Idea solutions

You will find it is possible to scan a large number of possible solutions, ideas, data from the memory, etc., much more rapidly than usual. The "right" solution will often appear along with a sort of intuitive "knowing" that it is the answer sought. You will also find that you can hold in conscious awareness a number of ideas or pieces of data processes simultaneously, to an uncommon extent. 

In addition to enabling you to better scope the innovation opportunity, Nine Windows can be used to generate solution ideas, to determine what resources are available at each level, or to review contradictions inherent in the particular dimensions that could affect the system. 

Use resource optimization when you need to come up with solution ideas that provide higher value than those in existence today—or when you need to refine and optimize a specific solution design. The key is to make sure you list as many resources as possible within and outside your immediate system or sphere of focus. After this, you can use any number of idea-generation techniques to figure out how your available resources can be applied to your inventive problem. 

You can use the Random Stimulus technique to generate solution ideas for a JTBD, or even for an outcome expectation (see Exhibit 21.3 for an example of the latter). 

If you can t find a solution to your problem in an existing knowledge base, you ll need to take a field trip (or several). Here s where someone experienced in biomimicry can point you in the right direction. At the very least, you ll need to identify an organism, ecosystem, or process that has solved a problem similar to yours, and then go where you can study the solution in its natural environment. Remember that solution ideas might be found in non-obvious environments. For example, if you need a way to dry out humid air, you can look in the tropics, or you can go to the desert where cockroaches drink water from the air. 

Evaluate your solution ideas in six different ways. 

Association ISEs Defining Feature Solution Idea... 

In this section, we provide the motivation for our research. First, we pinpoint the high degree of creativity of chemical engineering design and next, we outline the solution ideas behind our approach for its direct experience-based support. 

The PRIME " approach developed at our chair has been used as the integration framework for our process-integrated design support environment [367, 370]. PRIME fulfills the requirements for our design environment through four solution ideas ... 

First, when he came to my seminar in 1997 to discuss this case. Brown explained that he had had several meetings with Smith about the latter s proposed solution idea before the meeting with Veto s staff. At them he had expressed his concern that for fundamental reasons his solution did not appear to be workable. Indeed, Brown stated that prior to their meeting with Veto, he had already presented Smith with several optional approaches to [solving] Veto s problem which did address the unworkable aspects of his initial concepts. What Brown realized at the meeting with Veto was not what he already knew -that Smith s approach was structurally flawed - but that Smith s concept created far more new problems than it attempted to solve. But since Brown had conveyed his concerns to Smith before the meeting with Velo, Brown s ethical responsibility not to undermine his client s reputation and credibility with critical comments on Smith s plan was significantly diluted if not completely dissolved by Smith s public request for validation from the very person who had previously told him in private that his proposed solution idea was structurally flawed. 

The fiigacity has the dimension of pressure. Often we want a nondimensional representation of the fugacity, for example, in mass-action (chemical equilibrium) calculations. We will see in Chapter 12 that this requirement leads naturally to the definition of the activity. Furthermore, when we apply the ideal solution idea to nonideal solutions, we will need a measure of departure from ideality, just as the compressibility factor z is a measure of departure from ideal gas behavior. The logical choice for that measure is the activity coefficient, defined below. We will see that the activity and activity coefficient are dimensionless, and that for ideal solutions and many practical solutions the activity is equal to the mol fraction. 

In this phase, it is necessary to subject possible solution ideas to careful scrutiny. Possible solutions are carefully and critically examined and studied. There are many ways that this can be done. In certain instances, preliminary sketching of a device or casual analysis of a process will show that an idea is not worthy of further consideration. In other cases, a component may need to be examined by laboratory tests. In still other instances, a formal and comprehensive research program may need to be undertaken to examine the validity of a hypothesis or the efficacy of a proposed solution. 

Let u be a vector valued stochastic variable with dimension D x 1 and with covariance matrix Ru of size D x D. The key idea is to linearly transform all observation vectors, u , to new variables, z = W Uy, and then solve the optimization problem (1) where we replace u, by z . We choose the transformation so that the covariance matrix of z is diagonal and (more importantly) none if its eigenvalues are too close to zero. (Loosely speaking, the eigenvalues close to zero are those that are responsible for the large variance of the OLS-solution). In order to liiid the desired transformation, a singular value decomposition of /f is performed yielding... 

