The When Problem

When viewing effluent treatment methods, it is clear that the basic problem of disposing of waste material safety is, in many cases, not so much solved but moved from one place to another. The fundamental problem is that once waste has been created, it cannot be destroyed. The waste can be concentrated or diluted, its physical or chemical form can be changed, but it cannot be destroyed. 

Fluid samples may be collected downhole at near-reservoir conditions, or at surface. Subsurface samples are more expensive to collect, since they require downhole sampling tools, but are more likely to capture a representative sample, since they are targeted at collecting a single phase fluid. A surface sample is inevitably a two phase sample which requires recombining to recreate the reservoir fluid. Both sampling techniques face the same problem of trying to capture a representative sample (i.e. the correct proportion of gas to oil) when the pressure falls below the bubble point. 

Case-Based Reasoning. Case-Based Reasoning (CBR) systems base their solutions on previously solved problems (cases) which are stored in a case-base [Watson Marir, 1994]. When a new problem is presented to a CBR system a similar case(s) is/are retrieved from the case-base. Depending on the differences between the retrieved and the presented problem the retrieved solution may have to be more or less adapted to obtain a solution to the new problem. The solved problem may be retained in the case base if deemed useful. 

This paper presents solutions of two different NDT problems which could not be solved using standard ultrasonic systems and methods. The first problem eoncems the eraek detection in the root of turbine blades in a specified critical zone. The second problem concerns an ultrasonie thiekness measurement for a case when the sound velocity varies along the object surface, thus not allowing to take a predetermined eonstant velocity into account. 

More correctly, the regression problem involves means instead of averages in (1). Furthermore, when the criterion function is quadratic, the general (usually nonlinear) optimal solution is given by y = [p u ], i.e., the conditional mean of y given the observation u . 

A large percentage of eddy-current inspections are conducted in the field, away from the home base and often in remote or inaccessible locations. Using local telephone lines or mobile phone lines would allow the inspector to beam his data back to the office. In this way highly qualified personnel can be consulted when problems or difficult to interpret results occur. Inspectors no longer need to feel isolated on site. 

Moreover, well away from the critical point, the range of correlations is much smaller, and when this range is of the order of the range of the intenuolecular forces, analytic treatments should be appropriate, and the exponents should be classical . The need to reconcile the nonanalytic region with tlie classical region has led to attempts to solve the crossover problem, to be discussed in section A2.5.7.2. 

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

Another option is a q,p) = p and b q,p) = VU q). This guarantees that we are discretizing a pure index-2 DAE for which A is well-defined. But for this choice we observed severe difficulties with Newton s method, where a step-size smaller even than what is required by explicit methods is needed to obtain convergence. In fact, it can be shown that when the linear harmonic oscillator is cast into such a projected DAE, the linearized problem can easily become unstable for k > . Another way is to check the conditions of the Newton-Kantorovich Theorem, which guarantees convergence of the Newton method. These conditions are also found to be satisfied only for a very small step size k, if is small. 

Figure 2 40. To illustrate the isomorphism problem, phenylalanine is simplified to a core without representing the substituents. Then every core atom is numbered arbitrarily (first line). On this basis, the substituents of the molecule can be permuted without changing the constitution (second line). Each permutation can be represented through a permutation group (third line). Thus the first line of the mapping characterizes the numbering of the atoms before changing the numbering, and the second line characterizes the numbering afterwards. In the initial structure (/) the two lines are identical. Then, for example, the substituent number 6 takes the place of substituent number 4 in the second permutation (P2), when compared with the reference molecule.

There was a time when one could use only a few molecular descriptors, which were simple topological indices. The 1990s brought myriads of new descriptors [11]. Now it is difficult even to have an idea of how many molecular desaiptors are at one s disposal. Therefore, the crucial problem is the choice of the optimal subset among those available. 

In section 11.3 vie showed that the difficult problem of solving the flux relations can be circumvented rather simply when the stoichiometric relations are satisfied by the flux vectors, but the treatment given there was limited to the case of a single Independent chemical reaction, when the stoichiometric relations permit all the flux vectors to be expressed in terms of any one of them. The question then arises whether any comparable simplification is possible v en the reactants participate in more than one independent reaction. 

The eigenvalue problem defined by equations (12.56) and (12.37) has been studied by Lee and Luss l79j and, more recently, in considerable detail by Villadsen and Michelsen When - I it is easy to show... 

An undesirable side-effect of an expansion that includes just a quadratic and a cubic term (as is employed in MM2) is that, far from the reference value, the cubic fimction passes through a maximum. This can lead to a catastrophic lengthening of bonds (Figure 4.6). One way to nci iimmodate this problem is to use the cubic contribution only when the structure is ,utficiently close to its equilibrium geometry and is well inside the true potential well. MM3 also includes a quartic term this eliminates the inversion problem and leads to an t". . 11 better description of the Morse curve. 

There are two problems to consider when calculating 3D pharmacophores. First, unless the molecules are all completely rigid, one must take account of their conformational properties The second problem is to determine which combinations of pharmacophoric groups are common to the molecules and can be positioned in a similar orientation in space. More than one pharmacophore may be possible indeed, some algorithms can generate hundreds of possible pharmacophores, which must then be evaluated to determine which best fits the data. It is important to realise that all of these approaches to finding 3D pharmacophores assume that all of the molecules bind in a common manner to the macromolecule. 

How many iterations does it take to achieve self-consistency for the helium problem treated (partially) in Exercises 8-3 and 8-4 What is the % discrepancy between the calculated value of the first ionization potential and the experimental value of 0.904 hartiees when the solution has been brought to self-consistency ... 

In any case, I eventually recovered (and so did Jerry), but my immune system must have suffered serious damage, which manifested itself three years later, when I collapsed in my office one day and was found to be bleeding internally from a form of rare stomach cancer, which necessitated major surgery but was fortunately localized. I again recovered and have had no further difficulties since. Whether weakening and knocking out my immune system to overcome the previous problems had any effect is not clear, but it could have been a factor. Despite my health problems I was able to continue my work without much interruption, and the scientific productivity of my group has not... 

When using computational chemistry to answer a chemical question, the obvious problem is that the researcher needs to know how to use the software. The difficulty sometimes overlooked is that one must estimate how accurate the answer will be in advance. The sections below provide a checklist to follow. 

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