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In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; [1] "degeneracy" is the condition of being a degenerate case. [2] The definitions of many classes of composite or structured objects often implicitly include inequalities.
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a ...
Degeneracy (graph theory), a measure of the sparseness of a graph. Degeneration (algebraic geometry), the act of taking a limit of a family of varieties. Degenerate bilinear form, a bilinear form on a vector space V whose induced map from V to the dual space of V is not an isomorphism. Degenerate distribution, the probability distribution of a ...
The degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph. Degeneracy is also known as the k-core number, [1] width, [2] and linkage, [3] and is essentially the same as the coloring number [4] or Szekeres–Wilf number (named after Szekeres and Wilf ).
Degeneracy See "degenerate energy level". Degenerate energy level If the energy of different state (wave functions which are not scalar multiple of each other) is the same, the energy level is called degenerate. There is no degeneracy in a 1D system. Energy spectrum The energy spectrum refers to the possible energy of a system.
A neurodegenerative disease is caused by the progressive loss of neurons, in the process known as neurodegeneration. [2][3] Neuronal damage may also ultimately result in their death. Neurodegenerative diseases include amyotrophic lateral sclerosis, multiple sclerosis, Parkinson's disease, Alzheimer's disease, Huntington's disease, multiple ...
The noun (less commonly used) would be non-degeneracy. It's possible that someone might use proper as in a proper parabola, but I'm not sure about that. Duoduoduo 16:21, 29 August 2013 (UTC) Reply If "non-degenerate" is commonly used as antonym, then that is a sign that degenerate is not the same as non-generic.
A synonymous substitution (often called a silent substitution though they are not always silent) is the evolutionary substitution of one base for another in an exon of a gene coding for a protein, such that the produced amino acid sequence is not modified. This is possible because the genetic code is "degenerate", meaning that some amino acids ...