Translational representations

In order to allow the implementation of pre- and post-processors on computers that use different character representations, translation tables for conversion into and from such private alphabets may be defined. Exchanging neutral files with others using private alphabet coding is a matter of agreement between the exchanging partners. Files coded in a private alphabet are not considered as conforming to this specification ... 

The treatment of translational motion in three dimensions involves representation of particle motions in tenns... 

Single surface calculations with a vector potential in the adiabatic representation and two surface calculations in the diabatic representation with or without shifting the conical intersection from the origin are performed using Cartesian coordinates. As in the asymptotic region the two coordinates of the model represent a translational and a vibrational mode, respectively, the initial wave function for the ground state can be represented as. 

Let us introduce the coherent potential Vk(E) which is thought to be dependent on energy E and exciton momentum k. The coherent potential is translational invariant in the site representation. The Hamiltonian (1) is transformed with the coherent potential taken into account as... 

As was said in the introduction (Section 2.1), chemical structures are the universal and the most natural language of chemists, but not for computers. Computers woi k with bits packed into words or bytes, and they perceive neither atoms noi bonds. On the other hand, human beings do not cope with bits very well. Instead of thinking in terms of 0 and 1, chemists try to build models of the world of molecules. The models ai e conceptually quite simple 2D plots of molecular sti uctures or projections of 3D structures onto a plane. The problem is how to transfer these models to computers and how to make computers understand them. This communication must somehow be handled by widely understood input and output processes. The chemists way of thinking about structures must be translated into computers internal, machine representation through one or more intermediate steps or representations (sec figure 2-23, The input/output processes defined... 

Before considering other concepts and group-theoretical machinery, it should once again be stressed that these same tools can be used in symmetry analysis of the translational, vibrational and rotational motions of a molecule. The twelve motions of NH3 (three translations, three rotations, six vibrations) can be described in terms of combinations of displacements of each of the four atoms in each of three (x,y,z) directions. Hence, unit vectors placed on each atom directed in the x, y, and z directions form a basis for action by the operations S of the point group. In the case of NH3, the characters of the resultant 12x12 representation matrices form a reducible representation... 

From the information on the right side of the C3v eharaeter table, translations of all four atoms in the z, x and y direetions transform as Ai(z) and E(x,y), respeetively, whereas rotations about the z(Rz), x(Rx), and y(Ry) axes transform as A2 and E. Henee, of the twelve motions, three translations have A and E symmetry and three rotations have A2 and E symmetry. This leaves six vibrations, of whieh two have A symmetry, none have A2 symmetry, and two (pairs) have E symmetry. We eould obtain symmetry-adapted vibrational and rotational bases by allowing symmetry projeetion operators of the irredueible representation symmetries to operate on various elementary eartesian (x,y,z) atomie displaeement veetors. Both Cotton and Wilson, Deeius and Cross show in detail how this is aeeomplished. 

Two-Dimensional Representation of Chemical Structures. The lUPAC standardization of organic nomenclature allows automatic translation of a chemical s name into its chemical stmcture, or, conversely, the naming of a compound based on its stmcture. The chemical formula for a compound can be translated into its stmcture once a set of semantic rules for representation are estabUshed (26). The semantic rules and their appHcation have been described (27,28). The inverse problem, generating correct names from chemical stmctures, has been addressed (28) and explored for the specific case of naming condensed benzenoid hydrocarbons (29,30). 

R = (i/ r) require translations t in addition to rotations j/. The irreducible representations for all Abelian groups have a phase factor c, consistent with the requirement that all h symmetry elements of the symmetry group commute. These symmetry elements of the Abelian group are obtained by multiplication of the symmetry element./ = (i/ lr) by itself an appropriate number of times, since R = E, where E is the identity element, and h is the number of elements in the Abelian group. We note that N, the number of hexagons in the ID unit cell of the nanotube, is not always equal h, particularly when d 1 and dfi d. 

Next, translate the Fischer projection of i-serine to a three-dimensional representation, and orient it so that the lowest ranked substituent at the chirality center is directed away from you. 

Antisense Oligonucleotides. Figure 1 Schematic representation of the action of antisense oligonucleotides. They bind to their respective target mRNA preventing protein translation. 

The potential function on the left side of this can immediately be translated into the Fock representation by using Eq. (8-147) and (8-149) ... 

To make these notions precise, the transformation properties of the wavefunction x under spatial and time translations as well as under spatial rotations and pure Lorentz transformations must be specified and it must be shown that the generators of these transformations form a unitary representation of the group of translations and proper Lorentz transformations. This can in fact be shown5 but will not be here. 

We have noted that the unitary operators U(a,A) define a representation of the inhomogeneous group. If we denote by P and AT, the (hermitian) generators for infinitesimal translations and Lorentz transformations respectively, then... 

However, using translation invariance and the representation (11-655), the left-hand side of this last expression is also equal to... 

Fig. 2.—Representation of three mutually interpenetrating cubic frameworks of trisilver cobalticyanide, each displaced to another by translation by one third along the body diagonal of the unit cube.

Our interpretation of the finding from the study is that even within a single level of representation, i.e. sub-microscopic, some students were unable to translate between different modes of representation. In this case, there was evidence that students were unable to translate their verbal mode of understanding into the diagrammatic mode (or visual mode). If the translation between different modes within the same level is problematic, it would be very challenging when students are required to smoothly mentally move about and link all the three - the macro, the sub-microscopic and symbolic levels - of chemical phenomena. 

Stoichiometry, do not need these visualization skills. Rather, they involve the understanding of representational conventions, such as the meaning of arrows used in diagrams, and how the verbal or mathematical mode of representation relates to and is translated into the visual mode. 

Keig, P. F., Rubba, P. A. (1993). Translations of the representations of the structure of matter and its relationship to reasoning, gender, spatial reasoning, and specific prior knowledge. Journal of Research in Science Teaching, 30(%), 883-903. 

Based on a comprehensive review of chemistiy education literature, Wu and Shah (2004) suggest live principles for designing multimedia tools that help students understand concepts and develop their representational skills (e.g., making translations among representations, creating representations to externalize thinking, and... 

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