Relevant bibliographies by topics / Number concept

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Number concept'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Number concept"

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Jones, Max. "Number concepts for the concept empiricist." Philosophical Psychology 29, no. 3 (October 15, 2015): 334–48. http://dx.doi.org/10.1080/09515089.2015.1088147.

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Overmann, Karenleigh A. "Constructing a concept of number." Journal of Numerical Cognition 4, no. 2 (September 7, 2018): 464–93. http://dx.doi.org/10.5964/jnc.v4i2.161.

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Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition.
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Reshma, R., and Dr R. Balakumar. "The Concept of Fuzzy Number." International Journal of Mathematics Trends and Technology 65, no. 7 (July 25, 2019): 225–34. http://dx.doi.org/10.14445/22315373/ijmtt-v65i7p528.

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Overmann, Karenleigh A., Thomas Wynn, and Frederick L. Coolidge. "The prehistory of number concept." Behavioral and Brain Sciences 34, no. 3 (May 19, 2011): 142–44. http://dx.doi.org/10.1017/s0140525x10002189.

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AbstractCarey leaves unaddressed an important evolutionary puzzle: In the absence of a numeral list, how could a concept of natural number ever have arisen in the first place? Here we suggest that the initial development of natural number must have bootstrapped on a material culture scaffold of some sort, and illustrate how this might have occurred using strings of beads.
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Damerow, Peter. "Number as a Second-Order Concept." Science in Context 9, no. 2 (1996): 139–49. http://dx.doi.org/10.1017/s0269889700002386.

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My contribution will focus on a central issue of Yehuda Elkana's anthropology of knowledge — namely, the role of reflectivity in the development of knowledge. Let me therefore start with a quotation from Yehuda's paper “Experiment as a Second-Order Concept.”
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Wesley, Frank. "Number Concept Formation in the Rat." Zeitschrift für Tierpsychologie 16, no. 5 (April 26, 2010): 605–27. http://dx.doi.org/10.1111/j.1439-0310.1959.tb02077.x.

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Peacocke, Christopher. "The concept of a natural number." Australasian Journal of Philosophy 76, no. 1 (March 1998): 105–9. http://dx.doi.org/10.1080/00048409812348241.

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Gregorius, Hans-Rolf. "On the concept of effective number." Theoretical Population Biology 40, no. 2 (October 1991): 269–83. http://dx.doi.org/10.1016/0040-5809(91)90056-l.

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Gürefe, Nejla, and Gülfem Sarpkaya Aktaş. "The concept of prime number and the strategies used in explaining prime numbers." South African Journal of Education, no. 40(3) (August 31, 2020): 1–9. http://dx.doi.org/10.15700/saje.v40n3a1741.

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The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher’s knowledge effects the students’ knowledge. A teacher should use appropriate mathematical explanation to be understood well by her/his students. In the study reported on here we investigated how prospective mathematics teachers defined the concept of prime number and which strategies they employed to explain the concept. The study was a descriptive survey within qualitative research. Forty-eight participants took part in the study and all completed the abstract algebra courses where they learned about the concept in question. The data collection tool was a form comprising 3 open-ended questions challenging what the concept of prime number was and how this concept could be explained to secondary/high school students. The data were analysed and the results show that the preservice teachers experienced great difficulty in defining the concept of prime number and that they used rules to explain prime numbers.
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Chakraborty, Avishek, Sankar Prasad Mondal, Ali Ahmadian, Norazak Senu, Shariful Alam, and Soheil Salahshour. "Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications." Symmetry 10, no. 8 (August 7, 2018): 327. http://dx.doi.org/10.3390/sym10080327.

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In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.
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Dissertations / Theses on the topic "Number concept"

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Gordon, Lisa Lande. "Children's understanding of basic number concept." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186857.

