Sentence examples for exists an inner from inspiring English sources

Between these three aspects there exists an inner connection: transcendentals are the 'firsts', since they are most common; and because of their commonness they transcend the categories".

There exists an inner boundary at x2 + y2 = R S. We assume that the electric conductivity of the object is small, like an insulator.

A Jordan algebra V is said to be Euclidean if (iii) x 2 + y 2 = 0 ⇒ x = y = 0, equivalently, there exists an inner product on V such that ( x ∘ y | z ) = ( y | x ∘ z ).  . x 2 + y 2 = 0 ⇒ x = y = 0, equivalently, there exists an inner product on V such that ( x ∘ y | z ) = ( y | x ∘ z ).

Then there exists an inner function θ which is ( F ( p, p − 2, s ), F ( p, p − 2, t ) ) -improving, but θ does not belong to F ( p, p − 2, s ).

And yet there still exists an inner world, the life of the mind, fantasy, and the imagination.

Growth of enlightenment is the development of the purest state of love that exists, an inner state of Being that is not dependent on anything from the outside for its fulfillment.

There should exist an inner Ti(N) zone below spot 3. Aluminum was locally segregated at spots 3 to 6 due to its limited solubility in the nitrides [7]. Figure 4 TEM cross-sectional bright-field image of the Ti-6Al-4V after after nitriding at 850°C for 1 h. Figure 5a shows the cross-sectional image of the Ti-6Al-4V after after nitriding at 850°C for 12 h.

A Lau algebra A was said to be inner amenable if there exists a topological inner invariant mean on the (W^* -algebra (A^*), that is, a positive linear functional m of norm 1 on (A^*), such that (m(f.a) = m(a.f)) for all (fin A^*) and all (ain P_1(A) = {a in A : Vert aVert = 1}) (or equivalently, for all (ain A)).

There exists a locally inner automorphism g of L K ( E ) 0 for which L K F F ) ≅ L K ( E ) 0 [ t +, t -, g ∘ α ] as Z -graded K -algebras.  .

There exists a locally inner automorphism g of L K ( E ) 0 for which L K F F ) ≅ L K ( E ) 0 [ t +, t -, g ∘ α ] as Z -graded K -algebras.

It was revealed that the curvature of curves for the cross-section profiles can significantly affect the shear rate distributions, and there exists an optimal profile for the inner cylinder cross-section.