Main Results

The first work on heterogeneous hydroxyalkylation was conducted by Venuto and Landis [2]. They worked on the hydroxyalkylation of phenol with formaldehyde, benzaldehyde, acetone, and hexafluoroacetone using zeolite HY at 180 °C. Except for hexafluoroacetone (Table 1), the major product was always the bis-arylmethane. 

Substrate Electrophile Conversion Main product Selectivity (time)  

The first breakthrough was obtained using furan derivatives and H-Mordenite as the catalyst [9], The main results obtained are given in Table 2. 

To achieve those results, the conditions required are excess formaldehyde, a significant proportion of catalyst, and dealumination of the catalyst, mainly to enhance the hydrophobicity of the zeolite [10] (Table 3). 

Reactivity and selectivity observed for furan derivatives have been extended to aromatic phenols. The most interesting results have been obtained for the hydro-xymethylation of guaiacol with formaldehyde leading to pura-hydroxymethyl-guaiacol, the precursor for vanillin [11]. Use of H-Mordenite type catalyst with an Si to A1 ratio of 18, low temperature (40 °C), and well-defined conditions led to very good results-33 % conversion with 98 % alcohol selectivity can be obtained and para selectivity of 83 % [12] (Eq. 4). 

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From graph theory the main result needed in the present context is that the number of independent loops for a graph is given by ... 

Box-Jenkins model is chosen for building up a TF for identification of the material. MATLAB 5.0 was used for calculation of characteristics of the model. In the Figure 5 the main results of modeling are presented. 

As a fist attempt to see the influence of the tube drawing and the industrial environment on measured data, some experiments were performed for improving the measuring chamber and guidance as well optimizing the measuring condition. The main results were ... 

Let us cite the main centre in Ukraine, where investigations and developments in the field of NDT are performed, and consider some of the main results of this work. 

It is clear from our discussion of contact angle hysteresis that there is some degree of variability in reported contact angle values. The data collected in Table X-2, therefore, are intended mainly as a guide to the type of behavior to be expected. The older data comprise mainly results for refractory and relatively polar solids, while newer data are for polymeric surfaces. 

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 ... 

This is, in fact, the main result of the DH analysis. The activity coefficient is clearly given by... 

The main results are that the universal scaling fonu of the LS cluster distribution fimction fix) given above... 

We smmnarize here only the main results of the theory and refer to a recent review [27] for details. The total number of adiabatically open channels is computed by searching for chaimel potential maxima V The... 

The sign alternatives depend on the location of the zeros (or singulai ities) of x i). The above conjugate, or reciprocal, relations aie the main results in this section. When Eqs. (9) and (10) hold, ln x(f) and argx(t) are Hilbert transforms [245,246]. 

The theory predicts high stabilities for hard acid - hard base complexes, mainly resulting from electrostatic interactions and for soft acid - soft base complexes, where covalent bonding is also important Hard acid - soft base and hard base - soft acid complexes usually have low stability. Unfortunately, in a quantitative sense, the predictive value of the HSAB theory is limited. Thermodynamic analysis clearly shows a difference between hard-hard interactions and soft-soft interactions. In water hard-hard interactions are usually endothermic and occur only as a result of a gain in entropy, originating from a liberation of water molecules from the hydration shells of the... 

The main result of this subsection can be formulated as follows. 

In this case the crack is said to have a zeroth opening. The cracks of a zeroth opening prove to possess a remarkable property which is the main result of the present section. Namely, the solution % is infinitely differentiable in a vicinity of T, dT provided that / is infinitely differentiable. This statement is interpreted as a removable singularity property. In what follows this assertion is proved. Let x G T dT and w > (f in O(x ), where O(x ) is a neighbourhood of x. For convenience, the boundary of the domain O(x ) ia assumed to be smooth. 

The considered problem is formulated as a variational inequality. In general, the equations (3.140)-(3.142) hold in the sense of distributions. In addition to (3.143), complementary boundary conditions will be fulfilled on F, X (0,T). The exact form of these conditions is given at the end of the section. The assumption as to sufficient solution regularity requires the variational inequality to be a corollary of (3.140)-(3.142), the initial and all boundary conditions. The relationship between these two problem formulations is discussed in Section 3.4.4. We prove an existence of the solution in Section 3.4.2. In Section 3.4.3 the main result of the section concerned with the cracks of minimal opening is established. 

However, when it is obtained by pyrolysis of diethylmagnesium or by reaction of diethylmagnesium and LiAlH (11), it is very reactive with both air and water. This difference in reactivity mainly results from the much finer particle size of the product obtained by the pyrolysis route. 

Table 11 summarizes the main results on the tautomerism of mono-hydroxy-, -mercapto-, -amino- and -methyl-azines and their benzo derivatives, in water. At first sight the equilibrium between 2-hydroxypyridine (71) and pyridin-2-one (72) is one between a benzenoid and a non-benzenoid molecule respectively (71a 72a). However, the pyridinone evidently... 

We just quote the main results of [Leggett et al. 1987], which cover most of the possible situations. The spectral density is taken in the form... 

The main results of this miero-mechanical model in the quasi-static regime have been compared with experimental results obtained by placing polystyrene (PS)-polyvinyl pyridine (PVP) diblock copolymers with a short PVP block between PS and PVP homopolymers. The fracture toughness was found to increase linearly with E from that of the bare PS/PVP interface, while the slope of the line increased with the degree of polymerization of the block being pulled out. If the data for the different copolymers were plotted as AG vs. (where... 

