Estimate sums

Mathematics in Action: Prealgebra Problem Solving, Third Edition, is intended to help college mathematics students gain mathematical literacy in the real world and simultaneously help them build a solid foundation for future study in mathematics and other disciplines. Our authoring team used the AMATYC Crossroads standards to develop a threebook series to serve a large and diverse population of college students who, for whatever reason, have not yet succeeded in learning mathematics.
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Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Quantitative sum product estimates on diﬀerent sets...
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Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: A quantiﬁed version of Bourgain’s sumproduct estimate in Fp for subsets of incomparable sizes...
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The average American consumes an estimated 50 tons of food in a lifetime. This staggering amount of food represents the sum of daily choices each of us makes regarding the type, quality, and quantity of foods. These critical choices in turn reflect a complex interplay of many factors, including family upbringing, religious or philosophical beliefs, as well as practical matters, such as the cost and availability of foods and beverages. Importantly, Americans are increasingly selecting food for health reasons.
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The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of LaneEmden type, including the following two model problems: −∆p u = uq + µ, Fk [−u] = uq + µ, u ≥ 0, on Rn , or on a bounded domain Ω ⊂ Rn . Here ∆p is the pLaplacian deﬁned by ∆p u = div ( u up−2 ), and Fk [u] is the kHessian deﬁned as the sum of k × k principal minors of the Hessian matrix D2 u (k = 1, 2, . . . ,...
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Obviously, (1.2) implies the same estimate for M(Z(QN, P)). It was suggested in [2] that in this case the (1+logN) term could be omitted at the cost of multiplying by a constant. The above suggestion means that in the passage from the sum of moduli to the modulus of the sum in (1.1) essential cancellation should take place. As a contribution towards this end the authors showed that any straight line L intersects Z(QN, P) in a set FP of linear measure less than 2eP−1N. Further information about the complement of FP under certain conditions on {zk} is obtained in [1].
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Because an interest rate swap is just a series of cash flows occurring at known future dates, it can be valued by sim ply summing the present value of each of these cash flows. In order to calculate the present value of each cash flow, it is necessary to first estimate the correct discount factor (df) for each period (t) on which a cash flow occurs. Dis count factors are derived from investors’ perceptions of in terest rates in the future and are calculated using forward rates such as LIBOR. The following formula calculates a theoretical rate (known as the “Swap Rate”) for...
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For all buildings combined, the average plugload equipment density in units per 1000 gross ft 2 , was about 9 for office equipment and 14 for miscellaneous equipment, for a sum of about 23 units per 1000 gross ft 2 . Educational buildings, where large floor areas are devoted to classrooms, had the lowest density of both office and miscellaneous equipment. However, twothirds of computers and monitors found in educational buildings (and thus most of the energy savings potential) were concentrated in computerbased classrooms.
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There are many underutilized and vacant urban lots throughout the world, which are held by private investors who are interested in maximizing their wealth by land development. Three approaches are commonly used for property and land valuation (Appraisal Institute, 2001; Baum and Crosby, 1988; Isaac, 2002). The first is the cost approach, which estimates the property by summing the land value and the depreciated value of any improvements.
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Howarth et al. [10] developed an approach for estimating the net nitrogen inputs to a region N that is highly correlated with average nitrogen transport in the rivers draining temperate regions (Fig. 2). Net N input to a region was deﬁned as sum of N in fertilizer used, biological N ﬁxation of agricultural crops, oxidized N in atmospheric deposition in the region, and the N in food and feed imported to the region minus the N in food and feed exported from the region. This approach assumes that there is no net gain or loss of N from soil organic matter.
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Other additional compensation is comprised of retroactive payments, one‐time payments (i.e., those made annually in a lump sum, such as grievance awards, attendance incentives, uniform allowances and lump sum merit increases), and miscellaneous payments such as short term disability payments. The health related benefit costs per employee (excluding retirees) were $23,380 (for detail see Table 15).
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Multiple sclerosis (MS) is not a new disease. Its effects on the brain were described in the 1830s, and it was identified as a distinct clinical entity in the 1860s. In fact, writings from the Middle Ages appear to describe individuals with this condition. MS is the most common neurological disorder of young adults; there are approximately 350,000 people with MS in the United States and an estimated 2 million patients worldwide. Research on the disorder has been energetic over recent decades. In 1996, the U.S. National Institutes of Health (NIH) spent almost $83 million on MS research.
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Having ranked countries by their relative macroeconomic performance during the recent crisis, we explore possible explanations for this crosseconomy variation. Table 2 summarises four categories of variables measuring: banking system structure, trade openness, financial openness, and monetary and fiscal policy frameworks. Except where otherwise noted, all of these variables are measured at the end of 2007. We also consider the policy response to the crisis, looking at measures such as monetary policy easing, fiscal stimulus and bank bailouts.
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The level of poultry production for each region is given in the first column of table 4. It is the 1998 estimate of poultry meat production (obtained from the Food and Agriculture Organization FAOSTAT database). The level of poultry production in the two composite regions is determined by first identifying which countries are net poultry exporters in FAO trade data. Then, the level of poultry production in the ROWE region is the sum of production in these exporting countries. Poultry production for the ROWM region is obtained by subtracting the quantity of poultry meat produced...
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