Sentence examples similar to an extra hypothesis from inspiring English sources

A vectorxin a Banach space B is called hypercyclic for a bounded linear operatorT: B→B if the orbit {Tnx: n⩾1} is dense in B. Our main result states that ifTis a compact perturbation of an operator of norm ⩽1 and satisfies an appropiate extra hypothesis, then there is an infinite-dimensional closed subspace consisting, except for zero, entirely of hypercyclic vectors forT.

However, it should be stressed that the fulfilment of this property is not proved for the case of Δ p -Laplacian with p > 2 and, thus, should be considered as some extra hypothesis.

A limit cycle is a closed trajectory with a couple of extra hypotheses.

Thus proving an LCA group result would appear to be very difficult, undoubtedly involving extra hypotheses.

Under appropriate extra hypotheses on the commuting operator, stronger forms of cyclicity are possible, the most extreme being hypercyclicity (density of an orbit).

However, the proof in [18] of the formula (1.1) uses some subtle Fourier analysis similar to that employed by Brown [11, 12] and Boas [9] so that extra hypotheses would be very likely be needed.

on the standards of contemporary dynamo models theirs is extremely simple —in fact borderlining simplistic... To extrapolate such a model outside its calibration window, you need an extra, very strong hypothesis: that the physical systems underlying the magnetic field generation retain their coherence (Phase, amplitude, etc.).

To test this hypothesis an extra promoter was cloned in front of luxCDE to boost substrate synthesis, and indeed a 6-fold higher signal was obtained.

The accumulation of the signaling molecules glucose-6-P and trehalose [ 45, 76] and the specific dynamics of HEX and SPP found in the N starvation, provide an extra support to this hypothesis.

April 6, 1870 Clayton, California January 17 , 1946Swarthmore, Pennsylvania Clarence E. McClung, (born April 6, 1870, Clayton, Calif., U.S. died Jan . 17 , 1946Swarthmore, Pa ., American zoologist whose study of the mechanisms of heredity led to his 1901 hypothesis that an extra, or accessory, chromosome was the determiner of sex.

Nevertheless, it was also found in all other samples, supporting the hypothesis of an extra activity of PLA1 in processing the fatty acid at position sn-2, or being the consequence of a kind of instability of the LPC molecule (see Additional files 1, 2, 3, 4, and 5).