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Time-ordering arguments

The functions written in capital letters in (4.2.13)-(4.2.16) are the Fourier transforms of the functions written in small letters in (4.2.5)-(4.2.8). The superscript s indicates that the nonlinear transfer functions K (o)i,. .., o> ) in (4.2.15) and (4.2.16) are the Fourier transforms of impulse-response functions with indistinguishable time arguments, where the causal time order ti > >r is not respected. These transfer functions are invariant against permutation of frequency arguments. Equivalent expressions for the Fourier transforms of impulse-response functions with time-ordered arguments cannot readily be derived. [Pg.132]

The components removed by background subtraction include those which cannot be removed by time ordering arguments. In particular, for scans near T= 0, the delay between kLo and ks will be very close to the delays between k o... [Pg.191]

The starting point is equation (3.4), in which the interaction representation (3.5) has not yet been introduced. This equation can also be rewritten in a condensed form using time ordering by means of the following additional trick. Although W does not depend on time we write W(t), where the argument t merely serves to indicate its position in the chronological order. Similarly we write B(t) for the constant operator B. Then (3.4) is the same as... [Pg.392]

The lesser and greater functions are not time-ordered and arguments of the operators are not affected by time-ordering operator. Nevertheless we can write such functions in the same form (283). The trick is to use one time argument from the forward contour and the other from the backward contour, for example... [Pg.271]

Besides P, which showed not be confused with the momentum operator P of the H-bond bridge, is the Dyson time-ordering operator [57] acting on the Taylor expansion terms of the exponential operator in such a way so that the time arguments involved in the different integrals will be t > t > t". [Pg.414]

Fig. 4 illustrates the time-dependence of the length of top s water column in conical capillary of the dimensions R = 15 pm and lo =310 pm at temperature T = 22°C. Experimental data for the top s column are approximated by the formula (11). The value of A is selected under the requirement to ensure optimum correlation between experimental and theoretical data. It gives Ae =3,810 J. One can see that there is satisfactory correlation between experimental and theoretical dependencies. Moreover, the value Ae has the same order of magnitude as Hamaker constant Ah. But just Ah describes one of the main components of disjoining pressure IT [13]. It confirms the rightness of our physical arguments, described above, to explain the mechanism of two-side liquid penetration into dead-end capillaries. [Pg.617]

In 1913 Bohr showed, by an argument that was essentially a combination of classical mechanics and quantum mechanics as it was known at that time, that the energy spectrum (ordered set of energy values) of hydrogen is given by... [Pg.178]

The latest trend is to smaller beads in smaller columns, as this saves eluent and shortens the time for a chromatographic analysis. This argument can be correct if only one suitable detector is used. However, these modern small columns are not optimal for a combination of detectors. So-called multiple detection is a combination of some detectors with different measurement principles (differential refractometer, spectral photometer, light-scattering detector, on-line viscometer) behind the last column, mostly in series, seldom in a branched ( parallel ) order. In this way, the tedious preparative fractionation of a polymer sample can often be avoided. [Pg.440]

In Section II, we presented the computational model involved in branching from a node, cr, to a node aa,. In this model, it was necessary to interpret the alphabet symbol a, and ascribe it to a set of properties. In the same way, we have to interpret o- as a state of the flowshop, and for convenience, we assigned a set of state variables to tr that facilitated the calculation of the lower-bound value and any existing dominance or equivalence conditions. Thus, we must be able to manipulate the variable values associated with state and alphabet symbols. To do this, we can use the distinguishing feature of first-order predicates, i.e., the ability to parameterize over their arguments. We can use two place predicates, or binary predicates, where the first place introduces a variable to hold the value of the property and the second holds the element of the language, or the string of which we require the value. Thus, if we want to extract the lower bound of a state o-, we can use the predicate Lower-bound Ig [cr]) to bind Ig to the value of the lower bound of cr. This idea extends easily to properties, which are indexed by more than just the state itself, for example, unit-completion-times, v, which are functions of both the state and a unit... [Pg.304]


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See also in sourсe #XX -- [ Pg.173 , Pg.174 , Pg.175 , Pg.176 , Pg.177 ]




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