Sentence examples for formulas for their from inspiring English sources

Explicit formulas for their adjoints are shown for various classes of symbols.

In the present work, binary BMG composition formulas are established via dissociating dual-cluster formulas for their relevant eutectics.

We establish the existence of Lyapunov exponents, derive formulas for their calculation, and show that Lyapunov exponents of free variables are additive with respect to operator product.

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra.

We give criteria for the membership of Toeplitz operators and products of Hankel operators, with symbols of a certain type, in the Dixmier class, and formulas for their Dixmier trace, on a variety of weighted Segal Bargmann Fock spaces on the complex plane.

There is also the intriguing possibility of natural-language sentences that seem to require second-order formulas for their formalization.

The formula for their success?

We give a Lévy-Khinchin-type formula for their distributions.

Hot-tamale venders like to mention that they have a secret formula for their seasoning.

The formula for their demise was particularly jarring: the big-play offense produced no big plays.

Free schools can't negotiate directly for buildings because there is no agreed formula for their capital costs.