The new security measure has proven to have the properties of boundedness, commutativity, and unity.
Chun-Juan Ouyang, Ming Leng, Jie-Wu Xia, Huan Liu 2017, 'Vague Sets Security Measure for Steganographic System Based on High-Order Markov Model',Security and Communication Networkshttp://dx.doi.org/10.1155/2017/1790268. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Some problems allowed the use of either of two commutativity-based shortcut strategies.
Robert Gaschler, Bianca Vaterrodt, Peter A. Frensch, Alexandra Eichler, Hilde Haider 2013, 'Spontaneous Usage of Different Shortcuts Based on the Commutativity Principle', PLoS ONE10.1371/journal.pone.0074972. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.
Sonja Maria Hansen, Hilde Haider, Alexandra Eichler, Claudia Godau, Peter A. Frensch,Robert Gaschler 2015, 'Fostering Formal Commutativity Knowledge with Approximate Arithmetic', PLOS ONE10.1371/journal.pone.0142551. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Explicit commutativity conditions for the fifth-order systems are solved.
Muhammet Koksal, Mehmet Emir Koksal 2011, 'Commutativity of Linear Time-Varying Differential Systems with Nonzero Initial Conditions:A Review and Some New Extensions', Mathematical Problems in Engineeringhttp://dx.doi.org/10.1155/2011/678575. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Usual properties of convolutions are shown to hold: commutativity, associativity, commutation with translation.
Erik Talvila 2009, 'Convolutions with the Continuous Primitive Integral', Abstract and Applied Analysishttp://dx.doi.org/10.1155/2009/307404. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic.
Sonja Maria Hansen, Hilde Haider, Alexandra Eichler, Claudia Godau, Peter A. Frensch,Robert Gaschler 2015, 'Fostering Formal Commutativity Knowledge with Approximate Arithmetic', PLOS ONE10.1371/journal.pone.0142551. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Other related commutativity results are also obtained.
Hamza A. S. Abujabal 1991, 'Commutativity theorems for rings with constraints on commutators', International Journal of Mathematics and Mathematical Scienceshttp://dx.doi.org/10.1155/S0161171291000911. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Experiment 1 tested first graders who had not been instructed about commutativity in school yet.
Sonja Maria Hansen, Hilde Haider, Alexandra Eichler, Claudia Godau, Peter A Frensch,Robert Gaschler 2015, 'Fostering Formal Commutativity Knowledge with Approximate Arithmetic.', PLoS ONEhttp://europepmc.org/articles/PMC4652602?pdf=render. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness.
Jinming Zhou, Tomas Baležentis, Dalia Streimikiene 2019, 'Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operatorsand Their Application to the Sustainable Selection of Search and Rescue Robots', Symmetryhttps://www.mdpi.com/2073-8994/11/2/218. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)