Alternative Approach

Redox metal centers can also be grafted on to the surface of silica, or on to the internal surface of a molecular sieve, by ligand displacement with pendant silanol groups [33]. Alternatively metal complexes can be tethered to silica or the internal surface of a molecular sieve via a spacer that is attached to the surface. This approach is analogous to the tethering of organic bases to solid surfaces referred to earlier. Metal complexes can also be attached to oxidatively stable organic polymers such as polybenzimidazole [34]. 

In yet another approach metal complexes are encapsulated in zeolite cages to give so-called ship-in-a-bottle complexes [35] or, alternatively, in polydimethyl-siloxane membranes [36]. 

Finally, supported noble metals widely used as hydrogenation catalysts can be used to catalyze the reverse reaction-oxidative dehydrogenation-in the presence of oxygen. This is applied, for example, in the oxidative dehydrogenation of alcohols and carbohydrates (see Sections 9.2 and 9.3). 

The generation of new C-C bonds also occupies a prominent position in organic synthesis. This often involves condensation of carbonyl compounds referred to earlier in the context of solid-base catalysis (Section 1.5.2). There are, however, also many C-C bond-forming reactions that involve transition metal catalysis and some of these can be conveniently performed with heterogeneons catalysts, 

Moreover, tethering of organometallic complexes to a silica surface or to the internal surface of a mesoporous host can, in principle, be used to design heterogeneous catalysts for a variety of C-C bond-forming reactions [16]. 

In addition to the PPAR combinations mentioned above, additional approaches have been explored to modulate the PPARy-RXR heterodimer with the goal of improving glucose and lipid profiles while reducing liabilities, such as weight gain and edema, associated with the conventional PPARy agonists. These alternatives include 

The first option is to improve the calcination process, usually by a two-step calcination. Other different mild template-destructive methods have been proposed. 

They can be divided into thermal and chemical protocols. In addition, more ambitious protocols aimed at template recovery have been proposed. The major improvements are compiled in Table 6.1. 

Solvent extraction is the most important technique for recovering surfactants from mesoporous materials. However, it is not very effective when applied to microporous compounds. Davis et al. [186] successfully extracted borosilicate and silicate BEA stractures with acetic acid while a small template fraction could be removed for the aluminosilicate. 

Recent reports describe more sophisticated detemplation methods. However, they are limited to mesoporous materials for the reasons described before. We show how Fenton chemistry can fulfill various missing challenges (i) it provides a powerful oxidation capacity at low(er) temperatures and (ii) it can work for microporous compounds as well. 

The investigation of the aforementioned algorithm has shown that further accuracy improvements may be accomplished by the introduction of additional degrees of freedom. In view of this observation, an enhanced operator with optimal stability can be constructed. 

Considering the integral form of Maxwell s equations and (3.44), spatial derivatives are evaluated by 

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Ahmad, S., LinnhoflF, B., and Smith, R., Design of Multipass Heat Exchangers An Alternative Approach, Trans. ASME, J. Heat Transfer, 110 304, 1988. 

An alternative approach is to create a reducible structure that deliberately includes redundant features and then subject this to optimization. Redundant features are then removed by the optimization. 

An alternative approach is to assume that the low-pressure steam... 

The classical computer tomography (CT), including the medical one, has already been demonstrated its efficiency in many practical applications. At the same time, the request of the all-round survey of the object, which is usually unattainable, makes it important to find alternative approaches with less rigid restrictions to the number of projections and accessible views for observation. In the last time, it was understood that one effective way to withstand the extreme lack of data is to introduce a priori knowledge based upon classical inverse theory (including Maximum Entropy Method (MEM)) of the solution of ill-posed problems [1-6]. As shown in [6] for objects with binary structure, the necessary number of projections to get the quality of image restoration compared to that of CT using multistep reconstruction (MSR) method did not exceed seven and eould be reduced even further. 

Thus it is necessary to find alternative approach to describe the physical mechanism of two-side filling of conical capillaries with hquids. Theoretical model of film flow in conical dead-end capillary is based on the concept of disjoining pressure II in thin liquid film [13]... 

The alternative approach is to treat the film as a nonideal two-dimensional gas. One may use an appropriate equation of state, such as Eq. Ill-104. Alternatively, the formalism has been developed for calculating film activity coefficients as a function of film pressure [192]. 

Alternative approaches treat the adsorbed layer as an ideal solution or in terms of a Polanyi potential model (see Refs. 12-14 and Section XVII-7) a related approach has been presented by Myers and Sircar [15]. Adsorption rates have been modeled as diffusion controlled [16,17]. 

