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In particle physics, the doublet–triplet (splitting) problem is a problem of some Grand Unified Theories, such as SU(5), SO(10), and . Grand unified theories predict Higgs bosons (doublets of S U ( 2 ) {\displaystyle SU(2)} ) arise from representations of the unified group that contain other states, in particular, states that are triplets of ...
In quantum mechanics, a doublet is a composite quantum state of a system with an effective spin of 1/2, such that there are two allowed values of the spin component, −1/2 and +1/2. Quantum systems with two possible states are sometimes called two-level systems .
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Word ladder (also known as Doublets, [1] word-links, change-the-word puzzles, paragrams, laddergrams, [2] or word golf) is a word game invented by Lewis Carroll. A word ladder puzzle begins with two words, and to solve the puzzle one must find a chain of other words to link the two, in which two adjacent words (that is, words in successive ...
Then the word problem in is solvable: given two words , in the generators of , write them as words in and compare them using the solution to the word problem in . It is easy to think that this demonstrates a uniform solution of the word problem for the class K {\displaystyle K} (say) of finitely generated groups that can be embedded in G ...
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Examples of atoms in singlet, doublet, and triplet states. In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet".
In another molecule a proton resonates at 2.5 ppm and that proton would also be split into two by the proton at 1 ppm. Because the magnitude of interaction is the same, the splitting would have the same coupling constant 7 Hz apart. The spectrum would have two signals, each being a doublet. Each doublet will have the same area because both ...