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Filip Kobiela

Abstract

The paper addresses the family of questions that arose from the field of interactions between phenomenology and the cognitive sciences. On the one hand, apparently partial coextensivity of research domain of phenomenology and the cognitive sciences sets the goal of their cooperation and mutual inspiration. On the other hand, there are some obstacles on the path to achieve this goal: phenomenology and the cognitive sciences have different traditions, they speak different languages, they have adopted different methodological approaches, and last but not least, their prominent exponents exhibits different styles of thinking. In order to clarify this complicated area of tensions, the paper presents the results of philosophical reflections of such topics as: 1) philosophical presuppositions and postulates of the cognitive sciences 2) abstraction of some phenomena during idealisation and the dialectical model of science's development 3) argumentation based on prediction of future development of the cognitive sciences. This finally leads to the formulation of a phenomenology-based postulate for adequate model of mind and the discussion of humanistic dimension of cognitive sciences.

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Manal Ghanem and Emad Abu Osba

Abstract

Let R be a commutative ring with unity. The main objective of this article is to study the relationships between PP-rings, generalized morphic rings and EM-rings. Although PP-rings are included in the later rings, the converse is not in general true. We put necessary and sufficient conditions to ensure the converse using idealization and polynomial rings

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Erdal Ekici

References 1. AçiKGÖZ, A.; YÜKSEL, S.; NoíRI, T. - a-I-preirresolute functions and ß-I-preirressolute functions, Bull. Malays. Math. Sci. Soc, 28 (2005), 1-8. 2. BOURBAKI, N. - Elements of Mathematics. General Topology, Part 1, Hermann, Paris, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. 3. DONTCHEV, J. - Idealization of Ganster-Reilly decomposition theorems, arxiv:math.GN/9901017v1 (1999). 4. DONTCHEV, J.; GANSTER, M.; Rose, D. - Ideal resolvability

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Romain Pepy, Michel Kieffer and Eric Walter

Reliable Robust Path Planning with Application to Mobile Robots

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.

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Rafael Nogueras and Carlos Cotta

Abstract

Multimemetic algorithms (MMAs) are a subclass of memetic algorithms in which memes are explicitly attached to genotypes and evolve alongside them. We analyze the propagation of memes in MMAs with a spatial structure. For this purpose we propose an idealized selecto-Lamarckian model that only features selection and local improvement, and study under which conditions good, high-potential memes can proliferate. We compare population models with panmictic and toroidal grid topologies. We show that the increased takeover time induced by the latter is essential for improving the chances for good memes to express themselves in the population by improving their hosts, hence enhancing their survival rates. Experiments realized with an actual MMA on three different complex pseudo-Boolean functions are consistent with these findings, indicating that memes are more successful in a spatially structured MMA, rather than in a panmictic MMA, and that the performance of the former is significantly better than that of its panmictic counterpart

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N. Gowrisankar, A. Keskin and N. Rajesh

ideals and I-irresolute functions, Papers on general topology and applications (Slippery Rock, PA, 1993), 28-37, Ann. New York Acad. Sci., 767, New York Acad. Sci., New York, 1995. 5. Gowrisankar, N.; Keskin, A.; Rajesh, N. - Some new separation axioms in ideal topological spaces, submitted. 6. Hatir, E.; Noiri, T. - On decomposition of continuity via idealization, Acta Math. Hungar., 96 (2002), 341-349. 10.1023/A:1019760901169 7. Kuratowski, K. - Topology, Vol. I, Academic Press, New York-London; Pan

Open access

Ahmad Al-Omari and Takashi Noiri

. Hungar., 105 (2004), 27-37. 5. Dontchev, J. - On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2 (1996). 6. Hatir, E.; Noiri, T. - On decompositions of continuity via idealization, Acta Math. Hungar., 96 (2002), 341-349. 7. Hatir, E.; Noiri, T. - On semi-I-open sets and semi-I-continuous functions, Acta Math. Hungar., 107 (2005), 345-353. 8. Kuratowski, C. - Topologie. I. Espaces Métrisables, Espaces Complets (French), 2d ed. Monografie Matematyczne, vol. 20, Warszawa-Wroc law, 1948

Open access

Hiroyuki Okazaki

Probability on Finite and Discrete Set and Uniform Distribution

A pseudorandom number generator plays an important role in practice in computer science. For example: computer simulations, cryptology, and so on. A pseudorandom number generator is an algorithm to generate a sequence of numbers that is indistinguishable from the true random number sequence. In this article, we shall formalize the "Uniform Distribution" that is the idealized set of true random number sequences. The basic idea of our formalization is due to [15].

Open access

Erdal Ekici

properties of pairwise extremally disconnected bitopological spaces, Proc. A. Razmadze Math. Inst. 142 (2006), 1-7. [5] J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arxiv:math. GN/9901017v1 (1999). [6] E. Ekici and Ö. Elmah, On decompositions via generalized closedness in ideal spaces, Filomat, 29 (4) (2015), 879-886. [7] E. Ekici and S. Özen, A generalized class of τ* in ideal spaces, Filomat, 27 (4) (2013), 529-535. [8] E. Ekici, On A* I -sets, C I -sets, C* I -sets and decompositions

Open access

J. Sanabria, E. Acosta, M. Salas-Brown and O. Garcia

References [1] Abd El-Monsef M.E., Lashien E.F., Nasef A.A., On I-open sets and I-continuous functions, Kyungpook Math. J., 32(1992), 21-30. [2] Dontchev J., On Hausdorff spaces via topological ideals and I-irresolute functions, In papers on General Topology and Applications, Annals of New York Academy of Sciences, 767(1995), 28-38. [3] Hatir E., Noiri T., On descompositions of continuity via idealization, Acta. Math. Hungar., 96(4)(2002), 341-349. [4] Hayashi E., Topologies defined by local