Definition of invariant in English:

invariant

adjective

Never changing.
‘the pattern of cell divisions was found to be invariant’
- ‘Consistent with the close phylogenetic relationships of the species sampled, most nucleotide sites were invariant in pair wise comparisons.’
- ‘Skuladottir and Charnov collaborated on a paper in 2000 predicting that indeed there are invariant rules for sex change and presenting shrimp data to bolster their claim.’
- ‘This term is invariant to the change in reference genotype that allowed us to derive this equation.’
- ‘In villages, families throng at the lone hand pump for the stuff: this is a sight that is so invariant in India that you might be forgiven for thinking hand pumps go back to Vedic times.’
- ‘In contrast, was relatively invariant among populations because the number of segregating sites was largely determined by the presence of both alleles.’
- ‘The results reveal 23 nonsynonymous changes and 127 invariant sites in total in the hinge region.’
- ‘However, the scholarship of revivals has not emphasised the possibility of significant invariant qualities in appropriated or ‘revived’ folk culture.’
- ‘Replacement substitutions are extremely variable in rate, ranging from many sites that are essentially invariant to a few that evolve fairly rapidly.’
- ‘The interactions of the individual dipoles in a magnet do not depend on any particular direction, and their dynamics are rotationally invariant.’
- ‘For a transactional leader, there are no universal invariant principles, policies, or goals applicable to all situations and at all times.’
- ‘All these are invariant in our sequences, of both sets A and B.’
- ‘One of the diverged phenotypes in cultivated rice is observed in the patterns of coloration due to anthocyanin pigmentation in spite of invariant pigmentation in the wild forms of rice.’
- ‘The open time constants are invariant to ligand concentrations, suggesting that ligand binds exclusively to the closed channel.’
- ‘As outlined above, we assumed that both environmentally induced variability and colony growth rates were relatively invariant within a population.’
- ‘As in all mixture problems, this model is not identifiable as the likelihood is invariant under any relabeling of the populations.’
- ‘So looking at whether something makes people happy is largely futile. In statisticians' terms, you are looking for variance in something that is invariant.’
- ‘Results for ecstasy and traditional hard drug users were highly invariant, but the ecstasy users' rate of previous hard drug use was much higher than that of any other group.’
- ‘Among women, the long-term health effects of early parental support also appeared to be relatively invariant, with one exception.’
- ‘Further analysis of the data revealed the presence of at least two fluorescent species and fitting to a bi-exponential model was performed assuming invariant lifetimes.’
- ‘Absence of major oceanographic anomalies in the immediate vicinity of Johnston Atoll may contribute to relatively high and invariant survival in Brown Boobies.’
unalterable, immutable, invariable, unvarying, changeless, firm, fixed, hard and fast, cast-iron, set in stone, set, decided, established, permanent, deep-rooted, enduring, abiding, lasting, indestructible, ineradicable, irreversible, unfading, constant, perpetual, eternal, lifelong
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noun

Mathematics

A function, quantity, or property which remains unchanged when a specified transformation is applied.
- ‘At Freiburg, he took a course with Oskar Bolza on the theory of invariants, and a course on differential geometry and a history seminar with Alfred Loewy, one of the two professors at Freiburg.’
- ‘Under their direction he laid the basis for the important work he was later to achieve in the fields of foundations of geometry, projective geometry, topology, differential invariants and spinors.’
- ‘Also in 1887 Voigt first wrote down the transformations and showed that certain equations were invariant under these transformations.’
- ‘For example, in Euclidean geometry, the relevant invariants are embodied in quantities that are not altered by geometric transformations such as rotations, dilations, and reflections.’
- ‘Todd generalised the arithmetic genus and the invariants of the canonical system on an algebraic variety to a system of invariants of every codimension.’