# PDC bit vertical air

ES3 Liquid H Vortex Breaker [c.246]

In the fi structure, the positive charge is centered near one of the bases, rather than at a vertex, as in the Ai structures. [c.364]

A huge variety of topological descriptors are frequently applied in modeling physical, chemical, or biological properties of organic compounds. Topological descriptors represent the constitution of these compounds and can be computed from their molecular graph (see Section 2.4). The structural diagram of molecules can be considered as a mathematical graph. Each atom is represented by a vertex (or node) in the graph. Accordingly, the bonds are described by the edges. As an example, the graphical representation of a molecule of 2-methylbutane (1) is shown in Figure 8-2 it consists of five nodes, four edges, and the adjacency relationships implied in the structure. [c.407]

The number, n, of elements in the vertex set V(G) = vi, V2, v gives the [c.408]

Two vertices and Vj of a graph G are adjacent if they are incident with a common edge Bij. Two distinct edges of a graph G are called adjacent if they have at least one vertex in common. [c.408]

The degree, d(v), of a vertex v is the number of edges with which it is incident. The set of neighbors, N v), of a vertex v is the set of vertices which are adjacent to v. The degree of a vertex is also the cardinality of its neighbor set. [c.408]

Before we start to calculate the Laplacian matrix we define the diagonal matrix DEG of a graph G. The non-diagonal elements are equal to zero. The matrix element in row i and column i is equal to the degree of vertex v/. [c.409]

The Randic connectivity index, X, is also called the connectivity index or branching index, and is defined by Eq. (18) [7], where b runs over the bonds i-j of the molecule, and and dj are the vertex degrees of the atoms incident with the considered bond. [c.411]

Figure 5.5). Suppose our initial simplex contains vertices located at the points (9,9), (11,9) and (9,11), which have been generated by adding a constant factor 2 to each of the variables in turn. The values of the function at these points are 243, 283 and 323, respectively. The vertex with the highest function value is at (9,11) and so in the first iteration this point is reflected through the opposite face of the triangle to generate a point with coordinates (11,7) and a function value of 219 (we do not use the reflect-and-expand move in our [c.277]

The slow decay of the velocity autocorrelation function towards zero can be explained in terms of the of a hydrodynamic vortex. (Figure adapted from Alder B J and T E Wainwright 1970. Decay of the Velocity tation Function. Physical Review A 1 18-21.) [c.394]

Solid angle steradian sr The solid angle which, having its vertex in [c.77]

Let X be any angle whose initial side lies on the positive x axis and whose vertex is at the origin, and (x, y) be any point on the terminal side of the angle, (x is positive if measured along OX to the right, from the y axis and negative, if measured along OX to the left from the y axis. Likewise, y is positive if measured parallel to OY, and negative if measured parallel to OY. ) Let r be the positive distance from the origin to the point. The trigonometric functions of an angle are defined as follows [c.187]

Rule 1. Rank the response for each vertex of the simplex from best to worst. [c.671]

Rule 2. Reject the worst vertex, and replace it with a new vertex generated by [c.671]

Rule 3. If the new vertex has the worst response, then reject the vertex with the second-worst response, and calculate the new vertex using rule 2. This rule ensures that the simplex does not return to the previous simplex. [c.671]

Vertex Factor A Factor B Response [c.672]

In isotropic media, the pressure and shear wave slownesses are given by circles (see Fig. 4(a)). For the coupling of the trruasdiicer to transversely isotropic media the slowness diagram will change in the following way (see Fig. 5(a) and 6(a)) the upper part contains the circles of isotropic steel, because the transducer is designed for transmitting 45° shear waves into steel, and the lower part of the diagram shows the three non-circular curves for quasi pressure [qP), quasi shear verticcJ qSV) and shear horizontal SH) slownesses of transversely isotropic austenitic steel into which the wave is actually transmitted. Using the phase matching condition, it is seen that an incident shear wave under an angle of 45° (angles are counted counterclockwise from the normal pointing into the sample) will be transmitted into isotropic steel as a 45° shear vertical wave, into the anisotropic weld with perpendicular grain orientation under an angle of 35° and into the anisotropic weld with herringbone structure under an angle of 58° as a quasi shear vertical wave. It can also be seen that the phase velocity vector and the group velocity vector point in the isotropic case into the same direction, since the direction of the group velocity vector is obtained by drawing a line at right angles to a tangent to the respective slowness curve [9], because the group velocity vector is always perpendicular to the slowness curve. For both anisotropic cases the angle of the direction of the group velocity vector is smaller than 45°, i.e. 2° for perpendicular grain orientation and 25° for herringbone grain orientation. [c.154]

The third group is formed by exact methods of reconstruction. There are some mathematical formulas of the inverting in the basis of such approaches. In each such formula there are some steps to calculate 3D continuous function of the object represented through its integrals on beams crossing a given curve. These integrals assigned cone-beam projection data, and given curve assigned a trajectory of movement of cone vertix. Methods, on the basis of the formulas, offered by Smith [18-20], Grangeat [11], Gel fand [8] are appeared to be the [c.217]

Firstly the the completeness condition was offered by Kirillov. For its fulfdment it was required 2D distribution of sources, that is very impractibable. Further researches were directed to softening this restriction. Such result was obtained independently by the different researchers, but for the first time meets in Tuy paper[21]. Therefore this more acceptable restriction has the name of the Kirillov-Tuy condition and is formulated as follows If on evety plane, that intersects the object there lies a vertex, then one had complete information about the object. Geometries, that satisfy this condition are referred to as being complete. There are some advantages and disadvantages associated with each of following known geometries [c.218]

Figure C2.4.4. Schematic diagram of tire transfer process of LB fiims onto a hydrophiiic substrate. Verticai upward and downward strokes resuit in hydrophobic and hydrophiiic surfaces, respectiveiy. |

A simple graph can be thought of as a triple G = (V E,i), where Vand E are disjoint finite sets and I is an incidence relation such that each element of E is incident with exactly two distinct elements of V and no two elements of E are incident with the same pair of elements of V One gets general graphs, hypergraphs, infinite graphs, directed graphs, oriented graphs, etc., by variation of these requirements. We call V the vertex set and E the edge set of G. An edge connecting two vertices v/ and V is denoted as e, . [c.407]

One of the most widely used tools in structure-based ligand design is the GRID progran [Goodford 1985]. A regular grid is superimposed upon the binding site. A probe group i then placed at the vertices of the grid and the interaction energy of the probe with the proteir is determined using an empirical energy function. The result is a three-dimensional gric with an energy value at each vertex this data can then be analysed to find those locations where it might be favourable to position a particular probe. An example of the outpu produced by GRID is shown in Figure 12.32 (colour plate section) for the binding site oj neuraminidase. Parameters for many probes have been developed, covering a variety ol small molecules and common functional groups. An alternative to the use of a grid is tc [c.703]

Mitsoulis, E., Valchopoulos, J. and Mirza, F. A., 1985. A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell. Poly. Eng. Sci. 25, 677 -669. [c.139]

See pages that mention the term

**PDC bit vertical air**:

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Hudrocarbon exploration and production (1998) -- [ c.129 ]