Time, proper

The time difference t in IS is therefore always larger than the time difference r in IS, where the clock is at rest, i.e., a moving clock loses time as compared to a clock at rest. This phenomenon is called relativistic time dilation and might briefly be summarized by the statement that proper time is always the shortest time between two events . 

We close this section by considering the more general case of a time-dependent movement of the clock. With reference to the inertial frame IS the movement of the clock is now described by the velocity v t). In this case no global inertial frame IS can be found where the clock is at rest. However, for each moment t we may consider the inertial frame IS which is moving with the instantaneous velocity v t) relative to IS. In IS the clock is therefore at rest at time t. According to Eq. (3.91), the infinitesimal time intervals dr in IS and df in IS are related by 

The proper time between two events Ei at time and E2 at time fz (ii IS) as shown by the clock in IS is therefore given by the integral 

The most important property of the proper time t is its invariance under Lorentz transformations, i.e., t is a Lorentz scalar and therefore independent of the inertial system. Being defined as the time difference in the inertial system where the clock is at rest, this statement is obviously true. However, in order to formally prove this statement we consider the infinitesimal distance ds for the clock. According to Eq. (3.10) it is given by 

Since ds is a scalar, also dr is a scalar and therefore invariant under Lorentz transformations. 

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Evaluation data taken from the more than 8 thousand reports of the laboratory and field wire ropes inspections show that the visual methods and life time criteria are non adequate to real durability of the ropes in service [4]. The data show that only a very small percentage of all ropes was replaced in a proper time, when one has used a visual inspection. 

The proper choice and appHcation of an insecticide for pest control are predicated upon factors, eg, the life history and ecology of the pest, the relation of pest population to economic damage, the effect of the insecticide on the pest or its plant or animal host, related organisms in the ecosystem, and proper timing of the appHcation to prevent illegal residues at harvest and to avoid damaging of bees and other pollinating insects. 

Operating procedures must be written to clearly identify safety issues. Supervisors must be contacted when process conditions deviate from normal. Proper time and procedures must be maintained to transmit information at shift change. 

Ignition time function (to de-energize ignition at the proper time). 

This means that parts must be ordered in advance for the turnaround and other work must be planned so that the whole operation may proceed smoothly and without holdups that could have been foreseen. This usually means close collaboration with the manufacturer or consultant and the OEM (or specialty service shop) so that handling facilities, service men, parts, cleaning facilities, inspection facilities, chrome plating and/or metaliz-ing facilities, balancing facilities, and some cases even heat treatment facilities, are available and will be open for production at the proper time required. This is the planning, which must be done in detail before the shutdown with sufficient lead-time available in order to have replacement parts available at the job site. 

The only other variables that affect performance are the inlet-discharge valves, which control flow into and out of each cylinder. Although reciprocating compressors can use a variety of valve designs, it is crucial that the valves perform reliably. If they are damaged and fail to operate at the proper time or do not seal properly, overall compressor performance will be substantially reduced. 

It is well-known, for instance, that if one applies tension at properly timed intervals to pull a stretched wire or string, it begins to oscillate laterally. Lord Rayleigh performed an experiment of this kind by attaching a stretched wire to a prong of a tuning fork when the latter... 

In a previous section we mentioned the significance of myosin filament structure. In nematodes two forms of myosin-II, myosin A and B, are required for proper filament stmcture (Epstein, 1988). The two forms of myosin are expressed at the proper time to allow for correct filament assembly. An accessory protein called paramyosin is also required for correct filament assembly. In vertebrate cardiac muscle, there are also two isoforms of myosin-II a-myosin and p-myosin. The proper ratio of these two proteins is of utmost importance for proper muscle activity. The incorrect synthesis of a- and P-myosins results in a severe cardiac disorder known as hypertrophic cardiomyopathy. Genetic transmission of the disease occurs in about 55% of families. The inherited condition is called familial hypertrophic cardiomyopathy (FHC), and this condition is a leading cause of sudden death in young athletes. 

Figure 2. Experimental trial used to Identify transfer function. In this experiment, the reactant flow rate was deliberately varied and the reactant temperature measured on-line in the pilot plant. This allowed us to identify the proper time series model.

Figure 8.3 Normalized Information Index of kj and k2 versus time to determine whether the measurements have been collected at proper times (Ilmax=0.0885, I2max=0.0l23) [reprintedfrom Industrial Engineering Chemistry Fundamentals with permission from the American Chemical Society].

Gonc y This may be a semantic question, but is it possible that what is happening is that things are simply slowed down in the cdc2 mutant, and that this is the primary reason why asymmetric determinants cannot get in place at the proper time ... 

The interval ds is also known as the proper time between two nearby events ( r,t) and (r + dr,t + dt). This formulation does not imply that any one of the axes is transformable into any other by a rotation, since the complex... 

This expression demonstrates use of the Einstein summation convention 6. The significance of r is made clear by examining a particle momentarily at rest in a Lorentz system. The components of the vector, transformed dx = (0, 0, 0, icdt ) and dr2 = —(1 /c dx dx = [dt )2. Thus dr is the time interval on a clock travelling with the particle and is therefore referred to as the interval of the particle s proper time or world time. The relationship between dr and an interval of time as measured in a given Lorentz system can be derived directly by expanding the equation... 

The four-velocity u is defined as the rate of change of the position vector of a particle with respect to its proper time... 

The City Transit supervisors have received numerous complaints over the last several weeks about buses on several routes running hot. Drivers are reminded that each route has several checkpoints at which drivers should check the time. If the bus is ahead of schedule, drivers should delay at the checkpoint until it is the proper time to leave. If traffic makes it unsafe for a driver to delay at a particular checkpoint, the driver should proceed at a reasonable speed to the next stop and hold there until the bus is back on schedule. 

Introducing the proper-time variable r, we eventually find... 

We can easily see, from Eq. (54), that the q degree of freedom becomes superfluous and theory must become trivial in the limit m —> 0, which is equivalent to A —> 0 in the chiral limit all the observables must be independent of q. This salient feature is consistent with the form of DCDW. The integral with respect to the proper time r is not well defined as it is, since it is still divergent due to the r 0 contribution. Regularization proceeds by replacing the lower bound of the integration range by 1/A2, which corresponds to the momentum cut-off in the MCOR scheme. 

The disease is caused by a fungus growing superficially on stems and undersides of coffee leaves. At the proper time multitudes of microscopic spores are released into the air and are carried to other coffee trees. The spores lodge on coffee... 

Whitehead also found the proper timing of such applications to be very important. The best results were obtained when the applications were made the first or second day after starting the flooding of the fields the second time. 

Previous work at this station had shown that when heavy weevil infestations were present, drainage properly timed to control weevils resulted in higher yields. Evidence has also been found that drainage in the absence of heavy infestations depresses yields. The yield data on the experimental plots showed that the undrained plots, both treated and untreated, yielded almost 5 bushels more per acre than the drained plots. The weevil infestation in the plots was very light in 1953, which probably accounts for the fact that yields were not increased by controlling weevils by the use of insecticides. 

The next step (granting good motivation and inability to act within traditional structures) is to choose a course of action which has maximum impact. Pick a responsible public media expert to carry the message. Make sure the news gets to the proper people. It is extremely important to choose the proper place and the proper time. Perhaps the choice must be a period when there is a low input of other news. Get it to where the people will read it. If possible do it in association with the professional society so that there will be proper support in case of a threat. Many of the points on whistleblowing have been spelled out in currently available books (2). 

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