Relevant bibliographies by topics / Set theory. Number theory

Contents

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

Academic literature on the topic 'Set theory. Number theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Set theory. Number theory"

1

Ashok, Joshi B. "Number Set Theory and Collatz Conjecture." International Journal of Mathematics Trends and Technology 55, no. 3 (2018): 196–99. http://dx.doi.org/10.14445/22315373/ijmtt-v55p525.

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Enayat, Ali. "Counting models of set theory." Fundamenta Mathematicae 174, no. 1 (2002): 23–47. http://dx.doi.org/10.4064/fm174-1-2.

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CHANG, DARWIN, and PALASH B. PAL. "NUMBER THEORY AND QUANTUM MECHANICS." Modern Physics Letters A 09, no. 20 (1994): 1845–51. http://dx.doi.org/10.1142/s0217732394001702.

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We demonstrate a simple contradiction of naive deterministic theories with quantum mechanics by showing that the spin components cannot have deterministic values for many values of the total spin of a particle. Using a theorem in number theory, we work out the complete set of spin values which display such properties. The fact that the set is infinite should prompt some modifications in the usual statement about achieving the classical limit when the value of angular momentum becomes very large.
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Ramírez, Juan. "A New Set Theory for Analysis." Axioms 8, no. 1 (2019): 31. http://dx.doi.org/10.3390/axioms8010031.

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We provide a canonical construction of the natural numbers in the universe of sets. Then, the power set of the natural numbers is given the structure of the real number system. For this, we prove the co-finite topology, C o f ( N ) , is isomorphic to the natural numbers. Then, we prove the power set of integers, 2 Z , contains a subset isomorphic to the non-negative real numbers, with all its defining structures of operations and order. We use these results to give the power set, 2 N , the structure of the real number system. We give simple rules for calculating addition, multiplication, subtr
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Chiaselotti, G., T. Gentile, and F. Infusino. "Decision systems in rough set theory: A set operatorial perspective." Journal of Algebra and Its Applications 18, no. 01 (2019): 1950004. http://dx.doi.org/10.1142/s021949881950004x.

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In rough set theory (RST), the notion of decision table plays a fundamental role. In this paper, we develop a purely mathematical investigation of this notion to show that several basic aspects of RST can be of interest also for mathematicians who work with algebraic and discrete methods.In this abstract perspective, we call decision system a sextuple [Formula: see text] [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] are non-empty sets whose elements are called, respectively, objects, condition attributes, values, [Formula: see text] is a (possibly emp
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HENRICH, ALLISON, REBECCA HOBERG, SLAVIK JABLAN, LEE JOHNSON, ELIZABETH MINTEN, and LJILJANA RADOVIĆ. "THE THEORY OF PSEUDOKNOTS." Journal of Knot Theory and Its Ramifications 22, no. 07 (2013): 1350032. http://dx.doi.org/10.1142/s0218216513500326.

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Classical knots in ℝ3 can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that point. A pseudodiagram is a knot diagram that may be missing crossing information at some of its crossings. At these crossings, it is undetermined which strand passes over. Pseudodiagrams were first introduced by Ryo Hanaki in 2010. Here, we introduce the notion of a pseudoknot, i.e. an equivalence class of pseudodiagrams under an appropriate choice of Reidem
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Grabowski, Adam. "Efficient Rough Set Theory Merging." Fundamenta Informaticae 135, no. 4 (2014): 371–85. http://dx.doi.org/10.3233/fi-2014-1129.

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WEBER, ZACH. "TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY." Review of Symbolic Logic 3, no. 1 (2010): 71–92. http://dx.doi.org/10.1017/s1755020309990281.

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This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the exist
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Burr, S. A., and P. Erdös. "A Ramsey-type property in additive number theory." Glasgow Mathematical Journal 27 (October 1985): 5–10. http://dx.doi.org/10.1017/s0017089500006029.

