Sentence examples for connected and there exists from inspiring English sources
if K is connected and there exists a finite set (V_{0}subseteq K) called the boundary such that F_{w}Kcap F_{w'}Ksubseteq F_{w}V_{0} cap F_{w'}V_{0}quadtext{for }wneq w' text{ with } vert w vert = biglvert w' bigrvert, (1.2) with the intersection disjoint from (V_{0}).
Second, is not necessarily connected and there may exist several uncovered gaps on.
Corollary 1 If X is p-complete and G is weakly connected, then there exists an x ∗ ∈ X such that f n x → p x ∗ for all x ∈ X. Proof Fix any point x ∈ X.
Corollary 3.13 Assume (i) the C ρ -graph G is weakly connected and (ii) there exist nonnegative numbers l, c with l < c such that ∫ 0 ρ ( c ( T x − T y ) ) φ ( t ) d t ≤ η ∫ 0 ρ ( l ( x − y ) ) φ ( t ) d t . the C ρ -graph G is weakly connected and.
Corollary 3.14 Assume (i) the C ρ -graph G is weakly connected and (ii) there exist nonnegative numbers l 1, l 2, c with l 1, l 2 < c such that ∫ 0 ρ ( c ( T x − T y ) ) φ ( t ) d t ≤ β ∫ 0 [ ρ ( l 1 ( x − T x ) ) + ρ ( l 2 ( y − T y ) ) ] φ ( t ) d t . the C ρ -graph G is weakly connected and.
Corollary 3.15 Assume (i) the C ρ -graph G is weakly connected and (ii) there exist nonnegative numbers l 1, l 2, c with l 1, l 2 < c such that ∫ 0 ρ ( c ( T x − T y ) ) φ ( t ) d t ≤ γ ∫ 0 [ ρ ( l 1 2 ( x − T y ) ) + ρ ( l 2 2 ( y − T x ) ) ] φ ( t ) d t . the C ρ -graph G is weakly connected and.
Data from the most recent National Adult Literacy Survey (2003) indicate that an alarming proportion of US adults are functionally illiterate [ 16], and there exists evidence connecting low literacy with poorer health-related quality of life [ 17].
Let u,v∈V, since G is connected, there exists at least one shortest path P uv connecting u and v. From the definition of C EB, for any edge e∈P uv, C EB (e)>0.
Since Sp (n ) is connected there exists a C 1 path t ⟼ S t, 0 ⩽ t ⩽ 1 (in fact infinitely many) joining the identity to S in Sp (n ).
First, the removal of an edge destroys the shortest path between two periodic genes and there exists no other path in the TRN that could connect these genes.
