Sentence examples for exists a ground from inspiring English sources

We prove that there exists a constant 0<α0≪1 independent of σ>0 such that for all |→p|<1/3 and all values of the finestructure constant 0<α<α0, there exists a ground state eigenvalue of multiplicity two at the bottom of the essential spectrum.

There exists a ground state solution v of equation (1.1).

Hence, there exists a ground state solution of boundary value problem (5.1).

(i) There exists a ground state solution v of equation (1.1).

When a line of sight exists, a ground reflection is added if the distance between the transmitter and the receiver satisfies the following equation: (3).

Assume the hypotheses (H1 - H5) hold, boundary value problem (1.1) has a weak solution such that (I u)=m), i.e. there exists a ground state solution of boundary value problem (1.1).

Beyond the bright lights and tourist attractions exists a breeding ground for the savvy and assertive, driven by a relentless work ethic and spirit of achievement that draws people from across the globe.

Under assumptions ( f 1 ) ∼ ( f 3 ) and ( V 1 ), there exists a least-energy ground state solution of (1.1).

Under assumptions ( f 1 ) ∼ ( f 4 ) and ( V 2 ), there exists a least-energy ground state of (1.1), which is radially uniqueness solution, with the corresponding least-energy value c ∗.

As the Dagoty brothers expanded the premises, the main building came to resemble what exists today: a ground floor, two upper floors, and an attic lit by seven casement windows that look out onto the street and seventeen others overlooking a cobblestoned courtyard.

If evolutionary theory can demonstrate that religion is beneficial over all, then there might exist a common ground with true believers in religion, who from a very different perspective also argue that the benefits of belief outweigh the costs.