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The tables of elements are sorted in order of decreasing number of nuclides associated with each element. (For a list sorted entirely in terms of half-lives of nuclides, with mixing of elements, see List of nuclides.) Stable and unstable (marked decays) nuclides are given, with symbols for unstable (radioactive) nuclides in italics. Note that ...
More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis). The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge.
11 elements have 5 stable isotopes apiece; 9 elements have 4 stable isotopes apiece; 5 elements have 3 stable isotopes apiece; 16 elements have 2 stable isotopes apiece; 26 elements have 1 single stable isotope. These last 26 are thus called monoisotopic elements. [3] The mean number of stable isotopes for elements which have at least one ...
This list of nuclides shows observed nuclides that either are stable or, if radioactive, have half-lives longer than one hour. This represents isotopes of the first 105 elements, except for elements 87 ( francium ), 102 ( nobelium ) and 104 ( rutherfordium ).
There are 26 such elements, as listed. Stability is experimentally defined for chemical elements, as there are a number of stable nuclides with atomic numbers over ~ 40 which are theoretically unstable, but apparently have half-lives so long that they have not been observed either directly or indirectly (from measurement of products) to decay.
This is a list of radioactive nuclides (sometimes also called isotopes), ordered by half-life from shortest to longest, in seconds, minutes, hours, days and years. Current methods make it difficult to measure half-lives between approximately 10 −19 and 10 −10 seconds.
Proton number Z, also named the atomic number, determines the position of an element in the periodic table. The approximately 3300 known nuclides [7] are commonly represented in a chart with Z and N for its axes and the half-life for radioactive decay indicated for each unstable nuclide (see figure). [8]
A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).