Sentence examples for a exist from inspiring English sources

Suppose that both λ ∗ = Λ k D ( a, b ) and λ ∗ = Λ k D ( b, a ) exist and k ≥ 1.

It is well known that if the difference of self-adjoint operators A and B is of trace class, then the generalized wave operators W± B, A) = s-limt → ± ∞ exp itB) exp(−itA) Pac(A) exist.

If Λ k D ( a, b ) and Λ k D ( b, a ) exist, Γ k D ( a, b ) and Γ ˜ k D ( a, b ) are continuous, strictly decreasing, hyperbolic like curves.

Existential judgements are therefore not to be expressed in the subject-predicate form "S is P", but in the simple form "A exists", when "A" is a singular term, and "A's exist" or "Some A exist", when "A" is a general term.

"It's a Bunch of Magnets!" The magnets are coming in this magnet-tastic playset that features magnets, magnets, and, you guessed it … MORE MAGNETS!!!!!! Complete with magnets that both attract and repel, the kit teaches kids that magnets (a) exist and (b) exist in medium quantities.

A solution u* in A ⊂ S is a maximal solution in the set A if u* ≥ u for any other solution u ∈ A. The minimal solution in A is defined analogously by reversing the inequalities; when both a minimal and a maximal solution in A exist, we call them the extremal solutions in A. Next we pose our main result.

To further investigate whether paracrine or autocrine effects of fetuin-A exist, we determined the fetuin-A mRNA expression in human THP1 monocytes and human adipose tissue and for comparison in human liver.

Isoforms of VEGF-A exist in two distinct families, formed by alternative mRNA splicing [ 7].

Numerous isoforms of VEGF-A exist but their physiological significance is unclear.

However, at this time, only a few validation studies of the SRS-A exist [ 15, 27, 28].

Although encoded by a single gene, several distinct isoforms of VEGF-A exist as a result of alternative splicing and/or proteolytic cleavage.