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Three experiments were completed in this study in order to explore gist/verbatim independence/dependence. The first experiment was interested in developmental differences in verbatim memory performance, while the second and third experiments were concerned with developmental differences in verbatim memory and in relationships between verbatim and separate forms of gist memories. Extant data have demonstrated that accurate performance on reasoning tasks does not rely on accurate verbatim memory. However, how separate gists interact with each other, and each in relation to verbatim memory, has previously received scant attention. Results from Experiments 2 and 3 revealed stochastic independence between gists, and between separate gists and verbatim memory. In addition, distinct developmental patterns were uncovered. Younger subjects appear to have performed most accurately on nominal gist, while second grade subjects performed worst on nominal probes. Similarly, second graders responded most accurately on relational probes, while preschoolers performed poorest on relational probes. Additionally, consistent with recent literature on memory development that finds verbatim-reasoning independence, verbatim probes were not found to yield the highest rate of accuracy. If performance accuracy on reasoning tasks was dependent on accurate verbatim encoding, memory would have been better for verbatim information than for both relational and nominal. Experiment 3 explored the effects of training on gist extraction. Although training was not found to generate a statistically significant difference in performance for either age relative to the control groups' performance, indirect support for its impact on performance was found, and reviewed. Relative to those in the control group, the preschoolers in the experimental group seemed to benefit from training and demonstrated a performance pattern comparable to that of the second graders', although significance was not determined in these experiments. In summary, clear evidence of verbatim-gist independence was found, and indicates that separate gists may also function as distinct and individual processes. Additionally, there was some indication that training may elicit comparable gist performance patterns between age-groups, but the subject pool in these experiments appears to have been too small to exploit a training impact.
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Chan, Wai-lan Winnie. "An investigation into two-digit number processing among Chinese children and adults." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B42841495.

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Anderson, Ursula Simone. "Color, shape, and number identity-nonidentity responding and concept formation in orangutans." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42740.

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The ability to recognize sameness among objects and events is a prerequisite for abstraction and forming concepts about what one has learned; thus, identity and nonidentity learning can be considered the backbone of higher-order human cognitive abilities. Discovering identity relations between the constituent properties of objects is an important ability that often characterizes the comparisons that humans make so it is important to devote attention to understanding how nonhuman primates process and conceptualize part-identity as well as whole-identity. Because the ability to generalize the results of learning is to what concepts ultimately reduce, the series of experiments herein first investigated responding to part-identity and -nonidentity and whole-identity and -nonidentity and then explored the generality of such learning to the formation of concepts about color, shape, and cardinal number. The data from Experiments 1, 2, and 3 indicated that the two orangutans learned to respond concurrently to color whole-identity and -nonidentity and they responded faster to color whole-identity. Additionally, both subjects learned to respond concurrently to color and shape part- and whole-identity and for the most part, it was easier for them to do so with color part- and whole-identity problems than shape part- and whole-identity problems. Further, their learned responses to color and shape part- and whole-identity fully transferred to novel color part-identity problems for both subjects and fully transferred to novel color and shape whole-identity problems for one orangutan. The data from Experiments 4, 5, and 6 showed that one subject learned to judge numerical identity when both irrelevant dimensions were cue-constant, but the subject did not do the same when one or more irrelevant dimensions were cue-ambiguous. Further, the subject's accuracy was affected by the numerical distance and the numerical total of comparisons during acquisition of the conditional discrimination. The subject subsequently formed a domain-specific concept about numerical identity as evinced by the transfer of learning to novel numerosities instantiated with novel, cue-constant element colors and shapes and novel numerosities instantiated with cue-constant, familiar element colors and shapes. Given the adaptive significance of using concepts, it is important to investigate if and how nonhuman primates form identity concepts for which they categorize or classify the stimuli around them. This dissertation provided evidence about the extent to which orangutans learned to respond to color, shape, and number identity and nonidentity and subsequent concept formation from such learning. The findings from this study will help in understanding the convergence and divergence in the expression abstraction in the primate phylogeny, thus, informing our understanding about the origins and mechanisms of cognition in human and nonhuman primates.
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Cock, Josephine Judy. "Implicit learning : number rules and invariant features." Thesis, University of Reading, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320132.

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Wynn, M. Karen (Margaret Karen). "The development of counting and the concept of number." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/13719.

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Chan, Wai-lan Winnie, and 陳偉蘭. "An investigation into two-digit number processing among Chinese children and adults." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841495.

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Safi, Farshid. "Exploring the Understanding of Whole Number Concepts and Operations: A Case Study Analysis of Prospective Elementary School Teachers." Doctoral diss., Orlando, Fla. : University of Central Florida, 2009. http://purl.fcla.edu/fcla/etd/CFE0002811.

