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The relationship between bandpass and resolution is widely accepted in many disciplines and applications. It is the basis of the Heisenberg uncertainty relationship in quantum mechanics, information transmission limits in communication systems, and diverse resolution limits in imaging and measurement theory. Despite its popularity, however, the relationship is not inviolable. The Whittaker Shannon sampling theorem is a more precise statement of the link between bandwidth and resolution than is the uncertainty relationship. As discussed in Section 3.6, the sampling theorem tells us that the number of samples necessary to characterize a signal restricted to the frequency band [ B, B] and the spatial support [ X, X] is 4BX. The signi cance of this statement for the resolution of a continuous signal is not entirely clear. Assuming that these samples are uniformly distributed, the sampling theorem may suggest that the spatial resolution is equal to the sample spacing, 1/(2B). As discussed in Section 7.1, however, the sampling theorem also provides a prescription for interpolation between samples, meaning that the effective spatial resolution may be less than the sample period. We address this paradox by considering more carefully the measurement model g(x) sinc[2B(x y)] f ( y)dy n(x) (10:20)

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1. Click File Open or press Ctrl+O. The Open dialog box appears. 2a. If you don t see the list of disks in Windows 7, click the triangle to the left of Computer in the navigation pane. The list of available disks appears. You also could navigate to a save location using the Libraries choices in the navigation pane, if desired.

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Research actions required . . . For securing the supplies of fossil fuels - Exploration technologies . Basin modelling and geochemical methods . High resolution seismic methods . Other physical methods - Improving the oil recovery yield . Modelling and optimising production . Improving production architectures . Secondary and tertiary recovery methods - Offshore hydrocarbon production . Deep offshore production . Submarine production systems - Extra-heavy crudes . Development of environmentally friendly processes . Hot production with low CO2 emissions - Natural gas . Exploration technologies for discovering new gas resources (deep gas, nonconventional gas) . Offshore liquefaction and chemical conversion . Unconventional gas (coal bed methane, hydrates, dissolved gas, tight gas) . New transport technologies (by pipe and tankers, compressed natural gas or CNG, mini LNG) - Coal . Clean coal technologies ue gases treatment . Gasi cation technologies . High ef ciency power plants . Electricity generation with CO2 capture and storage (CCS) - Synthetic fuels . Synthetic gas production processes . Production pathways from coal and natural gas . Production with CCS

This chapter discussed ways in which SOA and cloud computing are interdependent and mutually reinforcing business initiatives for an enterprise. We suggested that SOA success can lead to cloud computing success based on the SOA patterns that have been pursued in the industry to date. While SOA and cloud offer some overlapping bene ts to your enterprise, they each bring unique value as well. The following are some suggestions for you, and some things you should begin doing tomorrow:

(7.28) dt The final inequality results from the fact that w ( q ,q'lp, p ' ) is nonnegative, and, in view of the monotonic behavior of the logarithm, the two remaining factors involving differences must have the same sign. We have thus found a functional H B that can only decrease or stay constant in the course of the time evolution described by Boltzmann's equation; (7.28) is Boltzmann's H theorem. It suggests that, as an increasing function with proper dimensions, S = -kBHB plays the role of an entropy. Furthermore, Boltzmann's equation clearly describes an irreversible time evolution. A steady state in the evolution of the single-particle distribution function can be reached when dHB/dt = 0; at this, collisionsestablish an equilibration in momentum space at each position T . In such a situation, we obtain

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