383,468 research outputs found
On Weakly Associative Lattices and Near Lattices
The main aim of this article is to introduce formally two generalizations of lattices, namely weakly associative lattices and near lattices, which can be obtained from the former by certain weakening of the usual well-known axioms. We show selected propositions devoted to weakly associative lattices and near lattices from Chapter 6 of [15], dealing also with alternative versions of classical axiomatizations. Some of the results were proven in the Mizar [1], [2] system with the help of Prover9 [14] proof assistant.Damian Sawicki - Institute of Informatics, University of BiaĆystok, PolandAdam Grabowski - Institute of Informatics, University of BiaĆystok, PolandGrzegorz Bancerek, CzesĆaw Bylinski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in
Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Grzegorz Bancerek, CzesĆaw Bylinski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9â32, 2018. doi:10.1007/s10817-017-9440-6.Garrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967.B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.Ervin Fried and George GrĂ€tzer. Some examples of weakly associative lattices. Colloquium Mathematicum, 27:215â221, 1973. doi:10.4064/cm-27-2-215-221.Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211â221, 2015. doi:10.1007/s10817-015-9333-5.Adam Grabowski and Markus Moschner. Managing heterogeneous theories within a mathematical knowledge repository. In Andrea Asperti, Grzegorz Bancerek, and Andrzej Trybulec, editors, Mathematical Knowledge Management Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 116â129. Springer, 2004. doi:10.1007/978-3-540-27818-4_9. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19â21, 2004.Adam Grabowski and Damian Sawicki. On two alternative axiomatizations of lattices by McKenzie and Sholander. Formalized Mathematics, 26(2):193â198, 2018. doi:10.2478/forma-2018-0017.Adam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49â64. Springer, 2006. doi:https://doi.org/10.1007/11618027 4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15â17, 2005, Revised Selected Papers.Adam Grabowski, Artur KorniĆowicz, and Christoph Schwarzweller. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45â54. IEEE, 2015. doi:10.15439/2015F229.George GrĂ€tzer. General Lattice Theory. Academic Press, New York, 1978.George GrĂ€tzer. Lattice Theory: Foundation. BirkhĂ€user, 2011.Dominik Kulesza and Adam Grabowski. Formalization of quasilattices. Formalized Mathematics, 28(2):217â225, 2020. doi:10.2478/forma-2020-0019.William McCune. Prover9 and Mace4. 2005â2010.William McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.Ranganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.StanisĆaw Zukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215â222, 1990.292778
Formalization of Quasilattices
The main aim of this article is to introduce formally one of the generalizations of lattices, namely quasilattices, which can be obtained from the axiomatization of the former class by certain weakening of ordinary absorption laws. We show propositions QLT-1 to QLT-7 from [15], presenting also some short variants of corresponding axiom systems. Some of the results were proven in the Mizar [1], [2] system with the help of Prover9 [14] proof assistant.Dominik Kulesza - Institute of Informatics, University of BiaĆystok, PolandAdam Grabowski - Institute of Informatics, University of BiaĆystok, PolandGrzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, Karol PÄ
k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261â279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Grzegorz Bancerek, CzesĆaw ByliĆski, Adam Grabowski, Artur KorniĆowicz, Roman Matuszewski, Adam Naumowicz, and Karol PÄ
k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9â32, 2018. doi:10.1007/s10817-017-9440-6.Garrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967.B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. A Compendium of Continuous Lattices. Springer-Verlag, Berlin, Heidelberg, New York, 1980.Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211â221, 2015. doi:10.1007/s10817-015-9333-5.Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Formalized Mathematics, 6(1):117â121, 1997.Adam Grabowski and Markus Moschner. Managing heterogeneous theories within a mathematical knowledge repository. In Andrea Asperti, Grzegorz Bancerek, and Andrzej Trybulec, editors, Mathematical Knowledge Management Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 116â129. Springer, 2004. doi:10.1007/978-3-540-27818-4_9. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19â21, 2004.Adam Grabowski and Damian Sawicki. On two alternative axiomatizations of lattices by McKenzie and Sholander. Formalized Mathematics, 26(2):193â198, 2018. doi:10.2478/forma-2018-0017.Adam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49â64. Springer, 2006. doi:https://doi.org/10.1007/11618027_4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15â17, 2005, Revised Selected Papers.Adam Grabowski, Artur KorniĆowicz, and Christoph Schwarzweller. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45â54. IEEE, 2015. doi:10.15439/2015F229.George GrĂ€tzer. General Lattice Theory. Academic Press, New York, 1978.George GrĂ€tzer. Lattice Theory: Foundation. BirkhĂ€user, 2011.William McCune. Prover9 and Mace4. 2005â2010.William McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.Ranganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.StanisĆaw Ć»ukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215â222, 1990.28221722
Special Libraries, September 1978
Volume 69, Issue 9https://scholarworks.sjsu.edu/sla_sl_1978/1007/thumbnail.jp
Using Sociocultural Theory to Guide Teacher Use and Integration of Instructional Technology in Two Professional Development Schools
This article demonstrates how sociocultural theories can be used to support strategic structuring of professional development activities for preservice and practicing teachers on technology use and integration. Examples are drawn from the authors\u27 experiences with teachers in two professional development schools that participated in a four-year Preparing Tomorrow\u27s Teachers in Technology (PT3) project. After a review of sociocultural theory and their context, the authors describe three activity systems in these schools: one for practicing teachers, one for preservice teachers, and a joint preservice/practicing teacher system. Important supports for use and integration of technology built into each of these activity systems included varied activities aimed at both beginning and advanced technology users, multiple levels of assisted performance, and a collaborative culture that offered numerous opportunities for shared work. Lessons learned and implications for teacher educators involved in similar partnerships are outlined
Special Libraries, December 1977
Volume 68, Issue 12https://scholarworks.sjsu.edu/sla_sl_1977/1008/thumbnail.jp
Learning styles: Individualizing computerâbased learning environments
In spite of its importance, learning style is a factor that has been largely ignored in the design of educational software. Two issues concerning a specific set of learning styles, described by Honey and Mumford (1986), are considered here. The first relates to measurement and validity. This is discussed in the context of a longitudinal study to test the predictive validity of the questionnaire items against various measures of academic performance, such as course choice and level of attainment in different subjects. The second issue looks at how the learning styles can be used in computerâbased learning environments. A reâexamination of the four learning styles (Activist, Pragmatist, Reflector and Theorist) suggests that they can usefully be characterized using two orthogonal dimensions. Using a limited number of pedagogical building blocks, this characterization has allowed the development of a teaching strategy suitable for each of the learning styles. Further work is discussed, which will use a multiâstrategy basic algebra tutor to assess the effect of matching teaching strategy to learning style
Enhancement of Image Resolution by Binarization
Image segmentation is one of the principal approaches of image processing.
The choice of the most appropriate Binarization algorithm for each case proved
to be a very interesting procedure itself. In this paper, we have done the
comparison study between the various algorithms based on Binarization
algorithms and propose a methodologies for the validation of Binarization
algorithms. In this work we have developed two novel algorithms to determine
threshold values for the pixels value of the gray scale image. The performance
estimation of the algorithm utilizes test images with, the evaluation metrics
for Binarization of textual and synthetic images. We have achieved better
resolution of the image by using the Binarization method of optimum
thresholding techniques.Comment: 5 pages, 8 figure
Special Libraries, July 1978
Volume 69, Issue 7https://scholarworks.sjsu.edu/sla_sl_1978/1005/thumbnail.jp
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