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Roy, George J. "Prospective teachers' development of whole number concepts and operations during a classroom teaching experiment." Orlando, Fla. : University of Central Florida, 2008. http://purl.fcla.edu/fcla/etd/CFE0002398.

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Lunken, Eugene Jonah. "Is subitizing simply canonical pattern matching." Thesis, Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/29426.

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Gea, Luis Daniel. "Genetic diversity and gain : the concept of a status number." Thesis, University of Canterbury. Forestry, 1997. http://hdl.handle.net/10092/7197.

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A trade-off always tends to exist involving genetic gains and selection intensity, on the one hand, and the remaining effective population size (usually known as Ne), on the other. A new approach is presented and analysed for different breeding situations, using stochastic simulations, in terms of mating designs and subline sizes, guiding breeders through a new concept of status number (Ns) and its trade-off with gain. Status number is defined as half the inverse of the average coancestry and depicts the current state of the population. The status number concept can easily be applied to deployment of different genotypes with unequal representation. Breeding schemes with small breeding groups are slightly more efficient in preserving status number through multiple generations than breeding schemes with large groups. Medium- to large-size breeding groups showed a comparatively small reduction in aggregated status number over generations but showed greater increases in gain compared with small groups. Inbreeding in small elites becomes so great that it is likely to cause fertility problems and disturb selection considerably. Small breeding groups will probably not be useful for a sustainable long-term breeding strategy. Substantial benefits on status number for subdividing the population into small breeding groups will only be seen after numerous generations. Selection schemes that maximise gain by unrestricted combined index selection will result in rapid inbreeding, and may not be sustainable in the long term. Selection procedures that place less emphasis on family information would best meet long-term diversity targets. However, gains may be too low for mating systems and selection procedures that do not include a between-family component, especially with low heritabilities. This is a good reason for using a large number of families as founders of the breeding population. Going from selection within only 0.5 or 1 available cross per parent per generation (made equivalent to within-family selection) to 2.5 crosses per parent (restricting the number of individuals chosen per full-sib family) resulted in substantial increases in genetic gain, depending on heritability. However, increasing the number of crosses per parent up to 2.5 does carry a modest penalty of increased coefficient of inbreeding and reduced status number. Higher levels of gain per unit of status number loss are obtained with a conservative within family selection strategy but to reach the same level of gain more cycles of breeding will be required. Effects of departures from assumptions (zero inbreeding coefficient and coancestry for the founders, genes being independently assorted, no mutation and interactions, or combinations from departures of the neutrality assumption) , singly and in various combinations will occur, meaning that calculations and predictions based on pedigrees will be biased. Future work will require modelling the effects for departures from the idealised assumptions and laboratory-based quantification of departures from some key assumptions.
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Books on the topic "Number concept"

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Aboff, Marcie. If you were an even number. Mankato, MN: Picture Window Books, 2009.

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Badiou, Alain. Number and numbers. Cambridge: Polity Press, 2008.

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Aboff, Marcie. If you were an odd number. Mankato, MN: Picture Window Books, 2009.

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Freeman, Marcia S. My sister is in third grade: Putting numbers in order. Vero Beach, FL: Rourke Pub., 2008.

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Number Concept. Independently Published, 2021.

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Number Concept. Independently Published, 2020.

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Conant, Levi Leonard. Number Concept. Independently Published, 2021.

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Conant, Levi. Number Concept. Independently Published, 2021.

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Conant, Levi. Number Concept. Independently Published, 2021.

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Number Concept. Independently Published, 2021.

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Book chapters on the topic "Number concept"

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Hutten, Ernest H. "The Concept of Number." In The Origins of Science, 126–41. London: Routledge, 2022. http://dx.doi.org/10.4324/9781003333579-13.

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Neal, Katherine. "Transformation of the Number Concept." In From Discrete to Continuous, 1–11. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-0077-1_1.

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Simon, Martin A. "Developing a Concept of Multiplication of Fractions: Building on Constructivist and Sociocultural Theory." In Constructing Number, 193–212. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00491-0_9.

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Bell, John L. "The Development of the Number Concept." In The Western Ontario Series in Philosophy of Science, 29–52. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4209-0_3.

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Maffei, Anthony C., and Teresa M. Hauck. "Chapter 6 The Concept of Number." In Purposeful Play with Your Preschooler, 33–39. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4899-6385-7_6.