The observed rate law depends on the type of catalyst used with promoted iron catalysts a rather complex dependence on nitrogen, hydrogen, and ammonia pressures is observed, and it has been difficult to obtain any definitive form from experimental data (although note Eq. XVIII-20). A useful alternative approach... 

An alternative approach is to consider ions of charge z e accelerated by the electric field strengtii, E, being subject to a frictional force, Kj, that increases with velocity, v, and is given, for simple spherical ions of... 

Since taking simply ionic or van der Waals radii is too crude an approximation, one often rises basis-set-dependent ab initio atomic radii and constnicts the cavity from a set of intersecting spheres centred on the atoms [18, 19], An alternative approach, which is comparatively easy to implement, consists of rising an electrical eqnipotential surface to define the solnte-solvent interface shape [20],... 

The calculation of the time evolution operator in multidimensional systems is a fomiidable task and some results will be discussed in this section. An alternative approach is the calculation of semi-classical dynamics as demonstrated, among others, by Heller [86, 87 and 88], Marcus [89, 90], Taylor [91, 92], Metiu [93, 94] and coworkers (see also [83] as well as the review by Miller [95] for more general aspects of semiclassical dynamics). This method basically consists of replacing the 5-fimction distribution in the true classical calculation by a Gaussian distribution in coordinate space. It allows for a simulation of the vibrational... 

To avoid these difficulties an alternate approach, labelled filter diagonalization, was developed [110. HI,... 

The fomialism outlined in the previous sections is very usefiil for small systems, but is, as explained, impractical for more than six to ten strongly interacting degrees of freedom. Thus, alternate approaches are required to represent dynamics for large systems. Currently, there are many new approaches developed and tested for this purpose, and these approaches are broadly classified as follows ... 

Smalley R E 1985 Supersonic cluster beams an alternative approach to surface science Comparison of Ab Initio Quantum Chemistry with Experiment for Small Molecules ed R J Bartlett (Boston Reldel)... 

An alternative approach envisages the stimulating idea to produce an all-carbon fullerene polymer in which adjacent fullerenes are linked by covalent bonds and align in well characterized one-, two- and tliree-dimensional arrays. Polymerization of [60]fullerene, with the selective fonnation of covalent bonds, occurs upon treatment under pressure and relatively high temperatures, or upon photopolymerization in the absence of a triplet quencher,... 

An alternative approach to obtaining microwave spectroscopy is Fourier transfonn microwave (FTMW) spectroscopy in a molecular beam [10], This may be considered as the microwave analogue of Fourier transfonn NMR spectroscopy. The molecular beam passes into a Fabry-Perot cavity, where it is subjected to a short microwave pulse (of a few milliseconds duration). This creates a macroscopic polarization of the molecules. After the microwave pulse, the time-domain signal due to coherent emission by the polarized molecules is detected and Fourier transfonned to obtain the microwave spectmm. 

Master equation methods are not tire only option for calculating tire kinetics of energy transfer and analytic approaches in general have certain drawbacks in not reflecting, for example, certain statistical aspects of coupled systems. Alternative approaches to tire calculation of energy migration dynamics in molecular ensembles are Monte Carlo calculations [18,19 and 20] and probability matrix iteration [21, 22], amongst otliers. 

There is also an interesting alternative approach by Aharonov et al. [18], who start by using projection operators, n = n) n to partition the Hamiltonian... 

We recently received a preprint from Dellago et al. [9] that proposed an algorithm for path sampling, which is based on the Langevin equation (and is therefore in the spirit of approach (A) [8]). They further derive formulas to compute rate constants that are based on correlation functions. Their method of computing rate constants is an alternative approach to the formula for the state conditional probability derived in the present manuscript. 

Harmonic analysis is an alternative approach to MD. The basic assumption is that the potential energy can be approximated by a sum of quadratic terms in displacements. 

The form of the Hamiltonian impedes efficient symplectic discretization. While symplectic discretization of the general constrained Hamiltonian system is possible using, e.g., the methods of Jay [19], these methods will require the solution of a nontrivial nonlinear system of equations at each step which can be quite costly. An alternative approach is described in [10] ( impetus-striction ) which essentially converts the Lagrange multiplier for the constraint to a differential equation before solving the entire system with implicit midpoint this method also appears to be quite costly on a per-step basis. 

An alternative approach is to generate twelve random numbers, ..., 2 and then calculal... 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

One alternative approach to the calculation of the diffusion and other transport coefficier is via an appropriate autocorrelation function. For example, the diffusion coefficie... 

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