Time interval

Intervals (hours) Number Observed. Number Expected. 

The complete expectations are given in the last column of Table 6.4. 

The closeness of fit can be tested with the test. Here a value of 6.13 is obtained which with (11 — 2) = 9 degrees of freedom corresponds to a probability to 75%. The fit is thus excellent. 

The time distribution of incidents when expressed in the present form is rather curious in that the commonest interval is the shortest. 

It is a valuable property of variance that if a process has a number of factors each making a contribution to the variance of the final product, then this total variance is equal to the sum of the component variances( ). 

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The cold filter plugging point (CFPP) is the minimum temperature at which a given volume of diesel fuel passes through a well defined filter in a limited time interval (NF M 07-042 and EN 116 standards). For conventional diesel fuels in winter, the CFPP is usually between —15 and —25°C. 

Data transmission rate per foot is a function of both pulse frequency and rate of penetration. Sensors acquire and transmit data samples at fixed time intervals and therefore the sampling per foot is a function of rate of penetration. Current tools allow a real time sampling and transmission rate similar to wireline tools as long as the penetration rate does not exceed about 100 ft/h. If drilling progresses faster or if there are significant variations in penetration rate, resampling by depth as opposed to time intervals may be required. 

In Austria, as well as all over Europe, the first and repetition tests of all pressure equipments including steam drums are required for security reasons within fixed time intervals. These repetitive inspections are done differently in the most European countries, but most time these inspections include, according to the European Pressure Equipment Directive" and the specific national law any kind of over-pressurisation (e.g. hydrotest) and visual inside inspection. 

The analog AE signals are converted into binary signals (0/1 = below/above floating tlireshold in the elementary sampling time interval), simultaneously on all channels fig-2). 

Finally, the concentrated localized AE events are represented on the monitor in the form of a histogram "number of localized AE events vs axial coordinate", which is automatically updated at user-defined time intervals. 

Data sailing automatic data saving occurs after a user-preselectable time interval, typically 1 to 3 minutes. 

Off-line analysis of stored data review of the stored data, organize data in different presentation windows, plot AE and plant parameters data so as to enable comparison and coirelation with the possibility to present data (histogram of AE events vs position, plant parameters and/or AE parameters vs time) conditioned in terms of time interval (initial time, final time) and/or position interval (defined portion of the component = initial coordinate, final coordinate) and/or plant parameters intervals (one or more plant parameters = initial value, final value). 

The specific results of well over 1 year of continued monitoring will be discussed in a second paper. It is pointed out here that the AEBIL monitoring system installed in the power plant for the above monitoring purposes has efficiently and continuedly performed during this time interval, with no instrumentation reliability problems. 

Figure 5 provides an example of AE monitoring data from 22.01.1997 to 03,03.1997, in terms of time history of the main plant parameters (fig.Sa), as well as of the AE RMS values (fig. 5b). Normally, very little or no events were recorded, with the exception of the above period, in which an AE activity, very much concentrated in time and space, could be observed a sharp step in cumulative AE events takes place in a short, well defined time interval. A smaller sharp step in EA events had been observed a few days earlier, in the same position. 

At - time span between two neighbouring time intervals. 

The process of mass transfer is repeated over and over to synchronize time intervals, used. 

To speed up the process of attainment of the temperature steady value one can use special operations calculation without a kiln rotation, using large time intervals and calculation in two-dimensional R-tp geometry without regard for heat and mass transfer along an axis The program for realization of discussed simulation algorithms enables to calculate temperature in cells, a total number of which can not exceed 130 thousands A circular kiln structure can contain up to three layers. 

Gate Start and Width. Define the start position and width, in millimetres, of the gate used for defining the time interval in which the peak amplitude of the signal will be measured. 

Shoe Delay. Defines the shoe, or wedge, delay, in tenths of microseconds, of the prohe being used. This control is used to adjust the zero point of time interval measurement to correspond to the instant that the ultrasound pulse enters the test piece. 

Converting to current dQldt where dt is an infinitesimal time interval and to resistance SA one can rewrite this equation in the fomi... 