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White, Sonia L. J. "Number Concept Development in Early Childhood." In The SAGE Handbook of Developmental Psychology and Early Childhood Education, 329–46. 1 Oliver's Yard, 55 City Road London EC1Y 1SP: SAGE Publications Ltd, 2019. http://dx.doi.org/10.4135/9781526470393.n19.

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Albano, Alexandre. "Upper Bound for the Number of Concepts of Contranominal-Scale Free Contexts." In Formal Concept Analysis, 44–53. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07248-7_4.

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Pollard, Stephen. "The Origin of the Concept of Number." In Essays on the Foundations of Mathematics by Moritz Pasch, 55–93. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-9416-2_4.

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Meena, Seema, and Bipul Kumar. "Number Plate Recognition: Concept and Its Applications." In Algorithms for Intelligent Systems, 667–72. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-6707-0_65.

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Maor, Eli. "Interlude: An Excursion into the Number Concept." In To Infinity and Beyond, 40–43. Boston, MA: Birkhäuser Boston, 1987. http://dx.doi.org/10.1007/978-1-4612-5394-5_7.

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Conference papers on the topic "Number concept"

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Galanopoulos, Damianos, Foteini Markatopoulou, Vasileios Mezaris, and Ioannis Patras. "Concept Language Models and Event-based Concept Number Selection for Zero-example Event Detection." In ICMR '17: International Conference on Multimedia Retrieval. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3078971.3079043.

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Saito, Chika, Takahiko Nakatani, Yukio Miyairi, Kazuya Yuuki, Mikio Makino, Hiroshi Kurachi, Wolfgang Heuss, et al. "New Particulate Filter Concept to Reduce Particle Number Emissions." In SAE 2011 World Congress & Exhibition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2011. http://dx.doi.org/10.4271/2011-01-0814.

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Zhao, Yizheng, and Renate Schmidt. "On Concept Forgetting in Description Logics with Qualified Number Restrictions." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/274.

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This paper presents a practical method for computing solutions of concept forgetting in the description logic ALCOQ(neg,and,or), basic ALC extended with nominals, qualified number restrictions, role negation, role conjunction and role disjunction. The method is based on a non-trivial generalisation of Ackermann's Lemma, and attempts to compute either semantic solutions of concept forgetting or uniform interpolants in ALCOQ(neg,and,or). It is so far the only approach to concept forgetting in description logics with number restrictions plus nominals, as well as in description logics with ABoxes. Results of an evaluation with a prototypical implementation have shown that the method was successful in more than 90% of the test cases from a large corpus of biomedical ontologies. In only 13.2% of these cases the solutions were semantic solutions.
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Marghescu, Andrei, Paul Svasta, and Emil Simion. "Optimising ring oscillator-based true random number generators concept on FPGA." In 2016 39th International Spring Seminar on Electronics Technology (ISSE). IEEE, 2016. http://dx.doi.org/10.1109/isse.2016.7563178.

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Hu, Jie, Guoniu Zhu, Jin Qi, Yinghong Peng, and Xiaohong Peng. "Design Concept Evaluation Based on Rough Number and Information Entropy Theory." In 2015 IEEE 12th Intl. Conf. on Ubiquitous Intelligence and Computing, 2015 IEEE 12th Intl. Conf. on Autonomic and Trusted Computing and 2015 IEEE 15th Intl. Conf. on Scalable Computing and Communications and its Associated Workshops (UIC-ATC-ScalCom). IEEE, 2015. http://dx.doi.org/10.1109/uic-atc-scalcom-cbdcom-iop.2015.257.

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Mitsudharmadi, Hatsari, and Yongdong Cui. "Implementation of Co-Flow Jet Concept on Low Reynolds Number Airfoil." In 40th Fluid Dynamics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-4717.

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Chaser, Ramon, L. McKinney, and M. Fronin. "A two stage-to-orbit high staging Mach number design concept." In 2000 World Aviation Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2000. http://dx.doi.org/10.2514/6.2000-5605.

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Liu, Qiang, Jie Li, and Zhou Zhou. "Low Reynolds Number High-Lift Airfoil Design for HALE Concept UAV." In 24th AIAA Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2006. http://dx.doi.org/10.2514/6.2006-3462.

