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For ordinary materials, the bulk compressibility (sum of the linear compressibilities on the three axes) is positive, that is, an increase in pressure squeezes the material to a smaller volume. This condition is required for mechanical stability. [8] However, under very specific conditions, materials can exhibit a compressibility that can be ...
The following is a list of notable unsolved problems grouped into broad areas of physics. [1]Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
There are several proposed solutions to solve the strong CP problem. The most well-known is Peccei–Quinn theory , involving new scalar particles called axions . A newer, more radical approach not requiring the axion is a theory involving two time dimensions first proposed in 1998 by Bars, Deliduman, and Andreev.
The strong CP problem is solved automatically if one of the quarks is massless. [7] In that case one can perform a set of chiral transformations on all the massive quark fields to get rid of their complex mass phases and then perform another chiral transformation on the massless quark field to eliminate the residual θ-term without also introducing a complex mass term for that field.
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
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A polynomial-time problem can be very difficult to solve in practice if the polynomial's degree or constants are large enough. In addition, information-theoretic security provides cryptographic methods that cannot be broken even with unlimited computing power. "A large-scale quantum computer would be able to efficiently solve NP-complete problems."
BPP is one of the largest practical classes of problems, meaning most problems of interest in BPP have efficient probabilistic algorithms that can be run quickly on real modern machines. BPP also contains P , the class of problems solvable in polynomial time with a deterministic machine, since a deterministic machine is a special case of a ...