Sentence examples for functions asserted from inspiring English sources

We first prove a relationship between polygamma functions and Riemann zeta functions asserted by Theorem 1.

we obtain further interesting identities involving binomial coefficients and generalized harmonic functions asserted by the following theorem.

However, by Tarski's undefinability result, no such truth-predicate exists.[78] So there must be a model of ZFC and a sentence φ true in that model such that φ* is false: not all 'Skolem functions' asserted to exist by φ* actually exist in the model.

2646, 33 L.Ed.2d 626 (1972) that "the informative function asserted by representatives of the organized press" to justify greater privileges under the First Amendment was also "performed by lecturers, political pollsters, novelists, academic researchers, and dramatists". Id., at 705, 92 S.Ct., at 2668.

The Shafer-Fink double inequality for the arctangent function asserts that frac{3x}{1+2sqrt{1+x^{2}}}< arctan x< frac{pi x}{1+2sqrt{1+x^{2}}} (1.3) holds for any positive real number x. Shafer's inequality was recently generalized by Qi et al. in [3], as follows: frac{ ( 1+a ) x}{a+sqrt{1+x^{2}}}< arctan x< frac{ ( frac{pi}{2} ) x}{a+sqrt{1+x^{2}}}, (1.4) where (0leq andqfrac{1}{2}) and (x>0).

They defined the field as "the scientific study of optimal human functioning" and asserted "a new commitment on the part of research psychologists to focus attention upon the sources of psychological health, thereby going beyond prior emphases upon disease and disorder".

This dual-aspect monism approach to brain mind functions, which asserts that emotional feelings may reflect the neurodynamics of brain systems that generate instinctual emotional behaviors, saves us from various conceptual conundrums.

Through quantifying the loss function, they assert that tolerance should be determined to minimize the loss function and contend that the first attempt to reduce the quality costs (including the costs associated with defective components, re-working and other costs) focuses on decreasing the costs related to defective components.

If similarities were computed in the preceding step, these similarities can be accessed and functions can be asserted.

We assume that specificity determinants, after mutation that allow for a new (sub- function, sub- functioner should negative selection to let this newly asserted function to persist.

In the sections below we describe the steps the RAST server implements to automatically produce two classes of asserted gene functions: subsystem-based assertions are based on recognition of functional variants of subsystems, while nonsubsystem-based assertions are filled in using more common approaches based on integration of evidence from a number of tools.