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whereT and j - I are the presentand previousiterations. To start the solution process,initial guesses must be made for the x's. A simple approach is to assumethat they are all zero.Thesezeroscan be substituted into Eq. (12.1a). which can be used to calculatea new value for -r1 : bt latr. Then we substitute this new valueof r1 alongwith the previous guess zerofor-rr into Eq. (12.1b)to compute'a of new is value for x2. The process repeated Eq. (12.1c)to calculatea new estimate x3. Then for for we return to the first equationand repeatthe entire procedureuntil our solutionconverges closely enoughto the true values.Convergence be checkedusing the criterion that for can .lli' Jri -r/'I e,,.': l--l lr;l :XAMPLE .l l2 Gouss-Seidel ethod M ProblemStqtemeni. Use the Gauss-Seidel methodto obtainthe solutionfor 3xr-0.1r2-0.2x3: 1.85 0.lxr* 7.r2-0.3xj: -19.3 0 . 3 1 10 . 2 t 2 + l 0 r 3 71.4 Note that the solutionis ixlr : |3 -2.5 i ). < x 100% r, rll rr
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This chapter has focused on kinematic model derivations, navigation mechanization, error analysis, initialization, and INS aiding. The main references for this chapter were [27, 33, 37, 50, 73, 95, 110, 111, 116, 126, 129, 138]. The simplifying notation in Table 11.1 is based on that de ned in [138]. More examples and more detailed discussion of the trajectories from the linearized inertial navigation system error dynamics is presented in [27, 138]. Gravity is discussed in [37, 67, 73, 127]. Inertial instruments have only been discussed very brie y herein. The various types of inertial instruments, their characteristics, and tradeo s are discussed in considerable depth in, for example, [73, 83, 126]. The distinction between inertial and kinematic accelerations is discussed well in, for example, [37, 73]. Detail technical descriptions of inertial sensor modeling and design can be found in [73, 126]. The sensor error models presented herein are drawn from [27, 93, 138]. Strap-down INS speci c implementation formulas are discussed in [15, 16, 115]. In particular, [115] presents numeric formulas for multi-rate implementations where the highest rate loops transform the speci c force measurements to navigation frame accounting for navigation frame rotation. The lower rate loops integrate the navigation frame velocity and position di erential equations. The topic of how to complete the mechanization equation computation most e ciently by performing certain subsets of the calculations in speci c coordinate frames is addressed in [15, 16].
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Wednesday, and Friday) so that in any workout you re not training more than two bodyparts utilizing giant sets. Doing too much of this particular training method will invariably prove too taxing for your central nervous system to produce any results whatever. On Monday, you will train your legs and shoulders (Workout One); on Wednesday, you will be training your chest and triceps (Workout Two); and on Friday, you ll be training your back and biceps (Workout Three). You ll rest over the weekend and then start the cycle over again on the following Monday. Here is the workout routine:
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tients with idiopathic pseudotumor cerebri. Their observation that the venous pressure drops immediately upon the reduction in CSF pressure supports the notion that the increased venous pressure is secondary (furthermore, they describe patients with normal venous pressures in the sagittal and transverse sinuses). The unsatisfactory nature of all the currently offered theories of causation of pseudotumor cerebri are reviewed extensively by Walker; but at the moment, our reading of the literature suggests that venous stenosis, from granulations or from some yet unde ned functional change, does account for a large proportion of what had previously been considered to be idiopathic. However, this mechanism does not apply in all cases. How the venous changes relate to obesity and gender is also unclear. Perhaps some individuals have a congenital con guration of the venous sinuses that is exaggerated with obesity of elevated systemic venous pressures. Some additional comments about the physiologic changes in CSF ow and pressure in relation to alternative mechanisms of pseudotumor may be informative. Using the method of constant infusion manometrics, Mann and coworkers demonstrated an increased resistance to CSF out ow, due in their view to an impaired absorptive function of the arachnoid villi. Other authors have attributed intracranial venous hypertension to raised intra-abdominal and cardiac lling pressures, the mechanical result of obesity (Sugerman et al). Others, on inconclusive evidence, have attributed benign intracranial hypertension to an increase in brain volume secondary to an excess of extracellular uid or blood volume within the cranium (Sahs and Joynt, Raichle et al). An interesting related nding has been an elevated level of vasopressin in the CSF but not in the blood (Seckl and Lightman). In the goat, this peptide causes a rise in ICP and a reduction in CSF absorption. This raises the possibility that the pseudotumor state is due to an aberration of the transit of water in the cerebrum. Finally, Jacobson and colleagues have made the provocative observation that serum vitamin A levels (in the form of retinol) are 50 percent higher than expected, on average, in patients with pseudotumor a difference that is not explained by obesity. Because the levels were considerably lower than in cases of hypervitaminosis A with pseudotumor (see below), the meaning of these ndings is uncertain. Symptomatic Causes of Pseudotumor Cerebri (Table 30-1) The main considerations in cases of generalized elevation of ICP and papilledema in the absence of an intracerebral mass are covert occlusion of the dural venous sinuses, gliomatosis cerebri, occult arteriovenous malformation, and carcinomatous, infectious, or granulomatous meningitis. Although occlusion of the dural venous sinuses and their large draining veins is sometimes equated with pseudotumor, these cases are not, strictly speaking, idiopathic. When papilledema occurs in the context of a persistent headache, particularly if the pain is centered near the vertex or medial parietal areas or if there are seizures, venous occlusion is likely. Venous sinus thrombosis can be detected in most instances by careful attention to the appearance of the superior sagittal and lateral sinuses on the T1-weighted MRI or on the contrast-enhanced CT scans, as discussed in Chap. 34 (page 734). Isolated cortical vein thrombosis on the cerebral convexity does not cause pseudotumor. A large cerebral arteriovenous malformation (AVM), by causing an increase both of venous pressure and cerebral blood volume, can also give rise to a pseudotumor syndrome. In a few of our cases, these changes in the physiology of the cerebral circulation were made evident by the appearance of early venous ow on the angiogram or by thrombosis of the superior sagittal sinus.
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The hypothalamus, like the thalamus, lies buried deep within the cerebrum. It contains a number of control centers for homeostasis. It includes, for instance, the temperature control center. Recall ( 1) that oral body temperature usually varies up-and-down in a roughly S-shaped pattern, within its normal range. And remember ( 13) how thermoregulation (homeostasis of body temperature) is maintained by processes occurring within the skin, such as sweating and vasodilation. The logical question we can ask is, Okay, just what part of the body is it, that controls the mechanisms responsible for carrying out thermoregulation The answer is this: Certain neurons within the temperature control center of the hypothalamus establish and maintain the set-point for oral body temperature. A set-point is de ned as the long-term average value of a body variable: that is, it is the point at which the variable seems to be set. Oral body temperature, for example, seems to be set at an average value of about 98.6 degrees F. [Study suggestion: Visualize the thermostat in your own house or apartment. What is the usual set-point temperature where you keep the thermostat ] Obviously, when certain factors raise the body temperature too far above this set-point (or too far below it), then some type of control system has to be engaged. Usually, the human body uses a negative feedback control system to correct or minimize the amount of change.
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