Sentence examples for must intersect from inspiring English sources

In the simplest original form it states that if a finite family $\Gamma$ of convex sets in $R^n$ has the property that every $n+1 $of the sets have a non-empty intersection, then all the convex sets must intersect.

Executive functions, such as working memory, must intersect with functions that determine value for the organism.

These environmental responses must intersect with the intrinsic developmental programme of the plant, which is responsible for the general formation and maintenance of the root system.

Urban wetlands potentially play an important role in nitrate (NO3−) removal from stormwater, but nitrogen loading from the atmosphere and surface water must intersect with soil properties optimal for NO3− removal for this potential to be realized.

The proof that the problem is impossible depends on the so-called Jordan curve theorem that a continuous closed curve in a plane divides the plane into an interior and an exterior region in such a way that any continuous line connecting a point in the interior with a point in the exterior must intersect the curve.

In determining the tool profile required to generate a desired helical groove (an inverse problem), this study exploits the condition that the common normal at the contact point between the tool and the helical groove surface must intersect the axis of the tool.

At present, polygons must be simple; that is they must not intersect themselves.

The two right-across lines must not intersect too near to the picture's centre.

We believe that in the enterprise of uncovering truth, the paths of the scientist and the humanist must often intersect.

The rock or meteoroid must eventually intersect the Earth's orbit, possibly hundreds of thousands or millions of years later, and be captured by its gravitational field into a decaying or unstable orbit.

Obviously any continuous deformation of I must still intersect C somewhere.