Geometric features

We have implemented all segmentation techniques described above, in an interactive software. The operator can chose and adapt the appropriate segmentation technique with the desired parameters. Some geometrical features can be extracted using a contour following such as length, width, surface, form, median axes of the selected defect. The selection is easy and can be done interactively using the mouse. 

The situation becomes more complex in the case of a three-dimensional foam. Since the septa should all be identical, again three should meet at 120° angles to form borders or lines, and four lines should meet at a point, at the tetrahedral angle of 109°28. This was observed to be the case by Matzke [179] in his extensive statistical study of the geometric features of actual foams. 

Localized erosion-corrosion caused by turbulence or impinging flow at certain points of the surface. In the majority of cases of impingement attack, a geometrical feature of the system results in turbulence at one or more parts of the surface. 

In order to represent further geometric features, modifications of Eq, (16) were introduced. The influence of the electronic current in double bonds was incorporated by Eq. (17). 

Incorporating Additional Geometric Features Into a 3D Pharmacophore... 

Aluminum, the most common material used for contacts, is easy to use, has low resistivity, and reduces surface Si02 to form interfacial metal-oxide bonds that promote adhesion to the substrate. However, as designs reach submicrometer dimensions, aluminum, Al, has been found to be a poor choice for metallization of contacts and via holes. Al has relatively poor step coverage, which is nonuniform layer thickness when deposited over right-angled geometric features. This leads to keyhole void formation when spaces between features are smaller than 0.7 p.m. New collimated sputtering techniques can extend the lower limit of Al use to 0.5-p.m appHcations. 

The data used to generate the maps is taken from a simple statistical analysis of the manufacturing process and is based on an assumption that the result will follow a Normal distribution. A number of component characteristics (for example, a length or diameter) are measured and the achievable tolerance at different conformance levels is calculated. This is repeated at different characteristic sizes to build up a relationship between the characteristic dimension and achievable tolerance for the manufacture process. Both the material and geometry of the component to be manufactured are considered to be ideal, that is, the material properties are in specification, and there are no geometric features that create excessive variability or which are on the limit of processing feasibility. Standard practices should be used when manufacturing the test components and it is recommended that a number of different operators contribute to the results. 

While it remains true that tetrahedral and octahedral coordination modes are the predominant stereochemistries adopted by the group 13 metals, nevertheless increasing diversity is being achieved by carefully selecting appropriate electronic and geometric features to enhance the stabilization of unusual stereochemistries. Some representative examples follow. 

Observed geometrical features or stabilities of small ring molecules containing an endocyclic double bond have been explained in terms of the Ji-a interactions [137, 138]. The n relaxation is predicted to stabilize such small ring unsaturated molecules of heavy atoms recently prepared [139-142],... 

The process of lithographic patterning determines the geometric features specified by the layout and patterning as the integrated circuit is fabricated layer by layer. A photomask, containing pattern information in... 

The low Ti content (up to 3 wt % in Ti02) makes the extraction of vibrational, energetic, and geometric features specific to Ti04 moieties a difficult task as the experimental data are dominated by the features of the siliceous matrix. This is the reason why the structure of the local environment around Ti(IV) species inside TS-1 was only definitively assessed more than 10 years after the discovery of the material, when the atomic selectivity of X-ray absorption spectroscopies (both XANES and EXAFS) were used [58-60]. 

To study geometric features of a potential field in detail, consider the curvature of the level surfaces. As is well known, the curvature of a curve y — f(x) is defined as... 

In view of the expected generality of application, the prospects of TCS-D are amazing. A tricky point that has to be solved is the final thermal decomposition of the M°/ /S nanocomposite that should be carried out at relatively low temperature for preserving the geometric features of metal nanoclusters. CFPs currently employed in this strategy do decompose at 290-330 °C and CFPs able to decompose at 250 °C are being looked for [8]. 

The form and shape of a molecule (i.e. its steric and geometric features) derive directly from the molecular genotype , but they cannot be observed without a probe. Furthermore, they vary with the conformational, ionization and tautomeric state of the compound. Thus, the computed molecular volume can vary by around 10% as a function of conformation. The same is true of the molecular surface area, whereas the key (i.e. pharmacophoric) intramolecular distances can vary much more. 

In fact, it has been demonstrated that geometrical features of stationary points (including the hydrogen bonded complexes) optimized at 6-311 +G(d,p) are very similar to those obtained with the very large, but too time-consuming, aug-cc-pVTZ basis.f... 

One of the aims of the crystallographic studies is to visualize the spatial conditions of non-H-bond type of interactions. Van der Waals forces (dispersion and exchange repulsion) and polarization are representatives of such interactive forces. They are governed by geometric features such as contact surfaces and volumes of the host and guest matrices. 

Kabsch, W., and C. Sander. 1983. Dictionary of Protein Secondary Structure Pattern Recognition of Hydrogen-Bonded and Geometrical Features. Biopol. 22,2577-2637. 

Fig. 22 The linkages between triacontahedra and prolate rhombohedra in Tsai-type 2/1 ACs (adapted from Fig. 20) afford some important clues for QC modeling. A trigonal pyramid with particular angles (as marked) and geometric features is formed when equivalent apex atoms of four prolate rhombohedra are linked. The same property exists for Bergman-type 2/1 ACs...

The chemical and physical properties of DMFL contrast most sharply with those of FL. The geometrical features, in particular the carbene-carbon bond angle, of these two carbenes are expected to be identical. The most important difference between DMFL and FL is that the spin multiplicities of the lowest electronic states appear to have been inverted. The experiments indicate that the ground-state of DMFL is the singlet. This conclusion is outlined in the reactions shown in Scheme 4. 

The concept of a gauge field and the notion of gauge invariance originated with a premature suggestion by Weyl [42] how to accommodate electromagnetic variables, in addition to the gravitational field, as geometric features of a differential manifold. 

---