Original state

The above discussion is now generalized to arbitrary spin values. First, we note that twice application of the time-reversal operator leads the system back to its original state v /, that is, T r t = ct t. Thus, we have T = cl. Next, consider the following two relations... 

We prove our statement in two steps First, we consider the special case of a Hilbert space of three states, the two lowest of which are coupled strongly to each other but the third state is only weakly coupled to them. Then, we extend it to the case of a Hilbert space of N states where M states are strongly coupled to each other, and L = N — M) states, are only loosely coupled to these M original states (but can be stiongly coupled among themselves). 

The reader may think of a finite dimensional subspace of the original state space. This subspace may, e.g., be associated with a suitable discretization in space. For a generalization of Thm. 3 to the infinitely dimensioned case, see [5]. 

The product of this nucleophilic substitution then re acts with water restoring the enzyme to its original state and giving the observed products of the reac tion... 

Natural resins are generally described as solid or semisolid amorphous, fusible, organic substances that are formed in plant secretions. They are usually transparent or translucent yeUow-to-brown colored, and are soluble in organic solvents but not in water. The principal uses for natural resins are in varnishes, printing inks, adhesives, paper size, and polymer compositions. The term natural resins includes tree and plant exudates, fossil resins, mined resins, and shellac. They often have been altered from their original state during isolation and processing. For some appHcations, the resins have been chemically modified to increase their industrial utiUty. 

If flow sheet cannot meet the product specs as originally stated, determine if they can be relaxed. Are products specs which can be obtained with given flow sheet actually satisfactory If yes, solution is complete. 

The ionized developers are then capable of diffusing. Transfer of an electron reduces the silver and generates the semiquinone ion radical of the auxiUary developer (eq. 10). In turn, a dye developer molecule of the adjacent layer transfers an electron to the semiquinone, returning the auxiUary developer to its original state and leaving the dye developer in the semiquinone state (eq. 11). Further oxidation of the semiquinone leads to the quinone state of the dye developer. 

This result was first discussed by Buckingham (8) and stated in its present form by Langhaar (23). It states in effect that an equation is dimensionally homogeneous if and only if it can be reduced to a relationship among a complete set of B-numbers. Buckingham s result (8) was originally stated as Theorem 2. 

Units employed in diffusivity correlations commonly followed the cgs system. Similarly, correlations for mass transfer correlations used the cgs or Enghsh system. In both cases, only the most recent correlations employ SI units. Since most correlations involve other properties and physical parameters, often with mixed units, they are repeated here as originally stated. Common conversion factors are listed in Table 1-4. 

The value of ( )b for water was originally stated as 2.6, although when the original data were reanalyzed, the empirical best fit was 2.26. 

Unlike the famous royal Pazyryk Kurgans, the ancient burials on the Ukok Plateau have been untouched by grave robbers they were discovered in their original state. Among numerous unique finds, the most remarkable ones are well-preserved human hair and nails, tails and manes of the horses buried together with the people and also the ash from the censer. 

A closed system moving slowly through a series of stable states is. said to undergo a reversible process if that process can be completely reversed in all thermodynamic respects, i.e. if the original. state of the system itself can be recovered (internal reversibility) and its surroundings can be restored (external irreversibility). An irreversible process is one that cannot be reversed in this way. 

ATP is synthesized at the T site and released from the O site. Two additional passes through this cycle produce two more ATPs and return the enzyme to its original state. 

Archer, owing to very unfortunate coincidences, had mistaken acid potassium tartrate for the acetylamino acid. Goldfarb et al. prepared authentic 5-acetylamino-2-thiophenecarboxylic acid, mp 230 232°C (methyl ester, mp 171-171.5°C ethyl ester, mp 161°C), through reduction of 5-nitro-2-thiophenecarboxylic acid with Raney nickel in acetic anhydride and proved the structure by Raney nickel desulfurization to 8-aminovaleric acid. They also confirmed that the acid mp 272-273°C (methyl ester, mp 135-136°C ethyl ester, mp 116-117°C) is 4-acetylamino-2-thiophenecar boxy lie acid as originally stated by Steinkopf and Miiller. The statement of Tirouflet and Chane that the acid obtained upon reduction and acetylation of 5-nitro-2-thiophenecarboxylic acid melts at 272°C must result from some mistake as they give the correct melting point for the methyl ester. 

As an alternate consideration, assume various pressure drops/foot of packing (same) and determine effect on calculated column diameter. Use the same input information as original stated conditions, then ... 

For any actual process, it is impossible to devise a means of restoring to its original state every system participating in the process. 

Recalling Bennett s and Fredkin s trick to erase the garbage bits, the way in which the reversible logic circuit in figure 6.9 can be made to act as a real reversible serial-adder circuit is to first operate the circuit as shown, store the desired output, and then operate it backwards using the output and all intermediary garbage bits as new input. After all operations are completed in the reverse direction, we will be left with our desired answer stored on the side and with the serial-adder circuit back in its original state ready for another run. 

Inelastic deformation can cause product failure arising out of a massive realignment of the plastic s molecular structure. A product undergoing inelastic deformation does not return to its original state when its load is removed. It should be remembered that there are plastics that are sensitive to this situation and others that are not. 

Though theories have been proposed (32-35) to explain this phenomenon, the mechanism of fluorescence is still not yet fully understood. Jankow and Willis (36) proposed a mechanism which involves a direct excitation of the molecule or an impurity to an excited state, followed by internal conversion and then reversion back to the original state with emission of light. This mechanism can be explained as follows A molecule in the lowest vibrational level of the ground state A is transferred to a certain vibrational level in the excited state D. The molecule tends to cascade into the lowest vibrational level of state D by collisions with other excited molecules. It passes from state D to state C and then to state B by radiationless transi-... 

A true fluid flows when it is subjected to a shear field and motion ceases as soon as the stress is removed. In contrast, an ideal solid which has been subjected to a stress recovers its original state as soon as the stress is removed, The two extremes of behaviour are therefore represented by ... 

Viscoelasticity illustrates materials that exhibit both viscous and elastic characteristics. Viscous materials tike honey resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain. Viscoelasticity is the result of the diffusion of atoms or molecules inside an amorphous material. Rubber is highly elastic, but yet a viscous material. This property can be defined by the term viscoelasticity. Viscoelasticity is a combination of two separate mechanisms occurring at the same time in mbber. A spring represents the elastic portion, and a dashpot represents the viscous component (Figure 28.7). 

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