Question: "What is the theory applied to?" Context: "for any constant c. Matrix groups over these fields fall under this regime, as do adele rings and adelic algebraic groups, which are basic to number theory. Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions. An advanced generalization of this idea, adapted to the needs of algebraic geometry, is the etale fundamental group." Answer:
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Answer: the needs of algebraic geometry

Question: "How can a USB be modified to have more power?" Context: "Some USB devices require more power than is permitted by the specifications for a single port. This is common for external hard and optical disc drives, and generally for devices with motors or lamps. Such devices can use an external power supply, which is allowed by the standard, or use a dual-input USB cable, one input of which is used for power and data transfer, the other solely for power, which makes the device a non-standard USB device. Some USB ports and external hubs can, in practice, supply more power to USB devices than required by the specification but a standard-compliant device may not depend on this." Answer:
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Answer: dual-input

Question: "What occurred in the 9th year of the 20th century?" Context: "In 1901, 10-inch disc records were introduced, followed in 1903 by 12-inch records. These could play for more than three and four minutes respectively, while contemporary cylinders could only play for about two minutes. In an attempt to head off the disc advantage, Edison introduced the Amberol cylinder in 1909, with a maximum playing time of 4 minutes (at 160 rpm), which in turn were superseded by Blue Amberol Records, which had a playing surface made of celluloid, a plastic, which was far less fragile. Despite these improvements, during the 1910s discs decisively won this early format war, although Edison continued to produce new Blue Amberol cylinders for an ever-dwindling customer base until late in 1929. By 1919 the basic patents for the manufacture of lateral-cut disc records had expired, opening the field for countless companies to produce them. Analog disc records would dominate the home entertainment market until they were outsold by the digital compact disc in the late 1980s (which was in turn supplanted by digital audio recordings distributed via online music stores and Internet file sharing)." Answer:
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Answer:
advantage, Edison introduced the Amberol cylinder