Different ways

The hierarchical nature of process design has been represented in different ways by different authors. A hierarchy of decisions and a process design ladder also have been suggested. 

Equipment items will be maintained in different ways, depending upon their... 

In the above example, the discount rate used was the annual compound interest rate offered by the bank. In business investment opportunities the appropriate discount rate is the cost of capital to the company. This may be calculated in different ways, but should always reflect how much it costs the oil company to borrow the money which it uses to invest in its projects. This may be a weighted average of the cost of the share capital and loan capital of a company. 

Decommissioning may be achieved in different ways, depending on the facilities type and the location. This section will also briefly look at the ways in which decommissioning can be deferred by extending the field life, and then at the main methods of well abandonment and facilities decommissioning. 

IP s have different parameters than x-ray films and so must be used in different ways. The system scanner-IP in the case at hand has a different characteristic curve. To make comparisons, one must have a conversion of the obtained grey scale values into the intensity values supplied by the film-light box system. 

We should also note that most of todays data acquisition systems are capable of producing enormous amounts of data which the traditional approach does not exploit for anything but verification of different ways to extract and combine features. To search in the. space of all such combinations is however a tremendous task. 

We have alluded to the comrection between the molecular PES and the spectroscopic Hamiltonian. These are two very different representations of the molecular Hamiltonian, yet both are supposed to describe the same molecular dynamics. Furthemrore, the PES often is obtained via ab initio quairtum mechanical calculations while the spectroscopic Hamiltonian is most often obtained by an empirical fit to an experimental spectrum. Is there a direct link between these two seemingly very different ways of apprehending the molecular Hamiltonian and dynamics And if so, how consistent are these two distinct ways of viewing the molecule ... 

We define the effect of a synnnetry operation on a wavefiinction in two different ways depending on whether the synnnetry operation concerned uses a moving or fixed reference frame (see [4]). Either we define its effect iismg the equation... 

The total of tliree interactions of the material with the field can be distributed in several different ways between the ket and the bra (or more generally, between left and right interactions of the field with the density operator). For example, the first temi in equation (Al.6.101) corresponds to all tliree interactions being with the ket, while the second temi corresponds to two interactions with the ket and one with the bra. The second temi can be fiirther subdivided into tliree possibilities that die single interaction with the bra is before, between or after the two interactions with the ket (or correspondingly, left/right interactions of the field with... 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

LB films of porjDhyrin and phtlialocyanine derivatives ean be made in different ways. 

In a mechanistic study, the aim is not to quantitatively reproduce an experiment. As a result it is not necessary to use the methods outlined above. The question here is what drives a reaction in a particular direction, or what would happen if the molecule is driven in different ways. The initial conditions are then at the disposal of the investigator to be chosen in a way to answer the relevant question, using a suitable spread of positions and energies. 

We illustrate the method for the relatively complex photochemistry of 1,4-cyclohexadiene (CHDN), a molecule that has been extensively studied [60-64]. There are four it electrons in this system. They may be paired in three different ways, leading to the anchors shown in Figure 17. The loop is phase inverting (type i ), as every reaction is phase inverting), and therefore contains a conical intersection Since the products are highly strained, the energy of this conical intersection is expected to be high. Indeed, neither of the two expected products was observed experimentally so far. 

In the context of this paper, the most important conservation property of QCMD is related to its canonical Hamiltonian structure which implies the symplecticncs.s of the solution operator [1]. There are different ways to... 

All three tasks are generally too complicated to be solved from first principles. They are, therefore, tackled by making use of prior information, and of information that has been condensed into knowledge. The amount of information that has to be processed is often quite large. At present, more than 41 million different compounds are known all have a series of properties, physical, chemical, or biological all can be made in many different ways, by a wide range of reactions all can be characterized by a host of spectra. This immense amount of information can be processed only by electronic means, by the power of the computer. 

Before discussing the different ways of representing a chemical compound, some terms have to be defined concerning the reproducibility or transformation of structures and notations. 

The matrix of a structure with n atoms consists of an array of n / u entries. A molecule with its different atoms and bond types can be represented in matrix form in different ways depending on wbat kind of entries are chosen for the atoms and bonds. Thus, a variety of matrices has been proposed adjacency, distance, incidence, bond, and bond-electron matrices. 

Almost all chemical information systems work with tlicir own special type of connection table. They often use various formats distinguishing between internal and external connection tables. In most cases, the internal connection tables arc redundant, thus allowing maximum flexibility and increasing the speed of data processing. The external connection tables are usually non-redundant in order to save disk space. Although a connection table can be cprcsented in many different ways, the core remains the same the list of atoms and the list of bonds. Thus, the conversion of one connection table format into another is usually a fairly straightforward task. 

Stereoisomerism at double bonds is indicated in SMILES by / and . The characters specify the relative direction of the connected atoms at a double bond and act as a frame. The characters frame the atoms of a double bond in a parallel or an opposite direction. It is therefore only reasonable to use them on both sides Figure 2-78). There are other valid representations of cis/trans isomers, because the characters can be written in different ways. Further details are listed in Section 2,3.3, in the Handbook or in Ref, [22]. 

Thus, if the user wants to look for literature including requested chemicals or reactions, it is possible to query the database by the first option Chemical Substance or Reaction , The compound can be entered as a query in three different ways drawing the chemical structure in a molecule editor (Chemical Structure) searching by names or identification number, such as the CAS Number (Structure Identifier) and searching by molecular formula (Figure 5-12). 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

There are a number of different ways that the molecular graph can be conununicated between the computer and the end-user. One common representation is the connection table, of which there are various flavours, but most provide information about the atoms present in the molecule and their connectivity. The most basic connection tables simply indicate the atomic number of each atom and which atoms form each bond others may include information about the atom hybridisation state and the bond order. Hydrogens may be included or they may be imphed. In addition, information about the atomic coordinates (for the standard two-dimensional chemical drawing or for the three-dimensional conformation) can be included. The connection table for acetic acid in one of the most popular formats, the Molecular Design mol format [Dalby et al. 1992], is shown in Figure 12.3. 

The approximation to the closed integral improves as the number of iterations increases up to a point. The actual values in Table 1-1 may be system specific, that is, different hardware and software combinations may give slightly different results because of different ways of storing numbers. One is tempted to think of approximations as getting better without limit, the sum approaching the integral... 

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