Chess board

The chess-board is the world the pieces are the phenomena of the universe the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. But we know that his play is always fair, just, and patient. But also we know to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance. 

Fig. 4 The structures of a Fe2(4,4 -azpy)4(NCS)4 (EtOH) and b Fe(4,4 -azpy)2(NCS)2, viewed approximately down the 1-D channels. Framework atoms are represented as sticks and atoms of the ethanol guests as spheres. In Fe2(4,4 -azpy)4(NCS)4-(EtOH) the ethanol guests occupy every second 1-D channel in a "chess board" arrangement. Removal of ethanol by heating gives single crystals of Fe(4,4 -azpy)2(NCS)2, which has empty, equivalent 1-D channels and a concomitant quartering of the unit cell. Hydrogen atoms are omitted for clarity. Reprinted with permission from [39]. Copyright 2002 American Association for the Advancement of Science...

Figure 7.2 The power of non-linear growth. Put a grain of rice in the first square, two in the second, four in the third, eight in the fourth. .. and calculate how many kilograms of rice you have at the end of the chess board ...

Evidence is accumulating that sialic acid residues mask tumor antigens.229 4I5 419 5I, 514 Accordingly, several chemically induced, malignant tumors of animals can be brought to regression, or even to disappearance, after re-injection of sialidase-treated tumor-cells. Similar observations have been made with spontaneous breast-tumors of the dog.512 A method of chess-board vaccination with sialidase-treated tumor-cells has been devised, and its results, the theoretical background, the probable involvement of sialidase molecules, and the use of an optimal number of cells have all been extensively discussed. 

Figure 10.10 Optical micrographs of etched domain-inverted patterns on the C " -face, exposed to electron beam Vo = 15 kV and r] = 300/tC/cm2. (a) Circles with 12 /tm diameter and period of 18.75 pm, (b) chess board pattern with 9.325 x 9.325 //2 m squares and period of 18.75 /.tm.

The tetragonal, mackinawite-like sulphide layers in these hydroxide/sulphide minerals (Table 3) contain various proportions of vacant M sites Feo-9S to Feo.78S " The fi actionally-occupied metal sites may be distributed in several different ways, Fig. 10 A, in tochilinite with a centred, orthorhombic motif B, in phases 1 and 2 and tochilinite III (Drits, private communication, 1979) with a simple chess-board pattern C, in tochilinite with a primitive tetragonal motif. (After long standing in aqueous suspension, the vacant sites in tochilinite I were found to have rearranged, also into a chess-board pattern, or to be completely random in their distribution . )... 

In a private communication (1979) Drits has described a (basically) II variety, tochilinite in, which occurs in the tochilinite specimens together with the other tochilinite types. The mutual orientation of the sulphide and brucite layers in this variety is the same as in tochilinite I. Besides having a chess-board distribution of partly occupied Fe te-trahedra in the sulphide layers, tochilinite III displays statistical disorder of octahedral cations in the brudte-like layers. The two lattices have dimensions hsuiphide = CsuipUde =... 

In phase 2 the mackinawite-like sulphide layer (with a chess-board pattern of partly-occupied sites) is said to alternate with an open hydrate/hydroxide layer which has additional water molecules between the octahedra. There is room for some doubt about the structural details of this latter layer set, but the compound does have an SC structure though perhaps without any clear modulation in the semicommensurate direction. Drits (private communication, 1979) reports that the electron diffraction patterns of some... 

Let us consider, for example, a hollow cubical vessel filled half with white and half with black balls, and let the balls be arranged like the squares of a chess-board, so that each white ball is separated by a black ball from the next. If the contents of this cubical vessel are poured into another vessel and then back again into the first, we know by experience that the regularity of the arrangement would in general be destroyed, and that, if we repeat this process several times, it would hardly... 

A typical adlayer structure obtained by the Monte Carlo simulation of 1/2 adsorption on a square lattice is shown in Fig. 8.3. As can be seen, two domains with completely ordered structure are separated by a mismatch boundary. The sublattices corresponding to these domains may be illustrated by the nets of white and black fields on a chess-board. 

A description of the palysepiole polysomatic series and related structures offers the opportunity to mention the main members of the lintisite series of which the crystal stmctures are based on three building modules. One of these modules is a cut of sili-naite [57] (NaLiSi205.2H20 C2/c, a = 14.383, b = 8.334, c = 5.061 A, 13 = 96.6°), a crystal structure that shows a chess-board arrangement of channels and ribbons comparable with that of palysepioles. Modules of silinaite (S) have been used [58] as one of three modules needed to describe the modularity in the lintisite group (Figure 17-14). The other two modules are slabs (L) of the structures of lorenzenite [59]... 

The dimeric structure of j8-CyD is most frequently observed as a building block of crystal structures. There are two types of arrangement of the dimer unit. In the head-to-head channel-type structure, the dimer unit is arranged to form an infinite linear channel. The other type is the layer-type structure, in which dimer units are arranged to form a chess-board-like pattern. Both ends of the dimer cavity are open to the intermolecular space in the adjacent layer. 

In the mixing of particulate solid materials the probability of getting an orderly arrangement of particles, which would represent the perfect mixing, is virtually zero. In practical systems the best mixture attainable is that in which there is a random distribution of the ingredients. An ideal random distribution of two solid components in equal proportions would resemble a chess board, that is, white and black squares in a perfect alternate pattern. In practice, however, a perfectly random mixture is commonly defined as one in which the probability of finding a particle of a constituent of the mixture... 

The chess-board is the world the pieces are the phenomena of the universe the rules of the game... 

The acquisitive Mr. Romney moved hundreds of companies around like people on a chess board. From that detached, distant perspective, perhaps companies seem like people you know, movable objects. 

The structure of Ag2Pb02 [251] bears some relation to that of red PbO. The coordination figure of the Pb atom is of the same type as in tetragonal PbO, but somewhat distorted and instead of forming a chess-board like array, the [Pb04] pyramids are connected in chains. These (Pb02)oo chains are linked by Ag atoms to a three-dimensional network. 

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