Sentence examples for analytic alternative from inspiring English sources

In Section 8, we deduce a Fan-type analytic alternative and its consequences.

From the intersection Theorem 7.1, we can deduce the following equivalent form of a generalized Fan-type minimax inequality or analytic alternative.

In 2001 [22], we obtained generalized forms of the von Neumann-Sion-type minimax theorem, the Fan-Ma intersection theorem, the Fan-Ma type analytic alternative, and the Nash-Ma-equilibrium theorem for -convex spaces.

(VIII) In 2001 [22], we obtained generalized forms of the von Neumann-Sion-type minimax theorem, the Fan-Ma intersection theorem, the Fan-Ma type analytic alternative, and the Nash-Ma-equilibrium theorem for -convex spaces.

In a weak sense, our paper also provides an analytic alternative to the Adams Barbasch theorem on Howe duality [R. Howe, Transcending invariant theory, J. Amer. Math. Soc. 2 (1989) 535 552].

From this, fan [9, 10] deduced Sion's minimax theorem [54], the Tychonoff fixed point theorem, solutions to systems of convex inequalities, extremum problems for matrices, and a theorem of Hardy-Littlewood-Pólya. From the intersection Theorem 7.3, we can deduce the following equivalent form of a generalized Fan-type minimax inequality or analytic alternative.

In three years, Doshi built Mixpanel into a real-time mobile and web analytics alternative to older firms like Omniture.

Or giving them the ability to delete their data — and so they started work on their open analytics alternative about four months ago.

Unencumbered by traditional health plan thinking and structures, Oscar launched a plan that leverages recent advances in big data analytics, alternative site options including telemedicine, and the best in mobile and web user experiences.

It was developed to overcome the limitations of traditional biostatistical methods on the one hand, and decision-analytic alternatives on the other.

Alternative analytic currents emphasize contrasting roles of instrumentation.