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Let A be a sequence of positive integers. Define P(A) to be the set of all integers representable as a sum of distinct terms of A. Note that if A contains a repeated value, we are free to use it as many times as it occurs in A. We call A complete if every sufficiently large positive integer is in P(A), and entirely complete if every positive integer is in P(A). Completeness properties have received considerable, if somewhat sporadic, attention over the years. See Chapter 6 of [3] for a survey.
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Cabbolet, Marcoen J. T. F. "A Finitely Axiomatized Non-Classical First-Order Theory Incorporating Category Theory and Axiomatic Set Theory." Axioms 10, no. 2 (2021): 119. http://dx.doi.org/10.3390/axioms10020119.

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It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the Löwenheim–Skolem theorem. This paper presents the axioms one has to accept to get rid of these two features. For that matter, some twenty axioms are formulated in a non-classical first-order language with countably many constants: to this collection of axioms is associated a universe of discourse consisting of a class of objects, each of
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Dissertations / Theses on the topic "Set theory. Number theory"

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Ki, Haseo Kechris A. S. Kechris A. S. "Topics in descriptive set theory related to number theory and analysis /." Diss., Pasadena, Calif. : California Institute of Technology, 1995. http://resolver.caltech.edu/CaltechETD:etd-10112007-111738.

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朱鏡江 and Kan-Kong Chu. "Exceptional set problems on some additive equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31212220.

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Chu, Kan-Kong. "Exceptional set problems on some additive equations /." [Hong Kong] : University of Hong Kong, 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B14763898.

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趙崇富 and Shung-fu Chiu. "An exceptional set problem on some binary additive equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31211331.

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Chiu, Shung-fu. "An exceptional set problem on some binary additive equations /." [Hong Kong : University of Hong Kong], 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13841002.

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Cruz, Quiñones Maria Dolores. "Introduction to pseudo-ordered groups." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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Bernstein, Brett David. "Higher natural numbers and omega words." Diss., Online access via UMI:, 2005.

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Jones, Rafe. "Galois martingales and the hyperbolic subset of the p-adic Mandelbrot set /." View online version; access limited to Brown University users, 2005. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3174623.

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Suresh, Arvind. "On the Characterization of Prime Sets of Polynomials by Congruence Conditions." Scholarship @ Claremont, 2015. http://scholarship.claremont.edu/cmc_theses/993.

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This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.
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Bristow, Andrew IV. "The INDEPENDENT SET Decision Problem is NP-complete." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/2573.

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In the 1970's computer scientists developed the theory of computational complexity. Some problems seemed hard-to-compute, while others were easy. It turned out that many of the hard problems were equally hard in a way that could be precisely specified. They became known as the NP-complete problems. The SATISFIABILITY problem (SAT) was the first problem to be proved NP-complete in 1971. Since then numerous other hard-to-solve problems have been proved to be in NP-complete. In this paper we will examine the problem of how to find a maximum independent set of vertices for a graph. This prob
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Books on the topic "Set theory. Number theory"

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Reischer, Corina. Nombres finis & nombres transfinis. Presses de l'Université du Québec, 2002.

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Kate, Petty, ed. Little Rabbits' first number book. Scholastic, 1999.

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Jourdain, Philip Edward Bertrand. Selected essays on the history of set theory and logics (1906-1918). CLUEB, 1991.

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Alan, Baker. Little Rabbits' first number book. Kingfisher, 1999.

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Alan, Baker. Little Rabbit's first number book. Kingfisher, 1998.

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Baker, Alan. Little Rabbit's first number book. Kingfisher, 1998.

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Kurepa, Đuro. Selected papers of Đuro Kurepa. Matematički institut SANU, 1996.

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Cantorian set theory and limitation of size. Clarendon Press, 1988.

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Hallett, Michael. Cantorian set theory and limitation of size. Clarendon, 1986.

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Mathematical problems and proofs: Combinatorics, number theory, and geometry. Plenum Press, 1998.

