These are trivial manifestations of a nontrivial problem.
nontrivial in American English
(nɑnˈtrɪviəl)
adjective
1.
not trivial
2. Math
noting a solution of a linear equation in which the value of at least one variable of the equation is not equal to zero
Word origin
[1910–15; non- + trivial]
Examples of 'nontrivial' in a sentence
nontrivial
Under suitable assumptions on the nonlinearities, we show the existence of nontrivial solutions.
Ali Djellit, Saadia Tas 2003, 'Existence of solutions for a class of elliptic systems in RN involvingthe p-Laplacian', Electronic Journal of Differential Equationshttp://ejde.math.txstate.edu/Volumes/2003/56/abstr.html. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Given this low dissociation constant, initiation and sustainability of transcription becomes nontrivial.
Xiaolin Tang, Mourad Bendjennat, Saveez Saffarian 2014, 'Vesicular stomatitis virus polymerase's strong affinity to its template suggests exotictranscription models.', PLoS Computational Biologyhttp://europepmc.org/articles/PMC4263359?pdf=render. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This paper presents a nontrivial application of the omitted ray fixed point theorem.
Douglas Anderson, R. I. Avery 2014, 'Application of the omitted ray fixed point theorem', Electronic Journal of Qualitative Theory of Differential Equationshttp://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2963. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We focus mainly on the construction and classification of nontrivial central extensions.
Jarnishs Beltran, Enrique G. Reyes 2015, 'Formal Pseudodifferential Operators in One and Several Variables, Central Extensions,and Integrable Systems', Advances in Mathematical Physicshttp://dx.doi.org/10.1155/2015/210346. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The sequences consist of only a few symbols yet possess several nontrivial properties.
Hoai Nguyen Huynh, Andri Pradana, Lock Yue Chew 2015, 'The Complexity of Sequences Generated by the Arc-Fractal System', PLOS ONE10.1371/journal.pone.0117365. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Organic matter decomposition varies with climate in complex nonlinear ways, rendering data aggregation nontrivial.
Lise Dalsgaard, Rasmus Astrup, Clara Antón-Fernández, Signe Kynding Borgen, JohannesBreidenbach, Holger Lange, Aleksi Lehtonen, Jari Liski 2016, 'Modeling Soil Carbon Dynamics in Northern Forests: Effects of Spatial and TemporalAggregation of Climatic Input Data', PLOS ONE10.1371/journal.pone.0149902. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
These methods give the first nontrivial upper bounds for the sizes of the systems.
Aleksi Saarela 2011, 'Systems of Word Equations and Polynomials: a New Approach', Electronic Proceedings in Theoretical Computer Sciencehttp://arxiv.org/pdf/1108.3637v1. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Both methods show a nontrivial dependence of the deconvolution quality on the oscillation amplitude.
Joachim Welker, Esther Illek, Franz J. Giessibl 2012, 'Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy',Beilstein Journal of Nanotechnologyhttps://doi.org/10.3762/bjnano.3.27. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions.
Kuo-Shou Chiu 2014, 'Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise ConstantArgument', The Scientific World Journalhttp://dx.doi.org/10.1155/2014/514854. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Regarding absolute perfusion values, nontrivial differences and variations remain when comparing the two methods.
Fabian Zimmer, Frank G Zöllner, Simone Hoeger, Sarah Klotz, Charalambos Tsagogiorgas,Bernhard K Krämer, Lothar R Schad 2013, 'Quantitative renal perfusion measurements in a rat model of acute kidney injury at3T: testing inter- and intramethodical significance of ASL and DCE-MRI.', PLoS ONEhttp://europepmc.org/articles/PMC3538736?pdf=render. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)