Durations

EXAMPLE Calculating the Modified and Macaulay Durations as of2009 of a Hypothetical Bond Having an Annual Coupon of 8 Percent and a Maturity Date of 2019  

Plugging these values into the modified-duration 

To obtain the bond s Macaulay duration, this modified duration is multiplied by (1 + r), or 1.07634, for a value of 7.28354 years. 

Duration varies with maturity, coupon, and yield. Broadly, it increases with maturity. A bond s duration is generally shorter than its maturity. This is because the cash flows received in the early years of the bond s life have the greatest present values and therefore are given the greatest weight. That shortens the average time in which cash flows are received. A zero-coupon bond s cash flows are all received at redemption, so there is no present-value weighting. Therefore, a zero-coupon bond s duration is equal to its term to maturity. 

Duration increases as coupon and yield decrease. The lower the coupon, the greater the relative weight of the cash flows received on the maturity date, and this causes duration to rise. Among the non-plain vanilla types of bonds are some whose coupon rate varies according to an index, usually 

---

Example 4.5 Given that a low rate of production is required, convert the continuous process from Example 4.4 into a batch process. Preliminary sizing of the equipment indicates that the duration of the processing steps are given in Table 4.7. ... 

The advantages of this method are its rapidity (maximum duration, 70 min), the small quantity of sample required (1 pi), and its ease of automation. 

The choice between X-ray fluorescence and the two other methods will be guided by the concentration levels and by the duration of the analytical procedure X-ray fluorescence is usually less sensitive than atomic absorption, but, at least for petroleum products, it requires less preparation after obtaining the calibration curve. Table 2.4 shows the detectable limits and accuracies of the three methods given above for the most commonly analyzed metals in petroleum products. For atomic absorption and plasma, the figures are given for analysis in an organic medium without mineralization. 

Table 5.22 indicates the test references to be conducted on engines according to procedures established by the Coordinating European Council (CEC). Note that these are long-duration tests, some lasting dozens or even hundreds of hours and they are costly. 

Pseudo-viscosity (bitumen) NF T 66-005 IP 72 measurement of flow duration... 

In summary, exploration activities require the integration of different techniques and disciplines. Clear definition of survey objectives is needed. When planning and executing an exploration campaign the duration of data acquisition and interpretation has to be taken into account. 

The time taken to complete a base line study and EIA should not be underestimated. The baseline study describes and inventorises the natural initial flora, fauna, the aquatic life, land and seabed conditions prior to any activity. In seasonal climates, the baseline study may need to cover the whole year. The duration of an EIA depends upon the size and type of area under study, and the previous work done in the area, but may typically take six months. The EIA is often an essential step in project development and should not be omitted from the planning schedule. 

Weathering and transportation is followed by the sedimentation of material. The depositional environment can be defined as an area with a typical set of physical, chemical and biological processes which result in a specific type of rock. The characteristics of the resulting sediment package are dependent on the intensity and duration of these processes. The physical, chemical, biological and geomorphic variables... 

The production profile for oil or gas is the only source ofrevenueior most projects, and making a production forecast is of key importance for the economic analysis of a proposal (e.g. field development plan, incremental project). Typical shapes of production profile for the main drive mechanisms were discussed in Section 8.2, but this section will provide some guidelines on how to derive the rate of build-up, the magnitude and duration of the plateau, the rate of decline, and the abandonment rate. 

When estimating the operating and maintenance costs for various options, it is recommended that the actual activities which are anticipated are specified and costed. This will run into the detail of frequency and duration of maintenance activities such as inspection, overhaul, painting. This technique allows a much more realistic estimate of opex to be made, rather than relying on the traditional method of estimating opex based on a percentage of capex. The benefits of this activity based costing are further discussed in Section 13.0 and 14.0. 

A technique widely used by the industry is Critical Path Analysis (CPA or Network Analysis ) which is a method for systematically analysing the schedule of large projects, so that activities within a project can be phased logically, and dependencies identified. All activities are given a duration and the longest route through the network is known as the critical path. 

In the example above the relationship between four activities of different duration is shown. In this case the critical path is indicated by the lowest route (six days), since the last activity cannot start until all the previous activities have been completed. 

In reality all activities are listed and dependency relationships are identified. Activities are given a duration, and an earliest start and finish date is determined, based on their dependency with previous activities. Latest start and finish dates (without incurring project delays) can be calculated once the network is complete, and indicate how much play there is in the system. 

Once a network has been constructed it can be reviewed to determine whether the completion date and intermediate key dates are acceptable. If not, activity duration reductions have to be sought, for example, by increasing manpower or changing suppliers. 

The "SIMON" Project ("On-line acoustic monitoring of structural integrity of critical power plant components operating at high temperatures") had a duration of 4 years (1.10.1993 -30.09.1997) the Project Consortium included CISE (Project Coordinator, I), MITSUI BABCOCK ENERGY (UK), HERIOT-WATT UNIVERSITY (IK), PROET / EDP (P) and ENEL (I). 

The application of eddy currents in non destructive testing was very developed during the recent years. Adding to the defects characterization, actual studies deal with the metallurgical evaluation of materials. Surface processing allow to increase the material endurance and consequently its life duration. 

The second signal (Signal 2 = Hat) comes from the measurement of duration of the first period of the oscillation voltage. The period is changing in the near of a material flaw. 

The tested blade is flowed through either with hot or cold compressed air with a duration of max. 5 seconds The maximum heat temperature can be adjusted at 250 °C. 

The operator sets TU on the area to be controlled and puts the button B Under the command of SC EDC impulse of proper value and duration is formed in source controllable current (SCC). 

As a result by using the energy accumulated in CB, current impulse of the value of 0.2...0.6 A and the duration of 10...200 ms is created, and this impulse goes through the area being controlled. 

In many industries a non-contact testing of vibrating parts of the various equipment is needed. To prevent the destruction of large aggregates rotating and moving in various directions with the large speed, the parameters of vibrations should be measured very carefully. Besides, vibrations reduce considerably the equipment s duration of life. 

Secondly, a short pulse duration is required in order to achieve a good axial resolution, i.e. two signals close together should be detected without interference. The task can be, for example, to detect a small reflector close to the surface or back wall of the test object, as the inspection has to cover the total volume as complete as possible, including the near-surface regions. 

Block 3 a device for management and synchronisation. Serves for adjusting the parameters of the system, gain factor, input impedance, amplitude and the duration of the initial pulse, as well as ensures a database communication for the further processing by the computer. 

Block 4 a high-voltage generator of the probe pulse, the output value of the amplitude is from 100 to 400V, the duration of the pulse is from 15 to 300 ns. 

The CCF is sensitive to variations in all the signal parameters carrier frequencies, phases, pulse forms, durations and amplitudes. Both signal amplitudes A, and J in formula (1) can factor outside the integral sign and do not define its value. Hence we let the CCF as N= MIA or in normalized form N = NIN . ... 

---