Translation action

For example, consider the translation action (R, R, cr) defined above. Let V denote the complex vector space of complex-valued functions of one real variable. The induced representation of the additive group R on V is given by... 

The group could be a geometrical group such as the group of all translations, rotations, scalings, etc. The desired classification of pattern is invariant under the action of the group, i.e. 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

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... 

Acetaldehyde [75-07-0] (ethanal), CH CHO, was first prepared by Scheele ia 1774, by the action of manganese dioxide [1313-13-9] and sulfuric acid [7664-93-9] on ethanol [64-17-5]. The stmcture of acetaldehyde was estabhshed in 1835 by Liebig from a pure sample prepared by oxidising ethyl alcohol with chromic acid. Liebig named the compound "aldehyde" from the Latin words translated as al(cohol) dehyd(rogenated). The formation of acetaldehyde by the addition of water [7732-18-5] to acetylene [74-86-2] was observed by Kutscherow] in 1881. 

Economic evaluation is an assessment of the probable benefit or reward of a proposed course of action, relative to other choices. Although the benefit usually takes the form of a financial return, in environmental management, transportation (qv), health care, and other social areas, the benefit may be a social gain instead. Some method is then developed to translate the social gain into a monetary equivalent. The discussion herein is limited to the financial return expected from some type of production or service activity. 

The action in these mills has been studied photographically and mathematically [Rumpf, Chem. Ing. Tech., 32(3 I29-I35 (5), 335-342 (I960h ATS translations, 668GT, S44GJ],... 

Batsanov, S.S., Chemical Reactions Under the Action of Shock Compression, in Detonation Critical Phenomena, Physicochemical Transformations in Shock Waves (edited by Dubovitskii, F.I.), Chernogolovko, 1978, pp. 197-210. Translation, UCRL-Trans-11444, pp. 187-196. 

Phase 4 - Production Planning. The critical process operations from Phase 3 are ranked with production requirement issues, ultimately translating the important customer requirements to production planning and establishing important actions to be taken. 

There are two different scales of deformation in any adhesive contact (1) the bulk scale of deformation which is characterized by the radius a of contact area over which the compressive forces are significant and (2) the zone of action of surface forces or the cohesive zone at the edge of the contact, characterized by the length d over which the tensile forces are dominant. When the contact boundary is moving with a speed u, the two scales of deformation translate into two time scales, one on the order of a/ v) and the other of the order of (d/v). 

The ESDs were then translated into associated event trees. A generic event tree was developed for all initiators not involving LOCA. The generic transient event tree for each category of the transient initiators and loss of offsite power were specialized by the impact of the initiators on the safety and support systems, from the success criteria of the mitigating systems, and the initiator-specific human actions which were modeled in the fault trees. 

The implementation plan you and your team developed (Chapter 5) provides the framework for the installation phase it defines your strategy, priorities, resources, and timetable. The specific PSM systems you have designed (Chapter 6) provide the substance they ate the activities you plan to install. What remains is the series of tasks requited to translate words on paper into tangible action. 

Couple. If two forces of equal magnitude, opposite direction, and different lines of action act on a body, they produce a tendency for rotation, but no tendency for translation. Such a pair of forces is called a couple. The magnitude of the moment... 

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

The elucidation of the X-ray structure of chymotrypsin (Ref. 1) and in a later stage of subtilisin (Ref. 2) revealed an active site with three crucial groups (Fig. 7.1)-the active serine, a neighboring histidine, and a buried aspartic acid. These three residues are frequently called the catalytic triad, and are designated here as Aspc Hisc Serc (where c indicates a catalytic residue). The identification of the location of the active-site groups and intense biochemical studies led to several mechanistic proposals for the action of serine proteases (see, for example, Refs. 1 and 2). However, it appears that without some way of translating the structural information to reaction-potential surfaces it is hard to discriminate between different alternative mechanisms. Thus it is instructive to use the procedure introduced in previous chapters and to examine the feasibility of different... 

The signals generated as described above have to be translated into an action that allows the cell to effectively adapt to a challenge (Figure 43-1). Much of this... 

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