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function A complete injury results in the total absence of all-voluntary movement or sensation below the level of injury An incomplete injury allows for the retention of some sensation or movement below the level of injury Thus, diagnosis describes the level of the vertebral fracture as well as the extent of the neurological de cit (eg, a complete lesion at the fth cervical vertebrae will be described as C5, complete ) Levels of Injury and Functional Goals The levels of injury to the spinal cord have been divided into ten general regions in which functional abilities cluster in persons with complete lesions Damage to the spinal cord in the cervical region results in the greatest functional variability Individuals with injuries to the cervical, or C region of the spinal cord between levels C1 and C3, are most likely to depend on ventilator assistance for breathing (see Figure 18.

(1.2) which agrees with the number of bits needed to describe X. In this case, all the outcomes have representations of the same length. Now consider an example with nonuniform distribution. Example 1.1.2 Suppose that we have a horse race with eight horses taking part. Assume that the probabilities of winning for the eight horses 1 1 1 1 1 are 1 , 1 , 1 , 16 , 64 , 64 , 64 , 64 . We can calculate the entropy of the horse 2 4 8 race as 1 1 1 1 1 1 1 1 1 1 H (X) = log log log log 4 log 2 2 4 4 8 8 16 16 64 64 = 2 bits. (1.3)

Alternatively, if labor (and other costs) have been broken down for use with CVP analysis (see 8) into their fixed and variable elements, then this information is already available for use in budgeting. Once all costs have been determined, they can be deducted from total sales revenue to determine each department s operating income.

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2) Implantation of a phrenic nerve pacemaker may be an option for mechanical assistance in breathing For individuals with C1 to C3 SCIs, talking may be dif cult, very limited, or impossible Movement of the head and neck is limited, and functional goals for these individuals focus on communication and wheelchair mobility Assistive technologies, such as a computer for speech or typing, and sip-and-puff chairs and switches, increase function and independence Head and neck control increases somewhat for individuals with a C3 or C4 SCI Ventilator assistance is usually required at the initial stages of rehabilitation but prolonged use is not likely With the relative increase in motor movement and the use of adaptive equipment at this level of injury, some individuals may have limited independence in feeding and control over environmental variables such as adjustable beds and wheelchair tilting to assist in pressure relief.

all but quicksands this turns out to be so small that is has no measurable effect on the elevation of the ground surface overlying the aquifer Poorly designed abstraction wells in uncon ned aquifers can cause localized subsidence if they withdraw so much sand from the aquifer that voids are created around the well This form of subsidence is often referred to as being due to migration of nes or sand pumping It occurs by the same processes of seepage erosion and piping which were described in Sections 823 As in natural manifestations of these processes, signi cant entrainment of sand in pumped groundwater can only occur where the hydraulic gradient exceeds 1 In practical terms this means that this type of subsidence is strictly limited to the innermost portions of the cone of depression developed around any one pumping well.

However, because sand pumping damages expensive pumping machinery and clogs pipes and reservoirs, groundwater engineers go to considerable lengths to prevent it from occurring Using industry-standard water well designs (with screens and gravel packs where necessary; see Figure 37), and proper well development immediately after drilling (see Section 331), most water wells yield no appreciable sand during long-term operation Where sand/gravel aquifers are con ned by mudstones, or where thick beds of mud occur within the sand/gravel aquifer, major land subsidence can result from sustained groundwater abstraction To understand why this occurs it is necessary to recall the concept of elastic storage which was introduced in Section 14 Groundwater is often under great pressure within con ned aquifers.