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| English | Russian |
| A new hypothesis has recently been put forward by | недавно была выдвинута новая гипотеза ... |
| by hypothesis | согласно предположению |
| by hypothesis | согласно гипотезе |
| by hypothesis | по условию |
| by the induction hypothesis | по предположению индукции (by the induction hypothesis (assumption), the matrix A is positive definite for n = 2) |