Formulation of questions

In formulation of questions due thought be given to expected responses. For a precise answer the question too should be precise. 

Style in scientific research is made up of two main elements, one practical, the other theoretical. The practical one concerns the methods used in experiments, the theoretical one concerns the kind of questions asked by the experimenter to which the experiments are to find an answer. It is characteristic of science that both experimental me odology and the formulation of questions change very rapidly, nowadays faster than ever. This implies a danger of becoming obsolete in techniques as well as in ideas. The scientist must be prepared to work very hard, just to remain up to date. He must study and learn continuously. 

An interesting question that arises is what happens when a thick adsorbed film (such as reported at for various liquids on glass [144] and for water on pyrolytic carbon [135]) is layered over with bulk liquid. That is, if the solid is immersed in the liquid adsorbate, is the same distinct and relatively thick interfacial film still present, forming some kind of discontinuity or interface with bulk liquid, or is there now a smooth gradation in properties from the surface to the bulk region This type of question seems not to have been studied, although the answer should be of importance in fluid flow problems and in formulating better models for adsorption phenomena from solution (see Section XI-1). 

At the outset of the work described in this thesis we formulated a number of questions. 

In this chapter we provide an introductory overview of the imphcit solvent models commonly used in biomolecular simulations. A number of questions concerning the formulation and development of imphcit solvent models are addressed. In Section II, we begin by providing a rigorous fonmilation of imphcit solvent from statistical mechanics. In addition, the fundamental concept of the potential of mean force (PMF) is introduced. In Section III, a decomposition of the PMF in terms of nonpolar and electrostatic contributions is elaborated. Owing to its importance in biophysics. Section IV is devoted entirely to classical continuum electrostatics. For the sake of completeness, other computational... 

The entire formulation of a chemical question can involve a number of issues, some of which are often obscure to the user. Questions such as what components can be substituted at a given atom site, what types of bonds are favorable for a given chemical fragment query (single, double, ring, chain, aromatic, etc.), and should the query contain explicit or implicit substitution, are just a few of the issues facing a user. 

Consequently, when selecting and blending the various raw materials used in all-polymer/all-organic formulations, the questions of thermal and hydrolytic stability and ability to transport or otherwise control colloidal iron oxides (in addition to possible adverse effects such as copper corrosion) become increasingly important at higher boiler temperatures and pressures. 

There are two complementary lines of approach to examining the part played by 3d orbitals in molecular orbital theory and to appreciating current doubts as to their role. On the one hand, there is the question of 3d orbitals in relation to the basic formulation of molecular orbitals by overlapping atomic orbitals on the other hand, there is the question of the effect of including or excluding 3d functions in molecular orbital calculations, particularly of the ab initio type. We shall consider each of these briefly in turn. 

For the third step, the formulation of educational guidelines, Kattmann and Gropengielier (1997) mention four main questions to be taken into account ... 

The formulation of the parameter estimation problem is equally important to the actual solution of the problem (i.e., the determination of the unknown parameters). In the formulation of the parameter estimation problem we must answer two questions (a) what type of mathematical model do we have and (b) what type of objective function should we minimize In this chapter we address both these questions. Although the primary focus of this book is the treatment of mathematical models that are nonlinear with respect to the parameters nonlinear regression) consideration to linear models linear regression) will also be given. 

On the other hand, one strength of the approach is the availability of algorithms (such as the slithering snake algorithm) by which undercooled polymer melts can be equilibrated at relatively low temperatures. This allows the static properties of the model to be established over a particularly wide parameter range. Furthermore, the lattice structure allows many questions to be answered in a well-defined, unique way, and conceptional problems of the approach can be identified and eliminated. Last but not least, the lattice structure allows the formulation of very efficient algorithms for many properties. 

In order to appreciate how understanding new statistical concepts can help us, let us look at an example of where we can better apply known statistical concepts, to understand phenomena currently afflicting us. To this end, let us pose the seemingly innocuous question When doing quantitative calibration, why is it that we use the formulation of the problem that makes the constituent values the dependent (i.e., the Y) variable, and make the spectroscopic data the X (or independent) variable, called the Inverse Beer s Law formulation (sometimes called the P-matrix formulation) (For that matter, why is the formulation that we most commonly use called Inverse Beer s Law instead of the direct Beer s Law )... 

About 10 years after the first formulation of DR and 5 years after its theoretical j ustifica-tion by Charney, some contradictory results emerged which make its validity questionable. 

Various questions that lead directly to the formulation of an objective function can be posed concerning reactors. Typical objective functions stated in terms of the adjustable variables are... 

The question as to the best formulation of structures and species in some binary fluoride systems was the subject of extensive experimental investigations, involving infrared and Raman spectroscopy in the molten state and in solutions as well as NMR spectroscopy and conductometric and cryoscopic measurements. Some crystal structure studies have also been published. The systems of SeF4 with BF3, SbF5, AsF5, NbF5, and TaFs have been studied recently. 

From the discussion so far, it is clear that the mapping to a system of noninteracting particles under the action of suitable effective potentials provides an efficient means for the calculation of the density and current density variables of the actual system of interacting electrons. The question that often arises is whether there are effective ways to obtain other properties of the interacting system from the calculation of the noninteracting model system. Examples of such properties are the one-particle reduced density matrix, response functions, etc. An excellent overview of response theory within TDDFT has been provided by Casida [15] and also more recently by van Leeuwen [17]. A recent formulation of density matrix-based TD density functional response theory has been provided by Furche [22]. 

The success and value of the spin-trapping experiment depend upon a number of features, all of which need to be taken into account when designing the experiment, or interpreting the spectroscopic results. These may be formulated as a series of questions. 

In the usual formulation of the extended Hiickel method, the elements of the hamiltonian matrix are computed according to a simple set of arithmetic rules, and do not depend on the molecular orbitals. In this way, there is no need for the iterations required by more sophisticated methods, and in practice the results may be obtained nowadays in a question of seconds for any reasonably sized complex. 

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