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Chase, Ramon L., L. E. Mckinney, and M. D. Froning. "A Two Stage-to-Orbit High Staging Mach Number Design Concept." In World Aviation Congress & Exposition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2000. http://dx.doi.org/10.4271/2000-01-5605.

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Sathya K., Premalatha J., Vani Rajasekar, Madhan Kumar M., Deepak M., and Manoj S. R. "Modified linear congruential generator to secure random number generation." In PROCEEDINGS OF THE 4TH NATIONAL CONFERENCE ON CURRENT AND EMERGING PROCESS TECHNOLOGIES E-CONCEPT-2021. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0068654.

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Reports on the topic "Number concept"

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MOSKALENKO, O. L., S. Yu TERESHCHENKO, and E. V. KASPAROV. INTERNET DEPENDENCE: CONCEPT, TYPES, PREVENTION. Science and Innovation Center Publishing House, April 2022. http://dx.doi.org/10.12731/2658-4034-2022-13-2-2-102-109.

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The article presents a review of the literature on the actual problem of modern society. The number of Internet addicts is increasing every year. In all age groups, and especially among young people, preventive measures should be taken. Psychological prevention, a healthy lifestyle, increasing self-esteem and stress resistance.
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Zarrieß, Benjamin, and Anni-Yasmin Turhan. Most Specific Generalizations w.r.t. General EL-TBoxes. Technische Universität Dresden, 2013. http://dx.doi.org/10.25368/2022.196.

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In the area of Description Logics the least common subsumer (lcs) and the most specific concept (msc) are inferences that generalize a set of concepts or an individual, respectively, into a single concept. If computed w.r.t. a general EL-TBox neither the lcs nor the msc need to exist. So far in this setting no exact conditions for the existence of lcs- or msc-concepts are known. This report provides necessary and suffcient conditions for the existence of these two kinds of concepts. For the lcs of a fixed number of concepts and the msc we show decidability of the existence in PTime and polynomial bounds on the maximal roledepth of the lcs- and msc-concepts. The latter allows to compute the lcs and the msc, respectively.
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Baader, Franz, Gerhard Brewka, and Oliver Fernández Gil. Adding Threshold Concepts to the Description Logic EL. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.215.

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We introduce an extension of the lightweight Description Logic EL that allows us to de_ne concepts in an approximate way. For this purpose, we use a graded membership function, which for each individual and concept yields a number in the interval [0, 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ then collect all the individuals that belong to C with degree ~ t. We generalize a well-known characterization of membership in EL concepts to construct a specific graded membership function deg, and investigate the complexity of reasoning in the Description Logic τEL(deg), which extends EL by threshold concepts defined using deg. We also compare the instance problem for threshold concepts of the form C>t in τEL(deg) with the relaxed instance queries of Ecke et al.
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Baader, Franz. Concept Descriptions with Set Constraints and Cardinality Constraints. Technische Universität Dresden, 2017. http://dx.doi.org/10.25368/2022.232.

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We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, both without and with TBoxes.
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Lutz, Carsten, Ulrike Sattler, and Lidia Tendera. The Complexity of Finite Model Reasoning in Description Logics. Technische Universität Dresden, 2002. http://dx.doi.org/10.25368/2022.123.

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We analyze the complexity of finite model reasoning in the description logic ALCQI, i.e. ALC augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that all relevant reasoning tasks such as concept satisfiability and ABox consistency are EXPTIME-complete, regardless of whether the numbers in number restrictions are coded unarily or binarily. Thus, finite model reasoning with ALCQI is not harder than standard reasoning with ALCQI.
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Lutz, Carsten. Adding Numbers to the SHIQ Description Logic - First Results. Aachen University of Technology, 2001. http://dx.doi.org/10.25368/2022.117.

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Recently, the Description Logic (DL) SHIQ has found a large number of applications. This success is due to the fact that SHIQ combines a rich expressivity with efficient reasoning, as is demonstrated by its implementation in DL systems such as FaCT and RACER. One weakness of SHIQ, however, limits its usability in several application areas: numerical knowledge such as knowledge about the age, weight, or temperature of real-world entities cannot be adequately represented. In this paper, we propose an extension of SHIQ that aims at closing this gap. The new Description Logic Q-SHIQ, which augments SHIQ by additional, 'concrete domain' style concept constructors, allows to refer to rational numbers in concept descriptions, and also to define concepts based on the comparison of numbers via predicates such as < or =. We argue that this kind of expressivity is needed in many application areas such as reasoning about the semantic web. We prove reasoning with Q-SHIQ to be EXPTIME-complete (thus not harder than reasoning with SHIQ) by devising an automata-based decision procedure.
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7

Brandt, Sebastian. Reasoning in ELH w.r.t. General Concept Inclusion Axioms. Technische Universität Dresden, 2004. http://dx.doi.org/10.25368/2022.140.

