Sentence examples for by this proposition from inspiring English sources

By this proposition we can construct the noncolliding RW, Ξ, as an h-transform of an absorbing RW, V, in (mathbb {W}_{N}).

By this proposition, a solution of system (25) reduces to a solution of the system of the form (25), where B has the Jordan normal form.

I know I'm not the only one baffled by this proposition; after all, it's legal drugs that have become our country's biggest problem -- prescription painkillers now cause more deaths than heroin and cocaine combined.

In 1961, Warhol was offered a three-man show by Allan Stone at the latter's 18 East 82nd Street Gallery with Rosenquist and Robert Indiana, but all three were insulted by this proposition.

By applying this proposition (n-1) times to different pairs of orthogonal directions and recalling (4.19) we find a set (widetilde{E}), with (|widetilde{E}|=|B|) such that begin{aligned} alpha (E) le C_0^{n-1} alpha (tilde{E}), quad D tilde{E}) le 2^{n-1} D(E).

By following this proposition and defining the closely linked markers as being less than 5 cM apart, 407 markers on the consensus map (19.8%) were identified as having skewed segregation in one or more of the component populations, covering 34% of the consensus map length.

The Yale paleontologists tested this proposition by looking at how much the specimens' skulls had fused together — a marker of maturity, they said — and concluded that many Triceratops skulls exhibit extensive cranial fusion.

A study published in Pediatrics last October by my team tested this proposition and found that parents with more knowledge about vaccination and infectious disease were not more likely to have their children vaccinated.

Now we prove this proposition by induction.

Proof We prove this proposition by induction.

By part (c) of this proposition, it implies that is a complete cone metric space.  .