A marvellous and rigorous treatment of non-relativistic quantum mechanics. Although best suited for readers with a fair degree of mathematical sophistication and a desire to understand the subject in great depth, the book contains all of the important ideas of the subject and many of the subtle details that are often missing from less advanced treatments. Unusual for a book of its type, highly detailed solutions are given for many illustrative example problems. 

We conclude this section by discussing an expression for the excess chemical potential in temrs of the pair correlation fimction and a parameter X, which couples the interactions of one particle with the rest. The idea of a coupling parameter was mtrodiiced by Onsager [20] and Kirkwood [Hj. The choice of X depends on the system considered. In an electrolyte solution it could be the charge, but in general it is some variable that characterizes the pair potential. The potential energy of the system... 

The principle ideas and main results of tlie theory at the level of the second virial coefficient are presented below. The Mayer/-function for the solute pair potential can be written as the sum of temis ... 

A quite different approach was adopted by Robinson and Stokes [8], who emphasized, as above, that if the solute dissociated into ions, and a total of h molecules of water are required to solvate these ions, then the real concentration of the ions should be corrected to reflect only the bulk solvent. Robinson and Stokes derive, with these ideas, the following expression for the activity coefficient ... 

Onsager s reaction field model in its original fonn offers a description of major aspects of equilibrium solvation effects on reaction rates in solution that includes the basic physical ideas, but the inlierent simplifications seriously limit its practical use for quantitative predictions. It smce has been extended along several lines, some of which are briefly sunnnarized in the next section. 

Cortona embedded a DFT calculation in an orbital-free DFT background for ionic crystals [183], which necessitates evaluation of kinetic energy density fiinctionals (KEDFs). Wesolowski and Warshel [184] had similar ideas to Cortona, except they used a frozen density background to examine a solute in solution and examined the effect of varying the KEDF. Stefanovich and Truong also implemented Cortona s method with a frozen density background and applied it to, for example, water adsorption on NaCl(OOl) [185]. 

An alternative, and closely related, approach is the augmented Hessian method [25]. The basic idea is to interpolate between the steepest descent method far from the minimum, and the Newton-Raphson method close to the minimum. This is done by adding to the Hessian a constant shift matrix which depends on the magnitude of the gradient. Far from the solution the gradient is large and, consequently, so is the shift d. One... 

The percolation argument is based on the idea that with an increasing Cr content an insoluble interlinked cliromium oxide network can fonn which is also protective by embedding the otherwise soluble iron oxide species. As the tlireshold composition for a high stability of the oxide film is strongly influenced by solution chemistry and is different for different dissolution reactions [73], a comprehensive model, however, cannot be based solely on geometrical considerations but has in addition to consider the dissolution chemistry in a concrete way. 

By analogy, ammonium salts should behave as acids in liquid ammonia, since they produce the cation NH4 (the solvo-cation ), and soluble inorganic amides (for example KNHj, ionic) should act as bases. This idea is borne out by experiment ammonium salts in liquid ammonia react with certain metals and hydrogen is given off. The neutralisation of an ionic amide solution by a solution of an ammonium salt in liquid ammonia can be carried out and followed by an indicator or by the change in the potential of an electrode, just like the reaction of sodium hydroxide with hydrochloric acid in water. The only notable difference is that the salt formed in liquid ammonia is usually insoluble and therefore precipitates. 

In a way, the limit set is thus the entire funnel between the two extreme cases qlc, and g o, Fig. 5. This effect is called Takens-chaos, [21, 5, 7]. As a consequence of this theorem each momentum uncertainty effects a kind of disintegration" process at the crossing. Thus, one can reasonably expect to reproduce the true excitation process by using QCMD trajectory bundles for sampling the funnel. To realize this idea, we have to study the full quantum solution and compare it to suitable QCMD trajectory bundles. 

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