Sentence examples for exists a complex from inspiring English sources

There exists a complex relationship between AM products and their process data.

Then there exists a complex number l such that (pmbox lim_{m,ntoinfty}|x_{mn}-l|=0).

Rather, there exists a complex and dynamic interplay between geography, socioeconomic status, market forces and policy––all of which shape the current broadband landscape.

The numerical results show that there exists a complex 3-D stress state in the adhesively-bonded joints under the solid projectile impact.

For unpredicted plates, workers used to request additional information for manufacturing, and during the process, there exists a complex information exchange between related departments, which is a time-consuming process.

Proof For A there exists a complex n × n -matrix K such that A = K − 1 B K, where B is the Jordan normal form of A. From D x = A x + a, we obtain D y = B y + b, where y = K x and b = K a. □.

We say that a function (f:{mathbb{Drightarrow C}}) is subordinate to a function (g:{mathbb{Drightarrow C}}), and write (f z prec g z)) (or simply (fprec g)), if there exists a complex-valued function w which maps ({mathbb{D}}) into itself with (w(0)=0), such that (f z)=g(w z))); (zin{mathbb{D}}).

By the assumptions of the lemma, there exists a complex-valued function ϕ such that |ϕ|=g (in the sense of almost everywhere) and int_{-infty}^{infty}phi(x e^{itx}dx=0,~~~tge 0 (see the proof of Theorem 1 in Lin 1997 for details, and Garnett 1981, p. 66, for the construction of ϕ).

On the other hand, there is another remarkable result of Pavlov (see [24]), which says that, for any (0exists a complex-valued potential V satisfying (|V|le Cexp (-c| x|^p)) and a complex number (theta ), such that the operator (-d^2/dx^2+V x)) with the boundary condition (psi '(0)=theta psi (0)) has infinitely many eigenvalues.

He told me about his most recent project: "The question is, does there exist a complex structure on the six-dimensional sphere?

There exists a highly complex feedback loop between the use of advanced technology and changes to the environment that are only slowly becoming understood.