Time order

Time-resolved fluorescence is perhaps the most direct experunent in the ultrafast spectroscopist s palette. Because only one laser pulse interacts with the sample, the mediod is essentially free of the problems with field-matter time orderings that arise in all of the subsequently discussed multipulse methods. The signal... 

The main cost of this enlianced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. Wlien the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is nnambiguous. When the pump and probe pulses temporally overlap in tlie sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feymuan diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to detenuine the various contributions to the sample response [125]. 

The market situation is that a few large producers of frozen and chilled foods supply a large number of retailers. This had led to the development of distribution stores, where goods are delivered in bulk, stored for a short time, order-picked and then sent out to the individual supermarkets and other outlets. 

As defined above, F consists of three operators acting simultaneously on the state G >. More generally, one may prescribe any of 10 possible time-orderings to the operators H, and. That is, specify certain intermediate state dependencies, so that, for example FilG >= (H )( G >) would in general be expected to yield results different from, say, F2 G > H( ( G>)). While we will be solely concerned with the synchronous time ordering defined above, we do not expect the qualitative results to depend critically on this choice. 

Let the time-ordering operator 16 S, when applied to the product... 

By introducing the time-ordering chronological operator8 P which rewrites a product of time labeled operators as the product of these same operators ordered according to their time label, the one with the earliest time label standing farthest to the right, we can rewrite the expansion (10-151) in the form... 

Thirring, W. E., 598,724 Thirteen moment solution of Boltzmann s equation, 40 Thomas, C. J., 313,317 Time averages, 114 of different time functions, 132 "Time development matrix, 410 Time-ordering chronological operator, 416,603 Time reversal... 

STAT order A one-time order given as soon as possible. 

LEUCOVORIN. When leucovorin is administered after a large dose of methotrexate, the timing of tiie administration is outlined by tiie primary health care provider. It is essential that the leucovorin be given at tiie exact time ordered because tiie purpose of folinic acid rescue is to allow a high dose of a toxic drug to remain in tiie body for only a limited time... 

To determine molecular motions in real time necessitates the application of a time-ordered sequence of (at least) two ultrafast laser pulses to a molecular sample the first pulse provides the starting trigger to initiate a particular process, the break-up of a molecule, for example whilst the second pulse, time-delayed with respect to the first, probes the molecular evolution as a function of time. For isolated molecules in the gas phase, this approach was pioneered by the 1999 Nobel Laureate, A. H. Zewail of the California Institute of Technology. The nature of what is involved is most readily appreciated through an application, illustrated here for the photofragmentation of iodine bromide (IBr). 

If the nucleus in the emitter is under the influence of time-dependent forces, it is convenient to modify Eq. (99) by introducing, instead of Eq. (96), the time-ordered operator ... 

Zeolites are formed by crystallization at temperatures between 80 and 200 °C from aqueous alkaline solutions of silica and alumina gels in a process referred to as hydrothermal synthesis.15,19 A considerable amount is known about the mechanism of the crystallization process, however, no rational procedure, similar to organic synthetic procedures, to make a specifically designed zeolite topology is available. The products obtained are sensitive functions of the reaction conditions (composition of gel, reaction time, order of mixing, gel aging, etc.) and are kinetically controlled. Nevertheless, reproducible procedures have been devised to make bulk quantities of zeolites. Procedures for post-synthetic modifications have also been described.20 22... 

High-temperature flow-reactor studies [60,61] on benzene oxidation revealed a sequence of intermediates that followed the order phenol, cyclopentadiene, vinyl acetylene, butadiene, ethene, and acetylene. Since the sampling techniques used in these experiments could not distinguish unstable species, the intermediates could have been radicals that reacted to form a stable compound, most likely by hydrogen addition in the sampling probe. The relative time order of the maximum concentrations, while not the only criterion for establishing a mechanism, has been helpful in the modeling of many oxidation systems [4,13]. 

Explanation. A user may ask for explanation of the line of reasoning at any time during an expert system consultation. RuleMaster presents explanation as a list of premises and conclusions in English-like text. The explanation describes the execution path which led up to the current conclusion or question. Explanation is presented in proof ordering, which usually differs from the order in which the questions and conclusions were encountered. This is perceived as more relevant and understandable than the time-ordered presentation of fired rules, as is present in most expert system approaches. 

The theory of statistical mechanics provides the formalism to obtain observables as ensemble averages from the microscopic configurations generated by such a simulation. From both the MC and MD trajectories, ensemble averages can be formed as simple averages of the properties over the set of configurations. From the time-ordered properties of the MD trajectory, additional dynamic information can be calculated via the time correlation function formalism. An autocorrelation function Caa( = (a(r) a(t + r)) is the ensemble average of the product of some function a at time r and at a later time t + r. 

Figure 15.7 Factor combinations for a completely randomized design investigating the effect of temperature. Fruit number is an arbitrarily assigned, qualitative factor. Numbers beside factor combinations indicate the time order in which experiments were run.

By plotting the sum T and difference D in time ordered sequence the variation of random and systematic errors can be monitored between analytical runs. 

Systematic error is evident in the clear ellipticity of the distribution. The time ordered sequence shows a non-random "walk" between systematic error quadrants. An excursion from one systematic quadrant to another and a subsequent return is evident. The distribution is non-normal, with too few points in the central region. 

---