Continuity/discontinuity

The orbital phase is continuons in the linear conjugate triene and discontinuous in the cross-conjugate trine. The electron delocalization between the terminal bonds is favored in the linear triene and disfavored in the cross-conjugate triene. The linear triene is more stable. The continuity-discontinuity of orbital phase underlies the thermodynamic stabilities of non-cyclic conjugated molecules. 

According to the theory of cyclic conjugation, the Hueckel rule is applicable only to a continuous cyclic conjugation, but not to a discontinuous one (Schemes 14 and 15). In the discontinuously conjugated molecules, electron donors and acceptors are alternately disposed along the cyclic chain [25].The thermodynamic stability depends neither on the number of n electrons nor the orbital phase properties, but on the number of neighboring donor-acceptor pairs. Chemical consequences of the continuity-discontinuity of cyclic conjugation are reviewed briefly here. 

Scheme 32 The continuity/discontinuity of cyclic conjugation and the orbital phase determining the equilibrium...

To summarize, the properties of triplet and singlet diradicals are closely related to the effectiveness of through-bond and through-space interactions, which are governed by the orbital phase continuity/discontinuity properties. In the next two sections, we will utilize this simple model to predict the spin preference and intramolecular reactivity for a broad range of diradicals. 

On the basis of the orbital phase continuity/discontinuity in the involved cyclic orbital interactions, some general rules were drawn for the Jt-conjugated and localized diradicals ... 

Once a smooth signal has been constructed, how is the trend represented Most of the available techniques do not provide a framework for the representation (and thus, interpretation) of trends, because their representations (in the frequency or time domains) do not include primitives that capture the salient features of a trend, such as continuity, discontinuity, linearity, extremity, singularity, and locality. In other words, most of the approaches used to represent process signals are in fact data compaction techniques, rather than trend representation approaches. Furthermore, whether an approach employs a frequency or a time-domain representation, it must make several major decisions before the data are compacted. For frequency-domain representations, assumptions about the... 

Thermal radiation emitted by an object can be continuous, discontinuous or, in most cases, a mixture. A continuous radiation profile corresponds to an ideal black body, where only the temperature of the emitting object determines the emission profile. Discontinuous thermal emission spectra are caused by photons emitted during the relaxation of excited vibrational states. Since vibrational states are quantised, this results in emission bands at the wavelengths of the corresponding IR absorption bands. 

Recent unpublished studies by Boatman and Luchtel (personal communication) in rabbits show that the mucus field is indeed continuous in the medium and smaller airways. Their morphologic techniques are currently being extended to the large airways. Differences in techniques may account for the discrepancy between this work and that of Van As and Webster. Further studies of the structure of the mucus layer in animals are therefore needed to resolve the continuity-discontinuity question. 

Large particle Continuous Discontinuous (short) Laminates Sandwich... 

Commercially available non-oxide ceramic reinforcements are in three categories continuous, discontinuous, and whiskers. The great breakthrough in the ceramic fibre area has been the concept of pyrolysing polymers under controlled conditions, containing the desired species to produce high-temperature ceramic fibres. Silicon carbide fibre is a major development in the field of ceramic reinforcements. 

Inagaki and coworkers46 predicted that the 2-aminoallyl anion resulting from an enamine would be more stable than the corresponding 1-aminoallyl anion on the basis of orbital phase continuity-discontinuity arguments. In support of their hypothesis, deprotonation of the enamine of 1-morpholinocyclohexen-l-ene with -BuLi-TMEDA took place at position 2 rather than at position 3 (equation 25). Their model is also supported by the results of Woodward and coworkers52 for 2-pyrrolidino-1,4-dihydro-naphthalene, which is also deprotonated at the a position. 

Exposure frequency The number of times an exposure occurs in a given period exposme may be continuous, discontinuous but regular (e.g. once daily) or intermittent (e.g. less than daily, with no standard quantitative definition) (REAP, 1995). 

SAR Index. The SAR Index (SARI) has recently been introduced to quantitatively capture the continuous, discontinuous, or heterogeneous nature of activity landscapes and SARs. Similar to SAS maps, it exclusively relies on the 2D structural similarity and potency distribution within a set of active compounds. However, SARI aims to categorize the SARs of a population of compound sets without employing idealized reference states. It generates a numerical index between 0 and 1 that reflects the (dis-)continuity of the SARs under consideration. SARI distinguishes between three major categories of... 

SARs continuous, discontinuous and heterogeneous. In the following, the conceptual framework of SARI will be presented and compound classes representative for the distinct SAR types are discussed. 

The polymerization sequence can be plotted using a phase diagram (Figure 14.1) [11]. This diagram is representative for nearly all polymer (rubber-polymer (glassy polymer)-common solvent systems. Point a is the composition of the feed. The critical point (phase separation) is reached at point b. Further polymerization generates more glassy polymer (SAN) and phase inversion occurs at point c (rubber continuous —> discontinuous). Point d is reached when all monomer is converted. 

Prescribe medications, including initiation, continuation, discontinuation, and altering therapy, based upon established formulary or protocols... 

In terms of the process time control, CVD can be divided into three categories, namely continuous, discontinuous and pulsed CVD (P-CVD). Discontinuous CVD is used in most CVD processes, whereas continuous CVD is extensively used for fibre coating and high-volume production of semiconductor devices. In order to improve the coating thickness uniformity and its microstructure, P-CVD is commonly used. 

Figure 1 A three-dimensional representation of the six concepts focused on in this paper. The six appear in three pairs, one pair relating to time (t symmetrical time, directional time), the second to space (3D external space relations, 3d internal structure), and the third to the continuity-discontinuity dichotomy (N number, discreteness, A association, continuity).

The degree of cyclic electron delocalization has been theoretically proposed to be a function of the mode of donor(D)-acceptor(A) arrangement of the component system as well as orbital phase continuity requirements. A novel notion of continuity-discontinuity of cyclic conjugation shows that there are nondelocalized (4 -f 2)n electron (or nonaromatic) systems and nonlocalized 4n7r electron (or nonantiaromatic) systems in discontinously conjugated systems. The notion was applied to explain the considerable stability of furano- and thieno[3,4-d]thiepines (7) and (8) <77JA7418,78MI 903-01 >. 

Distribution functions can be classified as discontinuous or continuous. Discontinuous distribution functions are subdivided into frequency distributions and cumulative distributions. Continuous distribution functions are further classified as differential and integral distribution functions. 

F Trees leaves, waste waters, fertilizers Chemical Potentiometry Continuous/discontinuous manifold stopped-flow... 

Oxaiate Urine, serum Biochemical Potentiometry Continuous/discontinuous manifold... 

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