Problem: Group (mathematics):

Finite symmetry groups such as the Mathieu groups are used in coding theory, which is in turn applied in error correction of transmitted data, and in CD players. Another application is differential Galois theory, which characterizes functions having antiderivatives of a prescribed form, giving group-theoretic criteria for when solutions of certain differential equations are well-behaved.u["] Geometric properties that remain stable under group actions are investigated in (geometric) invariant theory.

Geometric Invariant theory studies what kind of equations?
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A: unanswerable

Problem: Memory:

A UCLA research study published in the June 2006 issue of the American Journal of Geriatric Psychiatry found that people can improve cognitive function and brain efficiency through simple lifestyle changes such as incorporating memory exercises, healthy eating, physical fitness and stress reduction into their daily lives. This study examined 17 subjects, (average age 53) with normal memory performance. Eight subjects were asked to follow a "brain healthy" diet, relaxation, physical, and mental exercise (brain teasers and verbal memory training techniques). After 14 days, they showed greater word fluency (not memory) compared to their baseline performance. No long term follow up was conducted, it is therefore unclear if this intervention has lasting effects on memory.

Can one increase their brain unefficency?
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A: unanswerable

Problem: Geography of the United States:

By total area (water as well as land), the United States is either slightly larger or smaller than the People's Republic of China, making it the world's third or fourth largest country. China and the United States are smaller than Russia and Canada in total area, but are larger than Brazil. By land area only (exclusive of waters), the United States is the world's third largest country, after Russia and China, with Canada in fourth. Whether the US or China is the third largest country by total area depends on two factors: (1) The validity of China's claim on Aksai Chin and Trans-Karakoram Tract. Both these territories are also claimed by India, so are not counted; and (2) How US calculates its own surface area. Since the initial publishing of the World Factbook, the CIA has updated the total area of United States a number of times.

Which country is the worlds fourth largest?
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A: Canada

Problem: Hellenistic period:

Developments in painting included experiments in chiaroscuro by Zeuxis and the development of landscape painting and still life painting. Greek temples built during the Hellenistic period were generally larger than classical ones, such as the temple of Artemis at Ephesus, the temple of Artemis at Sardis, and the temple of Apollo at Didyma (rebuilt by Seleucus in 300 BCE). The royal palace (basileion) also came into its own during the Hellenistic period, the first extant example being the massive fourth-century villa of Cassander at Vergina.

What is a Greek royal palace called?
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A:
basileion