SET-BASED ORDERING ON SIMPLE MULTISETS OF INCOMPARABLE OBJECTS
Keywords:
: Simple multiset, Partial ordering, Incomparability, Difference gridAbstract
It is convincing that there exists an ordering on simple multisets of incomparable objects by means of the Jouannaud-Lascanne set-based multiset ordering. A successful attempt to show that a singleton multiset is dominated by a simple pair multiset despite the incomparability of their objects is made with respect to the ordering. Furthermore, an existence of the ordering among simple multisets of higher cardinalities where the cardinality of the preceding multiset is a unit or more less than that of the succeeding multiset is observed. Thus, we obtain an extension of the ordering to simple multisets of incomparable objects. No stronger set-based multiset ordering may be found to exist.
References
Akin-Osanaiye, B C, H C Nzelibe, and A S Agbaji. (2002). African Journal of Biotechnology. African Journal of Biotechnology. Vol. 4. Academic Journals.
Bello, Roger Hoel, Poliana Linzmeyer, Cláudia Maria Bueno Franco, Ozair Souza, Noeli Sellin, Sandra Helena Westrupp Medeiros, and Cintia Marangoni. (2014). “Pervaporation of Ethanol Produced from Banana Waste.” Waste Management 34 (8):1501–9. https://doi.org/10.1016/j.wasman.2014.04.013.
Dung, Thi Ngoc Bao, Biswarup Sen, Chin-Chao Chen, Gopalakrishnan Kumar, and Chiu-Yue Lin. (2014). “Food Waste to Bioenergy via Anaerobic Processes.” Energy
Procedia 61:307–12. https://doi.org/10.1016/j.egypro.2014.11.1113.
Fish, Wayne W, Benny D Bruton, and Vincent M Russo. n.d. “Biotechnology for Biofuels Watermelon Juice: A Promising Feedstock Supplement, Diluent, and Nitrogen Supplement for Ethanol Biofuel Production.” https://doi.org/10.1186/1754-6834-2-18.
Gabhane, Jagdish, S.P.M. Prince William, Abhijit Gadhe, Ritika Rath, Atul Narayan Vaidya, and Satish Wate. (2014). “Pretreatment of Banana Agricultural Waste for Bio-Ethanol Production: Individual and Interactive Effects of Acid and Alkali Pretreatments with Autoclaving, Microwave Heating and Ultrasonication.” Waste Management 34 (2):498–503. https://doi.org/10.1016/j.wasman.2013.10.013.
Goldemberg, José. (2007). “Ethanol for a Sustainable Energy Future.” Science (New York, N.Y.) 315 (5813):808–10. https://doi.org/10.1126/science.1137013.
Graf, Angela, and Tom Koehler. (2000). “OREGON CELLULOSE-ETHANOL STUDY An Evaluation of the Potential for Ethanol Production in Oregon Using Cellulose-
Based Feedstocks.”
Hossain, A B M S, and A R Fazliny. (2010). “Creation of Alternative Energy by Bio-Ethanol Production from Pineapple Waste and the Usage of Its Properties for Engine.” African Journal of Microbiology Research 4 (9):813–19.
Oberoi, Harinder Singh, Praveen V. Vadlani, Lavudi Saida, Sunil Bansal, and Joshua D. Hughes. (2011). “Ethanol Production from Banana Peels Using Statistically Optimized Simultaneous Saccharification and Fermentation Process.” Waste Management 31 (7):1576–84. https://doi.org/10.1016/j.wasman.2011.02.007.
Obire, O., and E. C. Anyanwu. (2009). “Impact of Various Concentrations of Crude Oil on Fungal Populations of Soil.” International Journal of Environmental Science & Technology 6 (2). Springer-Verlag:211–18. https://doi.org/10.1007/BF03327624.
Papong, Seksan, and Pomthong Malakul. (2010). “Life-Cycle Energy and Environmental Analysis of Bioethanol Production from Cassava in Thailand.” Bioresource
Technology 101 (1). Elsevier:S112–18. https://doi.org/10.1016/J.BIORTECH.2009.09.006.
Sathesh-Prabu, C., and A.G. Murugesan. (2011). “Potential Utilization of Sorghum Field Waste for Fuel Ethanol Production Employing Pachysolen Tannophilus and
Saccharomyces Cerevisiae.” Bioresource Technology 102(3):2788–92. https://doi.org/10.1016/j.biortech.2010.11.097.
Sun, Ye, and Jiayang Cheng. (2002). “Hydrolysis of Lignocellulosic Materials for Ethanol Production: A Review.” Bioresource Technology 83 (1):1–11. https://doi.org/10.1016/S0960-8524(01)00212-7.
Velásquez-Arredondo, H.I., A.A. Ruiz-Colorado, and S. De Oliveira. (2010). “Ethanol Production Process from Banana Fruit and Its Lignocellulosic Residues: Energy Analysis.” Energy 35 (7).Pergamon:3081–87. https://doi.org/10.1016/J.ENERGY.2010.03.052.
Wu, Ken-Jer, Ganesh D. Saratale, Yung-Chung Lo, Wen- Ming Chen, Ze-Jing Tseng, Ming-Ching Chang, Ben-Ching Tsai, Ay Su, and Jo-Shu Chang. (2008). “Simultaneous Production of 2,3-Butanediol, Ethanol and Hydrogen with a Klebsiella Sp. Strain Isolated from Sewage Sludge.” Bioresource Technology 99 (17). Elsevier:7966–70. https://doi.org/10.1016/J.BIORTECH.2008.03.062.
Zhang, Cunsheng, Haijia Su, Jan Baeyens, and Tianwei Tan. (2014). “Reviewing the Anaerobic Digestion of Food Waste for Biogas Production.” Renewable and Sustainable Energy Reviews 38:383–92. https://doi.org/10.1016/j.rser.2014.05.038.
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