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in the database If a match is not found, the entire block is sent uncompressed, requiring l log A bits A ag is used to tell the decoder whether a match location is being described or the sequence itself Parts (a) and (b) give some preliminaries you will need in showing the optimality of xed-database LZ in part (c) (a) Let xl be a -typical sequence of length l starting at 0, and let Rl (x l ) be the corresponding recurrence index in the in nite past , X 2 , X 1 Show that E Rl (X l )|X l = x l 2l(H + ) , where H is the entropy rate of the source (b) Prove that for any > 0, Pr Rl (X l ) > 2l(H + ) 0 as l .

3), the design of soil water management strategies for such purposes is far from easy, and expert guidance must be sought In terms of speci c toxicity effects, boron is particularly problematical, as it is toxic to many plants at relatively low absolute concentrations ( 3 mg/L), which are sometimes exceeded even in otherwise fresh groundwaters Besides their role as components of salinity, sodium and chloride are directly toxic to many plants when present at high concentrations (Table 73) Most other toxicity problems are highly crop-speci c; for detailed guidance the reader is referred to Ayers and Westcot (1985) Category B: Big industrial uses of groundwater Every industry has its own speci c requirements If the water is only required for swilling down work yards, then any old groundwater will do.

1. 2. 3. 4.

However, in many cases the water quality needs are so exacting that it is unreasonable to expect any natural groundwater to meet the users requirements; consequently, much pre-conditioning of feed water is undertaken by industry In the most stringent sectors (eg some activities in the microelectronics industry), preconditioning.

Budgeting is part of the planning process. It can involve decisions concerning the day-to-day management of an operation or involve plans for as far ahead as five years. The various types of budgets include capital, operating, departmental, master, fixed, and flexible. Budgeting has three main purposes: To provide estimates of future sales revenues and expenses To provide short- and long-term coordinated management policy To provide control by comparing actual results with budgeted plans and to take corrective action, if necessary In a small operation, budgets can be prepared by an individual or by a committee in a large organization. In all cases, whether for a day, a year, or some other period, budgets should be prepared in advance of the start of the period. There are several advantages of budgets: They involve participation of employees in the planning process, thus improving motivation and communication. They necessitate, in budget preparation, consideration of alternative courses of action. They provide a goal, and a standard of performance to be accomplished, with subsequent comparison of actual results with that standard. If flexible budgets are used, they permit quick adaptation to unforeseen, changed conditions. They require those involved to be forward-looking, rather than looking only at past events.

(Hint: Expand the probability by conditioning on strings x l , and break things up into typical and nontypical Markov s inequality and the AEP should prove handy as well) (c) Consider the following two xed databases: (i) D1 is formed by taking all -typical l-vectors; and (ii) D2 formed by taking the most recent L = 2l(H + ) symbols in the in nite past (ie, X L , , X 1 ) Argue that the algorithm described above is asymptotically optimal: namely, that the expected number of bits per symbol converges to the entropy rate when used in conjunction with either database D1 or D2 1311 Tunstall coding The normal setting for source coding maps a symbol (or a block of symbols) from a nite alphabet onto a variablelength string.

(19)

Event Activate BeforeDoubleClick BeforeRightClick Calculate Change Deactivate FollowHyperlink PivotTableUpdate* SelectionChange Action that triggers the event The worksheet is activated. The worksheet is double-clicked. The worksheet is right-clicked. The worksheet is calculated (or recalculated). Cells on the worksheet are changed by the user or by an external link. The worksheet is deactivated. A hyperlink on the sheet is clicked. A pivot table on the sheet is updated. The selection on the worksheet is changed.

The converse follows from Jensen s inequality, since E log S S log E log 1 = 0. S S (16.23)

R2 0.999 0.999 0.999