Connectedness

This analysis underscores the importance of examining failed components before they are cleaned or in any way altered. It also demonstrates the potential complexity of failure analysis and the need that exists to discard explanations that do not adequately account for all relevant observations. Important also to note is the potential connectedness of environmental factors, such that the seasonal development of seed hairs in a field of grass near a cooling tower would eventually contribute to perforations of tubes in a condenser. 

Molecular Complexity. A measure of the combined effects of molecular size, element and functional-group content, internal connectedness, stereocenter content, reactivity, and instability that lead to difficulties of synthesis. 

WriE72 Wright, E. M. The probability of connectedness of an unlabelled graph can be less for more edges. Proc. Am. Math. Soc. 35 (1972) 21-25. 

Examples of disconnected and connected grid domains are shown in Fig. 12.a and 12.b, respectively. The assumption on connectedness for a domain with a narrow bridge will be satisfied if we make the step small enough or refine the grid in this part of the domain. Fig. 12.b illustrates the case where the connectedness of the grid is stipulated by the proper choice of its step rather than by successive grid refinements. 

In the case of the difference scheme for the Dirichlet problem (24)-(26) of Section 1 the definition (4) of connectedness coincides with another definition from Section 1. The very definition implies that the point P may be boundary and, hence, the connectedness is to be understood that every point of the boundary belongs to the neighborhood Patt [P) of at least one inner node. 

Connectedness is defined indirectly as the lack of disconnectedness a topological space (X, T) is connected if it is not disconnected. A connected open subset is often called a domain. 

Figure 3.1. Schematic representation of dimensional reduction for a framework of corner-sharing MX6 octahedra. The M and X atoms are represented by black and white spheres, respectively. In a) though d), reaction with AbX incorporates additional X atoms into the M—X framework, progressively reducing the connectedness and effective dimensionality of the M—X framework. In d), after incorporating n units of AbX (n > 2), the structure is reduced to isolated oligomeric or monomeric components. For clarity, the A atoms are not shown in the figure. [Adapted with permission from [Ref. 16]. Copyright 2001 American Chemical Society.]...

The taste bud is a polarized structure with a narrow apical opening, termed the taste pore, and basolateral synapses with afferent nerve fibers. Solutes in the oral cavity make contact with the apical membranes of the TRCs via the taste pore. There is a significant amount of lateral connectedness between taste cells within a bud both electrical synapses between TRCs and chemical synapses between TRCs and Merkel-like basal cells have been demonstrated to occur [39]. Furthermore, there are symmetrical synapses between TRCs and Merkel-like basal cells [39]. In addition, these basal cells synapse with the afferent nerve fiber, suggesting that they may function in effect as interneurons [39]. The extensive lateral interconnections... 

As an example, the group of rotations about an axis is a connected group. The property of connectedness is not the same as the continuous nature of a group. A continuous group, for instance the rotation-inversion group in three dimensions may be disconnected. The parameter space of a continuous disconnected group consists of two or more disjoint subsets such that each subset is a connected space, but where it is impossible to go continuously from a point in one subset to a point in another without going outside the parameter space. 

Connectedness of the Hilbert scheme, Publ. Math. IHES 29 (1966), 261-304. 

The elements of stereoisomerism considered thus far consist of a point occupied by an atom and a line wholly occupied by one or more bonds. The ligands are joined directly to these elements. This emphasis on bonding relationships appears to be proper, as the distinction between constitutional and steric isomerism similarly depends on established patterns of connectedness. From this point of view it seems less than satisfactory if direct connectedness between specific atoms is assumed, when chemical theory envisions no such localized bond. This situation prevails in the description of ir complexes such as the metallocenes. Initially (44a), the 1,2- (22) or 1,3-heteroligated ferrocenes were considered to... 

Our definitions of the stereoisomeric center, line, and plane all stipulate the existence of bonds between the ligating element and its ligands. The exclusive use of these elements limits our analysis to classical stereochemistry and thus does not encompass the so-called topological isomerism (47) of interlocked rings—catenanes (48)—or of knots. As there is no bond between the rings of the catenanes we cannot expect to handle such compounds with a system based on connectedness. At the present stage of development, this limitation in scope... 

In this work, lacnnarity analysis of TEM images of a previously synthesized hybrid organosilica material incorporating a biphenyl moiety was carried out. The results obtained snch as degree of connectedness of holes in sample material were correlated to the visnally observed degree of roughness of the materiaTs surface. 

PSDVB copolymers and their ion exchange derivatives consist of a three dimensional four-connected network structure. Such networks may have a statistically isotropic structure that includes tetrahedral cells, such as the X" unit structure described by Flory (6). The four-connectedness results from the expected pairwise chain connecting function of... 

One reason is that firms who want to employ the new technology cannot merely invest in basic research. Cockburn and Henderson (1998) emphasize that it is also important for the firm to be actively connected to the wider scientific community (p. 158). They developed the concept of connectedness, as measured by the extent of collaboration in writing scientific papers across institutional boundaries, and conclude that firms wishing to public sector research must do more than simply invest in in-house basic research they must also actively collaborate with their public sector colleagues. The extent of this collaboration... is positively related to private sector research productivity (p. 180). The process by which firms acquire this new technology is not simple or direct, nor obtained without cost. 

This seventh and final level has considerable overlap with level 6. Managers sense of connectedness and holistic view of the world is now drawn upon to integrate themselves with the world around them. It is about doing something important and constructive, about changing the world. 

There has been a long-standing and unfruitful opposition between reductionist and holistic science in connection with agricultural and ecological research (see e.g. Lockeretz and Anderson 1993, Thompson 1995, Rowe 1997), which has hampered cross-disciplinary cooperation. From the holistic view, analytic, reductive methods are necessarily reductionist and are therefore bad science because they do not capture the connectedness of complex reality. Furthermore they are (at least in part) to blame for the present agricultural and environmental problems. From the reductionist view, analytic, reductive methods ensure the objectivity of science, and other methods are, therefore, not scientific. 

It appears that one can develop a qualitative understanding of the simple flow properties at moderate concentration without going beyond concepts which are already inherent either in the dilute solution theory of polymers or in the properties of particulate suspensions. The dependence of viscosity on c[i ] is believed to reflect a particle-like or equivalent sphere (127) hydrodynamics in solutions of low to moderate concentration. In particular, the experimental facts do not force the consideration of effects which might arise from the permanent connectedness of the polymer backbones. Situations conducive to the entangling of molecules may be present, e.g., overlap of the coils, but either entanglement contributions are small, or else they are overwhelmed by the c[f ] interactions. 

All the above theories attribute the enhanced friction in entangled systems to extra motions. In a crude way they speak to the main issue, which is the loss of relaxation pathways due to connectedness in the chain environment. However, all are rather arbitrary they select certain types of motion for examination and exclude others, while in fact the motions must be cooperative and interdependent. In addition, the theories have features which appear to be incorrect, or at least inconsistent, even within the limited realm of motions examined. 

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