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Avoided crossing. In quantum physics and quantum chemistry, an avoided crossing (sometimes called intended crossing, [1] non-crossing or anticrossing) is the phenomenon where two eigenvalues of a Hermitian matrix representing a quantum observable and depending on N continuous real parameters cannot become equal in value ("cross") except on a ...
Since every (n + m)-step self avoiding walk can be decomposed into an n-step self-avoiding walk and an m-step self-avoiding walk, it follows that c n+m ≤ c n c m. Therefore, the sequence {log c n} is subadditive and we can apply Fekete's lemma to show that the following limit exists: =. μ is called the connective constant, since c n depends ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
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Cauchy's functional equation is the functional equation : A function that solves this equation is called an additive function. Over the rational numbers, it can be shown using elementary algebra that there is a single family of solutions, namely for any rational constant Over the real numbers, the family of linear maps now with an arbitrary ...
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