The latter mainly results from the thermal emission current. The dark current is apparent mainly in the long-wavelength range of the spectrum when the photocurrent is appropriately small [53, 54, 131]. It is relatively small for alloy cathodes (e.g. Sb-Cs cathodes), but not small enough to be negligible. 

In the early years of this century the periodic table ended with element 92 but, with J. Chadwick s discovery of the neutron in 1932 and the realization that neutron-capture by a heavy atom is frequently followed by j6 emission yielding the next higher element, the synthesis of new elements became an exciting possibility. E. Fermi and others were quick to attempt the synthesis of element 93 by neutron bombardment of but it gradually became evident that the main result of the process was not the production of element 93 but nuclear fission, which produces lighter elements. However, in 1940, E. M. McMillan and P. H. Abelson in Berkeley, California, were able to identify, along with the fission products, a short-lived isotope of... 

Occasionally, equilibria between a quinoid and a diradicaloid form of tetraazafulvaleiies of type 77 have been discussed (66AG303 72NKK100 79JOC1241). Based on ESR measurements, only traces of radicals (0.1% at 200°C) could be observed and therefore 77 (Ar = Ph) exists at room temperature predominately in the quinoid structure. Other authors stated that the thermochromism of 77 mainly results from a change in intermolecular interaction, not from biradical formation (84MI1030). 

Polya s main results on tree enumeration are summarized at the beginning of Section IV of his paper. His equation (4.8) gives the functional equation for the generating function of rooted labelled trees, from which Cayley s result, referred to above, follows... 

In addition to these main results some others can be found in Polya s paper, notably the enumeration of doubly and multiply substituted alkanes. 

A further clear establishment of the absoiption due to singlet excitons and the phonons coupled to them is the electroabsorption experiment reported in Ref. [18]. The main results are shown in Figure 9-14 the top panel shows the absorption spectrum of m-LPPP at 20 K. It becomes clear that the peaks at 2.7, 2.9, and 3.1 eV, representing A0, A i, and A2 (see Fig. 9-10) are not the only vibronic replicas. There are additional peaks between these dominant ones if the experiment is conducted at low temperature. The bottom panel in Figure 9-14 shows a so-called electroabsorption spectrum which is obtained as the modulation (or change) of the absorption under the application of an electric field. Below 3.2 eV the electroab-... 

The origin of the success of fl-lactam antibiotics mainly results from the extreme low toxicity of these compounds with regard to human beings. In other words, P-lactam antibiotics have a highly selective toxicity for bacteria since they do not interfere with human metabolism, but inhibit the formation of the cell wall of growing bacteria. 

The main results following from the investigation of stoichiometrically not simple heterogeneous catalytic reactions carried out in our laboratory can be summarized in this way ... 

The poisoning effect of hydrogen when dissolved in palladium was for the first time properly described and interpreted by Couper and Eley (29) in 1950 in their study of the fundamental importance of the development of theories of catalysis on metals. The paper and the main results relate to the catalytic effect of an alloying of gold to palladium, on the parahydrogen conversion. This system was chosen as suitable for attempting to relate catalyst activity to the nature and occupation of the electronic energy... 

Thirdly, the multicomponent model was applied to the case of crystallization of a random A-B copolymer by Helfand and Lauritzen [127]. Their main result is that the composition of, 4 s and B s in the crystal is determined by kinetic, rather than equilibrium considerations the inclusion of excess B increases with growth rate. 

More definite evidence comes from an MO study of the S—O stretching in dimethyl sulphoxide9, where three basis sets were employed a STO-3G one (I), a 4-31G one (double-zeta, II) and a 3G + d one (III). Table 6 reports the main results the small effect of the double-zeta, and the dramatic effect of the 3d functions, are clearly visible. Notice also how the C—S bond length and the bond angles are by far less sensitive to basis set changes. 

The main result of the thermolysis of the three-membered ring sulfoxides and sulfones is the extrusion of the sulfur monoxide and the sulfur dioxide moieties (Section III.C. I)99 10 5. Only in the presence of a suitably disposed /J-hydrogen does the ordinary sulfoxide-sulfenic acid fragmentation take place in the thiirane oxide series (equation 9). 

The schemes in Figs. 44 and 45 may serve to summarize the main results on photoinduced microwave conductivity in a semiconductor electrode (an n-type material is used as an example). Before a limiting photocurrent at positive potentials is reached, minority carriers tend to accumulate in the space charge layer [Fig. 44(a)], producing a PMC peak [Fig. 45(a)], the shape and height of which are controlled by interfacial rate constants. Near the flatband potential, where surface recombination... 

A study of forced convection characteristics in rectangular channels with hydraulic diameter of 133-367 pm was performed by Peng and Peterson (1996). In their experiments the liquid velocity varied from 0.2 to 12m/s and the Reynolds number was in the range 50, 000. The main results of this study (and subsequent works, e.g., Peng and Wang 1998) may be summarized as follows (1) friction factors for laminar and turbulent flows are inversely proportional to Re and Re ", respectively (2) the Poiseuille number is not constant, i.e., for laminar flow it depends on Re as PoRe ° (3) the transition from laminar to turbulent flow occurs at Re about 300-700. These results do not agree with those reported by other investigators and are probably incorrect. 

The general features of two-dimensional flow with evaporating liquid-vapor meniscus in a capillary slot were studied by Khrustalev and Faghri (1996). Following this work we present the main results mentioned in their research. The model of flow in a narrow slot is presented in Fig. 10.16. Within a capillary slot two characteristic regions can be selected, where two-dimensional or quasi-one-dimensional flow occurs. Two-dimensional flow is realized in the major part of the liquid domain, whereas the quasi-one-dimensional flow is observed in the micro-film region, located near the wall. 

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