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  2. Multiplicity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Multiplicity_(mathematics)

    The graph crosses the x-axis at roots of odd multiplicity and does not cross it at roots of even multiplicity. A non-zero polynomial function is everywhere non-negative if and only if all its roots have even multiplicity and there exists an x 0 {\displaystyle x_{0}} such that f ( x 0 ) > 0 {\displaystyle f(x_{0})>0} .

  3. Multiplicity (statistical mechanics) - Wikipedia

    en.wikipedia.org/wiki/Multiplicity_(statistical...

    The goal is to determine the multiplicity as a function of U; from there, the entropy and other thermodynamic properties of the system can be determined. However, it is useful as an intermediate step to calculate multiplicity as a function of N ↑ {\displaystyle N_{\uparrow }} and N ↓ . {\displaystyle N_{\downarrow }.}

  4. Multiplicity (chemistry) - Wikipedia

    en.wikipedia.org/wiki/Multiplicity_(chemistry)

    However the multiplicity equals the number of spin orientations only if S ≤ L. When S > L there are only 2L+1 orientations of total angular momentum possible, ranging from S+L to S-L. [ 2 ] [ 3 ] The ground state of the nitrogen atom is a 4 S state, for which 2S + 1 = 4 in a quartet state, S = 3/2 due to three unpaired electrons.

  5. Multiset - Wikipedia

    en.wikipedia.org/wiki/Multiset

    This extended multiplicity function is commonly called simply the multiplicity function, and suffices for defining multisets when the universe containing the elements has been fixed. This multiplicity function is a generalization of the indicator function of a subset , and shares some properties with it.

  6. Multiplicity - Wikipedia

    en.wikipedia.org/wiki/Multiplicity

    Multiplicity (informatics), a type of relationship in class diagrams for Unified Modeling Language used in software engineering; Multiplicity (mathematics), the number of times an element is repeated in a multiset; Multiplicity (software), a software application which allows a user to control two or more computers from one mouse and keyboard

  7. Multiple comparisons problem - Wikipedia

    en.wikipedia.org/wiki/Multiple_comparisons_problem

    In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously [1] or estimates a subset of parameters selected based on the observed values. [2] The larger the number of inferences made, the more likely erroneous inferences become.

  8. Descartes' rule of signs - Wikipedia

    en.wikipedia.org/wiki/Descartes'_rule_of_signs

    Let () be the number of strictly positive roots (counting multiplicity). With these, we can formally state Descartes' rule as follows: Theorem — The number of strictly positive roots (counting multiplicity) of f {\displaystyle f} is equal to the number of sign changes in the coefficients of f {\displaystyle f} , minus a nonnegative even number.

  9. Minimal polynomial (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Minimal_polynomial_(linear...

    The multiplicity of a root λ of μ A is the largest power m such that ker((A − λI n) m) strictly contains ker((A − λI n) m−1). In other words, increasing the exponent up to m will give ever larger kernels, but further increasing the exponent beyond m will just give the same kernel.