345 research outputs found
A Homological Approach to Factorization
Mott noted a one-to-one correspondence between saturated multiplicatively
closed subsets of a domain D and directed convex subgroups of the group of
divisibility D. With this, we construct a functor between inclusions into
saturated localizations of D and projections onto partially ordered quotient
groups of G(D). We use this functor to construct many cochain complexes of
o-homomorphisms of po-groups. These complexes naturally lead to some
fundamental structure theorems and some natural homology theory that provide
insight into the factorization behavior of D.Comment: Submitted for publication 12/15/201
A Compact Representation of Preferences in Multiple Criteria Optimization Problems
[EN] A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The analytic hierarchy process introduces relative priority levels and cardinal preferences. Lexicographical orders combine both ordinal and cardinal preferences and present the additional difficulty of establishing strict priority levels. To enhance the process of setting preferences, we propose a compact representation that subsumes the most common preference schemes in a single algebraic object. We use this representation to discuss the main properties of preferences within the context of multiple criteria optimization.Salas-Molina, F.; Pla Santamaría, D.; Garcia-Bernabeu, A.; Reig-Mullor, J. (2019). A Compact Representation of Preferences in Multiple Criteria Optimization Problems. Mathematics. 7(11):1-16. https://doi.org/10.3390/math7111092S116711Ahmadi, A., Ahmadi, M. R., & Nezhad, A. E. (2014). A Lexicographic Optimization and Augmented ϵ-constraint Technique for Short-term Environmental/Economic Combined Heat and Power Scheduling. Electric Power Components and Systems, 42(9), 945-958. doi:10.1080/15325008.2014.903542González-Arteaga, T., Alcantud, J. C. R., & de Andrés Calle, R. (2016). A new consensus ranking approach for correlated ordinal information based on Mahalanobis distance. Information Sciences, 372, 546-564. doi:10.1016/j.ins.2016.08.071Miettinen, K., & M�kel�, M. M. (2002). On scalarizing functions in multiobjective optimization. OR Spectrum, 24(2), 193-213. doi:10.1007/s00291-001-0092-9Ignizio, J. P. (1983). Generalized goal programming An overview. Computers & Operations Research, 10(4), 277-289. doi:10.1016/0305-0548(83)90003-5Sitorus, F., Cilliers, J. J., & Brito-Parada, P. R. (2019). Multi-criteria decision making for the choice problem in mining and mineral processing: Applications and trends. Expert Systems with Applications, 121, 393-417. doi:10.1016/j.eswa.2018.12.001Zyoud, S. H., & Fuchs-Hanusch, D. (2017). A bibliometric-based survey on AHP and TOPSIS techniques. Expert Systems with Applications, 78, 158-181. doi:10.1016/j.eswa.2017.02.016Erdoğan, M., & Kaya, İ. (2016). A combined fuzzy approach to determine the best region for a nuclear power plant in Turkey. Applied Soft Computing, 39, 84-93. doi:10.1016/j.asoc.2015.11.013Chen, Y., Liu, R., Barrett, D., Gao, L., Zhou, M., Renzullo, L., & Emelyanova, I. (2015). A spatial assessment framework for evaluating flood risk under extreme climates. Science of The Total Environment, 538, 512-523. doi:10.1016/j.scitotenv.2015.08.094Zammori, F. (2010). The analytic hierarchy and network processes: Applications to the US presidential election and to the market share of ski equipment in Italy. Applied Soft Computing, 10(4), 1001-1012. doi:10.1016/j.asoc.2009.07.013Carter, C. R., & Rogers, D. S. (2008). A framework of sustainable supply chain management: moving toward new theory. International Journal of Physical Distribution & Logistics Management, 38(5), 360-387. doi:10.1108/09600030810882816Ignizio, J. P. (1976). An Approach to the Capital Budgeting Problem with Multiple Objectives. The Engineering Economist, 21(4), 259-272. doi:10.1080/00137917608902798Lonergan, S. C., & Cocklin, C. (1988). The use of lexicographic goal programming in economic/ecolocical conflict analysis. Socio-Economic Planning Sciences, 22(2), 83-92. doi:10.1016/0038-0121(88)90020-1González-Pachón, J., & Romero, C. (2014). Properties underlying a preference aggregator based on satisficing logic. International Transactions in Operational Research, 22(2), 205-215. doi:10.1111/itor.1211
On Koszulity for operads of Conformal Field Theory
We study two closely related operads: the Gelfand-Dorfman operad GD and the
Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal
algebra structure. We prove Koszulity of the Conformal Lie operad using the
Groebner bases theory for operads and an operadic analogue of the Priddy
criterion. An example of deformation of an operad coming from the Hom
structures is considered. In particular we study possible deformations of the
Associative operad from the point of view of the confluence property. Only one
deformation, the operad which governs the identity turns out to be confluent. We introduce a new Hom structure, namely
Hom--Gelfand-Dorfman algebras and study their basic properties.Comment: 24 page
Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
We prove a Cauchy identity for free quasi-symmetric functions and apply it to
the study of various bases. A free Weyl formula and a generalization of the
splitting formula are also discussed.Comment: 21 pages, Latex, 2 figure
Combinatorial bases for multilinear parts of free algebras with double compatible brackets
Let X be an ordered alphabet. Lie_2(n) (and P_2(n) respectively) are the
multilinear parts of the free Lie algebra (and the free Poisson algebra
respectively) on X with a pair of compatible Lie brackets. In this paper, we
prove the dimension formulas for these two algebras conjectured by B. Feigin by
constructing bases for Lie_2(n) (and P_2(n)) from combinatorial objects. We
also define a complementary space Eil_2(n) to Lie_2(n), give a pairing between
Lie_2(n) and Eil_2(n), and show that the pairing is perfect.Comment: 38 pages; 10 figure
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