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Book chapters on the topic "Set theory. Number theory"

1

Vaught, Robert L. "The Number Systems." In Set Theory. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0835-8_4.

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Komjáth, Péter. "Subgraph chromatic number." In Set Theory. American Mathematical Society, 2002. http://dx.doi.org/10.1090/dimacs/058/08.

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Hall, R. R., and G. Tenenbaum. "The Set of Multiples of a Short Interval." In Number Theory. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4757-4158-2_6.

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Nerney, John Mac Sheridan. "Conventions, Set Theory, Number Systems." In An Introduction to Analytic Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42085-7_1.

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Vaught, Robert L. "More on Cardinal Numbers." In Set Theory. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0835-8_5.

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Vaught, Robert L. "Cardinal Numbers and Finite Sets." In Set Theory. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0835-8_3.

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Hájek, Petr, and Pavel Pudlák. "Arithmetic as Number Theory, Set Theory and Logic." In Perspectives in Mathematical Logic. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-22156-3_3.

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Ruzsa, Imre Z. "A Small Maximal Sidon Set." In Analytic and Elementary Number Theory. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_6.

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Dasgupta, Abhijit. "Postscript I: What Exactly Are the Natural Numbers?" In Set Theory. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8854-5_4.

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Miller, Arnold W. "Covering number of an ideal." In Descriptive Set Theory and Forcing. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-662-21773-3_16.

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Conference papers on the topic "Set theory. Number theory"

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Ali, Andreas M., Ralph E. Hudson, Flavio Lorenzelli, and Kung Yao. "Simultaneous position and number of source estimates using Random Set Theory." In Optical Engineering + Applications, edited by Franklin T. Luk. SPIE, 2008. http://dx.doi.org/10.1117/12.793856.

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Ali, Andreas M., Ralph E. Hudson, and Kung Yao. "Tracking of random number of targets with random number of sensors using Random Finite Set Theory." In ICASSP 2009 - 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009. http://dx.doi.org/10.1109/icassp.2009.4960059.

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Fajriani, Alfiah, Noor Akhmad Setiawan, and Teguh Bharata Adji. "Applying rough set theory for filtering large number of coronary artery disease (CAD) rules." In 2017 2nd International Conferences on Information Technology, Information Systems and Electrical Engineering (ICITISEE). IEEE, 2017. http://dx.doi.org/10.1109/icitisee.2017.8285531.

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Ali, Andreas M., Ralph E. Hudson, and Kung Yao. "Target tracking for randomly varying number of targets and sensors using random finite set theory." In SPIE Defense, Security, and Sensing, edited by Belur V. Dasarathy. SPIE, 2009. http://dx.doi.org/10.1117/12.820425.

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Dhall, Sudarshan K., S. Lakshmivarahan, and Pramode Verma. "On the number and the distribution of the nash equilibria in supermodular games and their impact on the tipping set." In 2009 International Conference on Game Theory for Networks (GameNets). IEEE, 2009. http://dx.doi.org/10.1109/gamenets.2009.5137462.

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Cao, Tao, Huabing Zhang, Honglong Zheng, Yufeng Yang, and Xin Wang. "Quantitative HAZOP Risk Analysis for Oil Tanks Using the Fuzzy Set Theory." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90206.

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Oil storage tanks are identified as the major hazard installations because of the hazard of huge fire & explosion. Evaluating the risk and controlling the danger is the advancement of accident prevention and the compulsory requirement of laws. HAZOP (Hazard and Operability Analysis), is a simple but intensive, systematic, qualitative risk analytical method, is an important technique for the identification of hidden hazards in operation of tank facility. It can only qualitatively account for potential risks, but cannot quantify their possibility and severity. Thus, research involving HAZOP
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Iqbal, Numan, and Gary L. Kinzel. "An Approach to Represent Imprecision in Interactive Design Using Fuzzy Set Theory." In ASME 1992 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/cie1992-0002.

