Distance geometric

D G D/G Topological distance/geometric distance quotient matrix ... 

D G DAG Topological distance-geometric distance combined matrbc... 

The topological distance/geometric distance quotient matrix, denoted by D/G, is the reciprocal matrix of the G/D matrix, and the topological distance/topographic distance quotient matrix, denoted by D/T, the reciprocal matrix of the T/D matrix. 

Radius of gyration the radius of a thin hollow spherical shell of the same mass and moment of inertia as the macromolecule. In general, it is not easy to visualize this distance geometrically. However, for the simple case of a molecule consisting of a chain of identical atoms this quantity can be visualized as the root mean square distance of the atoms from the center of mass. It also depends on but is smaller than the root mean square separation by a factor of (1/6) (eqn 19.33). 

Since only the Pt atoms on the Pt particle surface can participate in the catalysis process, one way to maximize Pt atom utilization is to deposit an extremely thin layer of Pt on a non-Pt particle to form a core-shell structure with the Pt layer as the shell and the non-Pt particle as the core. The electron conductivity of the core particles is not important because they are covered by a highly electrical conducting Pt shell. In addition, when a submonolayer to several monolayers of Pt are made on certain core metal particles, the catalytic ability of Pt improves due to electronic interactions between the shell Pt atoms and the interior core metal atoms that increase the Pt 5d orbital vacancies and thus increases the n electron donation from O2 to Pt atoms (electronic effect), and due to the decrease in the Pt-Pt atomic distance (geometric effect). This mechanism is similar to the improved catalytic ability of PtM and PtM Ny alloys, where M and N represent different metals and X and y their atomic contents in the alloy. For the Pt/core, PtM or PtM Ny, if there is some leaching out of the non-Pt metals, their corresponding cations can replace the protons of the PFSA either in the catalyst layer or in the membrane to reduce its proton conductivity as well as the catalyst-PFSA-reactant three-phase boimdaries, and thus decrease the fuel cell performance. The shape and crystalline facet of the Pt nanoparticles can also affect the catalytic activity. 

The geometrical resolution or the resulting unsharpness in the radioscopic image is adjusted by the workpiece-detector distance. The relation between the focus-... 

To consider the geometrical magnification of the pipe image on film or IP in the tangential exposure technique according to the set-up shown in fig. 4 a correction of the measured wall thickness (w ) must be performed. The true wall thickness (w) depends in a rather complicated way on the film-focus-distance (f), the radius of the pipe (r) and the radius of the insulation (R) as shown in equation 2 ... 

Equations 1 and 2 shows that the distance b between the radiation source and the object has big influence on the X-ray image [8]. Therefore you have to find a compromise between a small geometrical unsharpness and a sufficient high magnification to archive an optimal... 

The distance distribution fiinction p(r) has a clear geometrical definition. It is defined as... 

The location of the crossing seam (or seam) for an X3 system is established from the requirement that /-ab = rec = r c, where j-ab, rec, and fAc are the interatomic distances. Since the goal are the the geometric properties produced by this seam, hyperspherical coordinates (p,0,atomic masses are equal, say iiiB = me, the seam is defined [5] by... 

Figure 2-15, Distance matrices of ethanal with a) geometric distances in A and b) topological distances. The matrix elements of b) result from counting the number of bonds along the shortest walk between the chosen atoms,...

The elements of a distance matrix contain values which specify the shortest distance between the atoms involved. Distances can be expressed either as geometric distances (in A) or as topological distances (in number of bonds) (Figure 2-15a,b). 

Distunct matrix describes geometric distances no bond types or bond orders no number of free electrons cannot be represented by bits... 

Full structure search can be developed by using similar approaches to those employed in the case of 2D structure search. Thus, some topological indices can be modified in such a way that they include geometrical information. For example, the global index given by Eq. (4) can be modified to Eq. (11), where are real interatomic distances. 

Each combination of four atoms (A, B. C. and D) is characterized by two parameters, e and e.. As for the CICC, is a parameter that depends on atomic properties and on distances, and is calculated by Eq. (27), with r, again being the sum of bond lengths between atoms on the path with the minimum number of bond counts. However c is now a geometric parameter (dependent on the conformation)... 

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