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We then recover the nite-dimensional version of the canonical quantization: [a, a ] = I N N |N 1 N 1| The Pegg Barnett construction, which amounts to an adequate change of orthornormal basis in CN , gives for the ground number state |0 a random phase that avoids some of the drawbacks encountered in previous developments Note that taking the limit N is questionable within a Hilbertian framework; this process must be understood in terms of mean values restricted to some suitable subspace and the limit has to be taken afterwards In [193] the pertinence of the states (1445) was proved by the expected value of the commutator with the number operator The problem appears when the limit is taken since it leads to an approximate result More recently an interesting approach to the construction of a phase operator was used by Busch, Lahti, and their collaborators within the framework of measurement theory [194, 195, 197] (see also [196]) Phase observables are characterized as phase-shift-covariant positive operator measures, with the number operator playing the part of the shift generator



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2 Download and Install OCR Feature: If you haven't installed the OCR component yet, a pop-up window will appear then. Press the "Click to Download " button to ...

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a country to control its wealth Today, what would a conqueror do, for example, with tiny but rich Singapore Chain every factory worker to their electronics assembly lines so that they could ll orders for Apple and Sony Tom Friedman certainly agrees with Angell His Dell Theory of Con ict Prevention posits that no two countries that are both part of a major global supply chain for multinational companies like Dell Computer ght wars against each other2 While tongue-in-cheek, Friedman notes how nations in today s globalized economy bear huge nancial costs attacking other nations with which they have strong economic ties Countries still compete with one another and have different national interests; however, the changes in cross-border economic competition have also altered the ideas of security and power From about 1500 to 1900, nations that possessed valuable land and key natural resources also held power A country could increase power by seizing weaker nations and exploiting their physical resources But then the terms of global competition shifted from territory to trade By the period following World War II, a nation s power was not tied to the resources it conquered but to its productive workforce and state-of-the-art factories For example, Germany and Japan which both lost so much in WWII grew stronger globally through cultivating skilled labor and competitive products, not remilitarizing Economic power has continued to grow in importance relative to military power Today, natural resources remain incredibly useful and armed forces have their place, but true Macro Quantum power is measured in factories and workforces that produce goods, of ces and studios that cultivate creative brainpower and services, and money for mobile investment The historic evolution from violent competition of nation-states to a world where complex nancial and trade interconnections have nearly eliminated classic cross-border warfare (see Figure 41) is the de ning feature of our era But if cross-border trade encourages peace, you may wonder why the two world wars occurred after this evolution began and if a world war could happen today Trade alone is not enough to discourage war Complex interdependence (interdependence in economics, security, energy, and other policy areas), cemented by international institutions,.





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Let us now reformulate the construction of the Pegg Barnett phase operator along the lines of coherent state quantization The observation set X is the set of N equidistant angles on the unit circle: 2 m , m = 0, 1, , N 1 N We equip X with the discrete equally weighted normalized measure: X = m = 0 + f (x) (dx) =

UV resonance Raman spectroscopy (UVRR), Sec 61, has been used to determine the secondary structure of proteins The strong conformational frequency and cross section dependence of the amide bands indicate that they are sensitive monitors of protein secondary structure Excitation of the amide bands below 210 nm makes it possible to selectively study the secondary structure, while excitation between 2 10 and 240 nm selectively enhances aromatic amino acid bands (investigation of tyrosine and tryptophan environments) (Song and Asher, 1989; Wang et al, 1989, Su et al, 1991) Quantitative analysis of the UVRR spectra of a range of proteins showed a linear relation between the non-helical content and a newly characterized amide vibration referred to as amide S, which is found at 1385 cm (Wang et al, 1991) UV resonance Raman saturation spectroscopy (Sec 6.

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60 50 40 30 20 10 0 Intrastate conflicts Internationalized intrastate Interstate conflicts Extrastate conflicts

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