Figure A3.1.2. A collision cylinder for particles with velocity v striking a small region of area A on the surface of a contamer within a small time interval 5f Here is a unit nomial to the surface at the small region, and pomts into the gas.

We again assume that there is a time interval 5/which is long compared with the duration of a binary collision but is too short for particles to cross a cell of size 5r. Then the change in the number of particles in 8r8v in time 8/ can be written as... 

We suppose that each particle in the small region suffers at most one collision during the time interval t, and calculate the change in f. 

If we wish to know the number of (VpV)-collisions that actually take place in this small time interval, we need to know exactly where each particle is located and then follow the motion of all the particles from time tto time t+ bt. In fact, this is what is done in computer simulated molecular dynamics. We wish to avoid this exact specification of the particle trajectories, and instead carry out a plausible argument for the computation of r To do this, Boltzmann made the following assumption, called the Stosszahlansatz, which we encountered already in the calculation of the mean free path ... 

The unimolecular rate law can be justified by a probabilistic argument. The number (A Vdc x dc) of particles which react in a time dt is proportional both to this same time interval dt and to the number of particles present (A Vc x c). However, this probabilistic argument need not always be valid, as illustrated in figure A3.4.2 for a sunple model [20] ... 

Case 1. The particles are statistically distributed around the ring. Then, the number of escaping particles will be proportional both to the time interval (opening time) dt and to the total number of particles in the container. The result is a first-order rate law. 

One may justify the differential equation (A3.4.371 and equation (A3.4.401 again by a probability argument. The number of reacting particles VAc oc dc is proportional to the frequency of encounters between two particles and to the time interval dt. Since not every encounter leads to reaction, an additional reaction probability has to be introduced. The frequency of encounters is obtained by the following simple argument. Assuming a statistical distribution of particles, the probability for a given particle to occupy a... 

To detemiine k E) from equation (A3.12.9) it is assumed that transition states with positivefomi products. Notmg that / f = p dqf/dt, where p is the reduced mass of the separating fragments, all transition states that lie within and + dq with positive will cross the transition state toward products in the time interval dt = pj dqf p. Inserting this expression into equation (A3.12.9), one finds that the reactant-to-product rate (i.e. flux) through the transition state for momenPim p is... 

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefimctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval r has elapsed r may be called the lifetime of the almost stationary resonance state. 

Mbelonging to the complementary manifold = M, In a second time interval the superposition... 

In the present section, we concentrate on coherent preparation by irradiation with a properly chosen laser pulse during a given time interval. The quantum state at time t may be chosen to be the vibrational ground... 

To be more specific, we assume that for a possible preparation step the Hamiltonian might be given during the preparation time interval [I jTo] expression ... 

IVR in tlie example of the CH clnomophore in CHF is thus at the origin of a redistribution process which is, despite its coherent nature, of a statistical character. In CHD, the dynamics after excitation of the stretching manifold reveals a less complete redistribution process in the same time interval [97]. The reason for this is a smaller effective coupling constant between the Fenni modes of CHD (by a factor of four) when... 

Figure A3.13.il. Illustration of the time evolution of redueed two-dimensional probability densities I I and I I for the exeitation of CHD between 50 and 70 fs (see [154] for further details). The full eurve is a eut of tire potential energy surfaee at the momentary absorbed energy eorresponding to 3000 em during the entire time interval shown here (as6000 em, if zero point energy is ineluded). The dashed eurves show the energy uneertainty of the time-dependent wave paeket, approximately 500 em Left-hand side exeitation along the v-axis (see figure A3.13.5). The vertieal axis in the two-dimensional eontour line representations is...

Figure A3.13.12. Evolution of the probability for a right-handed ehiral stmetnre (fiill eiirve, see ( equation (A3,13.69))) of the CH eliromophore in CHD2T (a) and CHDT2 ( ) after preparation of ehiral stnietures with multiphoton laser exeitation, as diseussed in the text (see also [154]). For eomparison, the time evolution of aeeording to a one-dimensional model ineluding only the bending mode (dashed enrve) is also shown. The left-hand side insert shows the time evolution of within the one-dimensional ealeulations for a longer time interval the right-hand insert shows the time evolution within the tln-ee-dimensional ealeulation for the same time interval (see text).

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