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In the area of Description Logic (DL) based knowledge representation, research on reasoning w.r.t. general terminologies has mainly focused on very expressive DLs. Recently, though, it was shown for the DL EL, providing only the constructors conjunction and existential restriction, that the subsumption problem w.r.t. cyclic terminologies can be decided in polynomial time, a surprisingly low upper bound. In this paper, we show that even admitting general concept inclusion (GCI) axioms and role hierarchies in EL terminologies preserves the polynomial time upper bound for subsumption. We also show that subsumption becomes co-NP hard when adding one of the constructors number restriction, disjunction, and `allsome', an operator used in the DL k-rep. An interesting implication of the first result is that reasoning over the widely used medical terminology snomed is possible in polynomial time.
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8

Küsters, Ralf, and Ralf Molitor. Computing Most Specific Concepts in Description Logics with Existential Restrictions. Aachen University of Technology, 2000. http://dx.doi.org/10.25368/2022.108.

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Computing the most specific concept (msc) is an inference task that can be used to support the 'bottom-up' construction of knowledge bases for KR systems based on description logics. For description logics that allow for number restrictions or existential restrictions, the msc need not exist, though. Previous work on this problem has concentrated on description logics that allow for universal value restrictions and number restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. More precisely, we show that, for the description logic ALE (which allows for conjunction, universal value restrictions, existential restrictions, negation of atomic concepts) the msc of an ABox-individual only exists in case of acyclic ABoxes. For cyclic ABoxes, we show how to compute an approximation of the msc. Our approach for computing the (approximation of the) msc is based on representing concept descriptions by certain trees and ABoxes by certain graphs, and then characterizing instance relationships by homomorphisms from trees into graphs. The msc/approximation operation then mainly corresponds to unraveling the graphs into trees and translating them back into concept descriptions.
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9

Baader, Franz, and Barbara Morawska. Matching with respect to general concept inclusions in the Description Logic EL. Technische Universität Dresden, 2014. http://dx.doi.org/10.25368/2022.205.

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Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics (DLs) almost 20 years ago, motivated by applications in the Classic system. For the DL EL, it was shown in 2000 that the matching problem is NP-complete. It then took almost 10 years before this NP-completeness result could be extended from matching to unification in EL. The next big challenge was then to further extend these results from matching and unification without a TBox to matching and unification w.r.t. a general TBox, i.e., a finite set of general concept inclusions. For unification, we could show some partial results for general TBoxes that satisfy a certain restriction on cyclic dependencies between concepts, but the general case is still open. For matching, we solve the general case in this paper: we show that matching in EL w.r.t. general TBoxes is NP-complete by introducing a goal-oriented matching algorithm that uses non-deterministic rules to transform a given matching problem into a solved form by a polynomial number of rule applications. We also investigate some tractable variants of the matching problem.
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10

Baader, Franz, and Oliver Fernández Gil. Extending the Description Logic τEL(deg) with Acyclic TBoxes. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.226.

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In a previous paper, we have introduced an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we have defined a graded membership function deg, which for each individual and concept yields a number in the interval [0; 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ 2 ∈ {<, ≤, >, ≥} then collect all the individuals that belong to C with degree ~ t. We have then investigated the complexity of reasoning in the Description Logic τEL(deg), which is obtained from EL by adding such threshold concepts. In the present paper, we extend these results, which were obtained for reasoning without TBoxes, to the case of reasoning w.r.t. acyclic TBoxes. Surprisingly, this is not as easy as might have been expected. On the one hand, one must be quite careful to define acyclic TBoxes such that they still just introduce abbreviations for complex concepts, and thus can be unfolded. On the other hand, it turns out that, in contrast to the case of EL, adding acyclic TBoxes to τEL(deg) increases the complexity of reasoning by at least on level of the polynomial hierarchy.
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