Dot matrix representation

In dot matrix representations, the basic idea is to use the sequences as the coordinates of a two-dimensional graph and then plot points of correspondence within the inte-... 

The matrix representation is convenient because dot-product multiplication is equivalent to standard matrix multiplication. In terms of the matrix representation, Eq. (5.7) is expressed as... 

Chih-Kung L., Wen-Jong W., Sheng-Lie Y., (2000) Optical configuration and color representation range of a variable-patch dot matrix holographic printer. Applied Optics Vol.39, No.l, 40. 

Figure 6. Evolution of the membrane structure as a function of water content, 1 (moles of water per mole of sulfonic acid sites). The pictures are cross-sectional representations of the membrane where the gray area is the fluorocarbon matrix, the black is the polymer side chain, the light gray is the liquid water, and the dotted line is a collapsed channel. (Reproduced with permission from ref 89. Copyright 2003 The Electrochemical Society, Inc.)...

Fig. 29. Schematic representation of vertical cross section of nacre. R-groups are indicated as black dots and oxygens as open circle. M = mineralizing matrix and C = carrier protein...

Fig. 3a-c. Schematic representation of the three residues involved in the formation of the catalytic triad of chymotrypsin [82] with the pseudo-atom vectors (arrows) overlaid a the positions of real non-hydrogen atoms in the sidechains, residues b the S and E pseudo-atom positions with the associated distances between them (dotted lines) (for clarity the MM distances are not shown) c the search matrix for this grouping of sidechains, the distances, all of which are in A, being for the SS, SE, ES and EE distances respectively... 

Here the dot indicates contraction over Cartesian coordinates, tK is a component of the vector tjf(r) = (r — rK)/ATrsf r — rK 3, and M is the 3 x 3 block, corresponding to the Tfth and 7th atoms, of the so-called relay matrix, which gives an atomic representation of the molecular polarizability. The supermatrix M has dimension 3Na x 3Na, and is defined as ... 

Fig. 18. Redox-coupled conformational change in a loop between helices I and II of subunit I. A stereoview (A, see color insert) and a schematic representation of the hydrogen bond network connecting Asp-51 with the matrix space (B). (A) The molecular surface on the intermembrane side is shown by small dots. Maroon and green sticks represent the structures in the fully oxidized and reduced states. (B) Dotted lines show hydrogen bonds. The rectangle represents a cavity near heme a. The two dotted lines connecting the matrix surface and the cavity represent the water path. The dark balls show the positions of the fixed water molecules.

Figure 1. Graphical representation of the transfer matrix. The primed variables are associated with the circles and combine into the left index of the matrix the dots go with the right index and the unprimed variables. Coincidence of a circle and a dot produces a S function. An edge indicates a contribution to the Boltzmann weight. Repeated application of this matrix constructs a lattice with nearest-neighbor boncft and helical boundary conditions.

Fig. 4. Inclusion matrix of Dianin s compound (i) (schematic representation) Individual Dianin molecules are represented by a specified hydroxy group attached to an elUpsoid. The characteristic hydrogen bridge networks are indicated by the shaded hexagons (H-bonds in dotted lines). The hatched sphere in the centre of the cavity pictures an included guest molecule, e.g. chloroform...

Figure 2.10 Schematic representation of the structure of a gel. The black lines show the polymer chains forming the matrix of the gel. The black dots represent the cross-linking zones that can result from different mechanisms of gel formation. The grey colour of the background represents the liquid phase filling the channels formed In the matrix of polymer.

Fig. M.I. Four Slater-Condon rules (I,n,in, TV) for easy remembering. On the left side we see pictorial representations of matrix elements of the total Hamiltonian H. The squares inside the brackets represent the Slater determinants. Vertical lines in bra stand for those spinorbitals, which are different in bra and in ket functions. On the right we have two square matrices collecting the hij s and ij ij) - for = N. The dots in the matrices symbolize non-zero elements.

A more compact rotationally invariant representation of the atomic environment can be built in the form of a matrix by using the bond vectors r, i = 1,..., TV between the central atom and its N neighbours. The elements of the matrix are given by the dot product... 

Figure 3.35. Schematic representation of microsphere cross sections in matrix under plane strain for circled areas in Figure 34(b) (a) partially debonded and broken with tom marks, solid line circles (b) fully debonded and pulled out from matrix, dashed line circles and (c) fuUy bonded but broken without torn marks, dash-dotted line circles [37]...

Here R)mn is a symmetry matrix of the representation F, for the symmetry operation R. This implies the dot-product of two one-dimensional representations is zero when m = m = n = n =1, they are orthogonal However, the theorem also applies to individual (m, n) and (m, n ) elements of (2 X 2) representations of odd-fold rotations such as or Csv-... 

Fig. 3.4. Lowest-order diagrams associated with cation-anion orbital hybridization. Unlike the representations used in the many-body problem, the diagram vertices - a dot for an anion and a rectangle for a cation - here symbolize the matrix elements of Gj, while the arrowed lines indicate hopping processes associated with Hnd- Only bubble diagrams of the cl - and c3-types are kept to derive the local charge transfer.

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