One replaces the Kuratowski pair ⟨x,y⟩ with a variant, ({0}× a)∪ ({1}× b).
"Another one replaces you.
With more women running against other women, one replaces another.
We provide a new proof of Nevai's result that if γ>12, the Szegő condition holds, which works also if one replaces (−1)n by cos (μn).
In the above paragraph, if one replaces the word 'ball' with 'microbe' then one will find a description of our experiment.
When one replaces "Black Lives Matter" with "All Lives Matter," one may be slipping into a false assumption that we are all similarly situated.
In equities, which is a less complicated market, they will run for a few months before a new one replaces them.
"The hierarchy of substances is abolished: a single one replaces them all," wrote the philosopher Roland Barthes, in 1972.
To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP).
Finally, we show that the main results remain true if one replaces the Ambrosetti Rabinowitz condition on the nonlinearity by weaker assumptions and thus we establish the existence and multiplicity results for a wider class of nonlinearity, see Section 7 for more details.
The same is valid if one replaces the exponential function in the product by functions of the Kato class, that is, by real-valued Borel measurable functions f defined on the non-negative real axis obeying 0⩽f(x)⩽1, f(0)=1 and f′(+0)=−1, with some additional smoothness property at zero.