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Abstract Imprecision in the values of design parameters is an inherent character of the analysis stage of engineering design when the ideas have not yet converted to precise values and some of the design parameters remain flexible. The goal of this paper is to illustrate the application of the concepts of fuzzy set theory to represent this imprecision in design after a basic analytical model of the part being evaluated is developed. The idea is to help the designer efficiently study the effect of changing the values of certain parameters so that the number of iterations required to reach a fin
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Krishna, Kota Murali, Subramanyam Krishnamurthi, and Steven N. Kramer. "Application of Fuzzy Set Theory to Planar and Spatial Mechanism Design." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0189.

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Abstract This paper describes how Fuzzy Set Theory and Fuzzy Numbers can be applied to the synthesis of planar and spatial mechanisms. The main advantage of using Fuzzy Set Theory over other methods of mechanism synthesis is that uncertainties in positions, rotations and link lengths can be quantified using the concept of membership functions. A membership function is an explicit representation of the deviation of the value of a parameter from its specified value. Numerical examples include the synthesis of a four-bar path generating mechanism with uncertain prescribed timing as well as uncert
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Gadsden, S. Andrew. "An Adaptive PID Controller Based on Bayesian Theory." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5340.

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One of the most popular trajectory-tracking controllers used in industry is the PID controller. The PID controller utilizes three types of gains and the tracking error in order to provide a control gain to a system. The PID gains may be tuned manually or using a number of different techniques. Under most operating conditions, only one set of PID gains are used. However, techniques exist to compensate for dynamic systems such as gain scheduling or basic time-varying functions. In this paper, an adaptive PID controller is presented based on Bayesian theory. The interacting multiple model (IMM) m
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Sbutega, Krsto, and Ivan Catton. "Application of Fourier-Galerkin Method to Volume Averaging Theory Based Model of Heat Sinks." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65244.

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Efficient analysis of heat sink performance is a crucial step in the optimization process of such devices. Accurate analysis of these complex geometric systems with CFD and FE methods requires fine meshes, which imply significant computational time. In this study, Volume Averaging Theory (VAT) is rigorously applied to obtain a geometrically simplified but physically accurate model for any periodic heat sink geometry. The governing equations are averaged over a Representative Averaging Volume (REV) to obtain a set of integro-differential equations. Some information about lower level phenomena i
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Reports on the topic "Set theory. Number theory"

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Molinari, Francesca, Arie Beresteanu, and Ilya Molchanov. Partial identification using random set theory. Institute for Fiscal Studies, 2010. http://dx.doi.org/10.1920/wp.cem.2010.4010.

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Fisher, Michael, Mike Bardzell, and Kurt Ludwick. PascGalois Number Theory Classroom Resources. The MAA Mathematical Sciences Digital Library, 2008. http://dx.doi.org/10.4169/loci002637.

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Gluckman, Albert G., and Aivars Celmins. Cost Effectiveness Analysis Using Fuzzy Set Theory. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada274003.

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Goodman, I. R., and V. M. Bier. A Re-Examination of the Relationship between Fuzzy Set Theory and Probability Theory. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada240243.

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Esteva, Francesc. On Negations and Algebras in Fuzzy Set Theory. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada604012.

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Blasch, Erik, and Lang Hong. Set Theory Correlation Free Algorithm for HRRR Target Tracking. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada385466.

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Sternheimer, R. M. Some remarks concerning my research in number theory. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6829851.

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McPheron, Benjamin, and Josiah Kunz. Development of a Set of Pre-class Videos for Electromagnetic Theory. Purdue University, 2019. http://dx.doi.org/10.5703/1288284316886.

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Casey, Stephen D. Number Theoretic Methods in Harmonic Analysis: Theory and Application. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada413800.

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Lindesay, James V. A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory. Office of Scientific and Technical Information (OSTI), 2001. http://dx.doi.org/10.2172/784915.

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