pair. It would clearly simplify things if it were possible to specify one or two general parameters for each monomer which would correctly represent its contribution to all reactivity ratios. Combined with the analogous parameters for its comonomer, the values rj and t2 could then be evaluated. This situation parallels the standard potential of electrochemical cells which we are able to describe as the sum of potential contributions from each of the electrodes that comprise the cell. With x possible electrodes, there are x(x - l)/2 possible electrode combinations. If x = 50, there are 1225 possible cells, but these can be described by only 50 electrode potentials. A dramatic data reduction is accomplished by this device. Precisely the same proliferation of combinations exists for monomer combinations. It would simplify things if a method were available for data reduction such as that used in electrochemistry. 

There are three advantages to study molecular recognition on surfaces and interfaces (monolayers, films, membranes or soHds) (175) (/) rigid receptor sites can be designed (2) the synthetic chemistry may be simplified (J) the surface can be attached to transducers which makes analysis easier and may transform the molecular recognition interface to a chemical sensor. And, which is also a typical fact, this kind of molecular recognition involves outside directed interaction sites, ie, exo-receptor function (9) (see Fig. 5b). 

This is a generalized formula to simplify the equation. In fact, the actual switching current will be much less than this, due to circuit impedance. For more accurate... 

For a simplified case, one can obtain the rate of CL emission, =ft GI /e, where /is a function containing correction parameters of the CL detection system and that takes into account the fact that not all photons generated in the material are emitted due to optical absorption and internal reflection losses q is the radiative recombination efficiency (or internal quantum efficiency) /(, is the electron-beam current and is the electronic charge. This equation indicates that the rate of CL emission is proportional to q, and from the definition of the latter we conclude that in the observed CL intensity one cannot distii pish between radiative and nonradiative processes in a quantitative manner. One should also note that q depends on various factors, such as temperature, the presence of defects, and the... 

---