Sentence examples for the original conjecture from inspiring English sources

Subsequently, it was found that the original conjecture is not true when extended to full generality.

But close isn't good enough in mathematics, so the original conjecture remains unproven.

Dyatlov Guillarmou [73] considered the more complicated non-compact case and essentially settled the original conjecture of Smale.

Both experimental observations and theoretical models indicate that the phase stability of HEAs goes beyond the original conjecture that these alloys are stabilized by configurational/mixing entropy; rather, it results from competition between the homogeneously disordered phase and phase separation/intermetallic compound formation.

Note that Simon's and Kato's papers discussed in the historical part of Sect. 9 were both preprinted in early 1972 after this conjecture, so the original conjecture was made for a local Stummel space rather than (L^2_{loc}) but eventually, it was updated to (L^2_{loc}).

In this case reverse the process, work backwards, and try to deduce your original conjecture via the inverse route from the indubitable truth to the dubitable conjecture.

In particular, when N : R → R, y ↦ N ( y ), is a scalar function and D, E T ∈ R n, the above conjecture is exactly a discrete-time version of the original Aizerman conjecture which was formulated first for ordinary differential systems, see [1].

At the time of this writing, we could for example let $A(n)$ express that $n$, if greater than 2, is the sum of three primes; $\forall n A(n)$ then expresses the (original) Goldbach conjecture that every number greater than 2 is the sum of three primes.

From Galen original conjecture [2], with a meningeal involvement in the throbbing pain, several centuries passed before Willis, in 1672, hinted for the first time at a "vascular hypothesis" of migraine [3].

For n = 3, this reduces to his original conjecture.

Some further work is necessary to solve Lou and Lutscher's original conjecture.