Arrays, one-dimensional

Fig. 3. Alignment of amide dipoles in polyamide crystals (a) for a two-dimensional array of an odd nylon, nylon-7, (b) for a one-dimensional array of an odd—odd nylon, nylon-5,7 (c) for one-dimensional arrays of polyamides containing even segments an even nylon, nylon-6 an even—even nylon, nylon-6,6 ...

Fig. 44.22. Three commonly used Kohonen network structures, (a) One-dimensional array (b) two-dimensional rectangular network (each unit, apart from the borderline units has 8 neighbours) and (c) two-dimensional hexagonal network (each unit, apart from the borderline units, has 6 neighbours). (Reprinted with permission from Ref. [70]).

Fig. 3 Structural arrangement in (DIET)2[Crm(isoq)2CNCS)4] (phase a) of the inorganic and organic moieties showing the one-dimensional arrays and the remarkably short intermolecular contacts (thin gray line) between iodine-substituted donors and sulfur atoms of the isothiocyanato ligands...

As shown in Fig 1. the model is a one-dimensional array of equal mass, hard-point particles, the even-numbered particles form a set of... 

Fig. 8. Concentration B in reaction mechanism for diffusion coefficient of X much less than that of Y, necessary to achieve instability in a system in which the autocatalytic mechanism occurs on a one-dimensional array of local sites, versus logarithm of site density a (solid line). Dashed and dotted lines are for the isolated and continuum site limit, respectively.

Finally, secondary Au- -C bonds have been found in some adducts of the triangular gold(I) complex [Au3(MeN=COMe)3], where they function as electron donors, with nitro-9-fluorenones as acceptors. The solid-state structures of [Au3(MeN=COMe)3]-[2,4,7-trinitro-9-fluorenone] and [Au3(MeN=COMe)3]-[2,4,5,7-tetranitro-9-fluorenone] [50] consist of one-dimensional arrays in which the planar gold(I) trimers and the nearly planar organic molecules are interleaved with the gold trimers, making face-to-face contact with the nitro-aromatic portion of... 

The degree of association through —H- -Au bonds can vary depending on the complex analyzed and, thus, we can find one-dimensional arrays, such as in the... 

We can analyze the connection between randomness at small scales and order at large scales by an infinite one-dimensional array of discrete boxes which are positioned along the x-axis (Csanady, 1973). The boxes are numbered by m = 0, 1, 2,... where the box m = 0 is situated at x = 0 (Fig. 18.1). Let us assume that at time t = 0 an object (molecule, particle, etc.) begins its random walk at box m = 0 (Fig. 18.1, top line). At fixed times t = At, 2At, 3At... the object jumps randomly either to the left or to the right. The path marked by A represents the path of an object which jumps twice to the left, then once to the right and once to the left again and finally twice to the right. At time t = 6At, the object happens to end up in the same box (m = 0) from which it started. 

We have considered scalar, vector, and matrix molecular properties. A scalar is a zero-dimensional array a vector is a one-dimensional array a matrix is a two-dimensional array. In general, an 5-dimensional array is called a tensor of rank (or order) s a tensor of order s has ns components, where n is the number of dimensions of the coordinate system (usually 3). Thus the dipole moment is a first-order tensor with 31 = 3 components the polarizability is a second-order tensor with 32 = 9 components. The molecular first hyperpolarizability (which we will not define) is a third-order tensor. 

Consider a hypothetical material consisting of an infinite one-dimensional array of hydride ions (H ). 

Figure 8.20 Condition for constructive interference for a one-dimensional array of scattering centers (top). Constructive interference occurs along the cones that reflect the rotational symmetry of the one-dimensional arrangement (middle). For a two-dimensional crystal, constructive interference is obtained along lines (bottom).

Two different of supramolecular synthons have been detected in the two polymorphs of the carbamazepine-saccharin cocrystal system [45]. In the Form-I structure, the carbamazepine molecules formed a homo-synthon, with the saccharine molecules also forming a hydrogen-bonded homodimer. The interaction of these two synthons resulted in formation of a one-dimensional array of molecules in a crinkled tape motif. In the Form-II structure, a heterosynthon is formed by the interaction of a carbamazepine and a saccharin molecule. This latter synthon packs in one-dimensional chains that extended along the crystallographic c-axis. 

The process is as follows the term number m is first input, then two one-dimensional arrays will be created as a = Array[t, m, u = Array[l, m[. a circle sentence Do[c = [[ ]] /. 1 + c, i,m ] with introducing the parameter 2 is used to produce the expression... 

It was known from experiment that all the spectral lines of an element could be represented as the differences of a relatively small number or terms. If these terms are arranged in a one-dimensional array 7 = Ti,T2,..., the atomic frequencies form a two-dimensinal array of elements u nm) = Tn—Tm,... 

Longitudinal Elastic Waves on a 1-D Line of Equidistant Equal Atoms. Consider next the longitudinal motion of a one-dimensional array of E equal atoms of mass M (Fig. 5.7). These atoms at rest are equidistant—that is, spaced a (meters) apart—and can interact via Hooke s law with force constant kH (N m ), but only with their nearest neighbors. Let u be the longitudinal displacement of atom n from its equilibrium position. The net Hooke s law force on atom n, due to the displacements un, un v and un +, is... 

Figure 21 Schematic illustrating the one-dimensional array of layers considered in the mixed potential model of nuclear fuel corrosion in a failed (flooded) nuclear waste container.

Increasing the amount of XIV Cl in a solution containing 2 + C60 complex also resulted in the rapid decrease of absorption at 452 nm (attributed to fullerene-fullerene interactions in a closed-packed one-dimensional array of C6o inside the nanotubular cavity), indicating that the encapsulation of ammonium ions led to partial disruption of the close-packed C60 array resulting in the formation of a mixed complex ion-pair/C6o host-guest complex, where the ion pair is intercalating between the fullerenes. 

To simplify the solution, imagine an analogous one-dimensional array as shown in Fig. 3.6. Carry out a direct-space summation of the long-range attractive and repulsive forces felt by any arbitrary ion, extending across this one-dimensional... 

Figure 3.6. Calculation of the Madelung constant for a one-dimensional array of cations and anions, before and after aliovalent ion exchange.

---