Relevant bibliographies by topics / 010101 Algebra and Number Theory

Academic literature on the topic '010101 Algebra and Number Theory'

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Published: 10 December 2022
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Journal articles on the topic "010101 Algebra and Number Theory"

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W., H. C., and Michael Pohst. "Algorithmic Methods in Algebra and Number Theory." Mathematics of Computation 55, no. 192 (October 1990): 876. http://dx.doi.org/10.2307/2008461.

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Passow, Eli, and Theodore J. Rivlin. "Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory." Mathematics of Computation 58, no. 198 (April 1992): 859. http://dx.doi.org/10.2307/2153227.

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Askey, Richard. "CHEBYSHEV POLYNOMIALS From Approximation Theory to Algebra and Number Theory." Bulletin of the London Mathematical Society 23, no. 3 (May 1991): 311–12. http://dx.doi.org/10.1112/blms/23.3.311.

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Borwein, Peter B. "Chebyshev polynomials: From approximation theory to algebra and number theory." Journal of Approximation Theory 66, no. 3 (September 1991): 353. http://dx.doi.org/10.1016/0021-9045(91)90038-c.

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Charafi, A. "Chebyshev polynomials—From approximation theory to algebra and number theory." Engineering Analysis with Boundary Elements 9, no. 2 (January 1992): 190. http://dx.doi.org/10.1016/0955-7997(92)90065-f.

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Charnow, A., and E. Charnow. "69.40 An Application of Algebra to Number Theory." Mathematical Gazette 69, no. 450 (December 1985): 292. http://dx.doi.org/10.2307/3617580.

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Бедратюк, Леонід Петрович, and Ганна Іванівна Бедратюк. "Computer algebra systems in the elementary number theory." Eastern-European Journal of Enterprise Technologies 6, no. 4(66) (December 16, 2013): 10–13. http://dx.doi.org/10.15587/1729-4061.2013.18892.

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Cheung, Y. L. "Learning number theory with a computer algebra system." International Journal of Mathematical Education in Science and Technology 27, no. 3 (May 1996): 379–85. http://dx.doi.org/10.1080/0020739960270308.

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Yackel, C. A., and J. K. Denny. "Partial Fractions in Calculus, Number Theory, and Algebra." College Mathematics Journal 38, no. 5 (November 2007): 362–74. http://dx.doi.org/10.1080/07468342.2007.11922261.

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Gaj, Kris, and Rainer Steinwandt. "Hardware architectures for algebra, cryptology, and number theory." Integration 44, no. 4 (September 2011): 257–58. http://dx.doi.org/10.1016/j.vlsi.2011.04.002.

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Dissertations / Theses on the topic "010101 Algebra and Number Theory"

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Bingham, Aram. "Commutative n-ary Arithmetic." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/1959.

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Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Higher order operations yield wider factorization and representation possibilities which correspond to reductions in the set of primes as well as tiered notions of primality. This comes at the expense of familiar algebraic properties such as associativity, and unique factorization. Criteria for primality and a naive testing algorithm are given for the ternary arithmetic, drawing heavily upon modular arithmetic. Finally, connections with the theory of partitions of integers and quadratic forms are discussed in relation to questions about cardinality of primes.
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Sordo, Vieira Luis A. "ON P-ADIC FIELDS AND P-GROUPS." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/43.

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The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second part deals with the theory of finite groups. We treat computations of Chermak-Delgado lattices of p-groups. We compute the Chermak-Delgado lattices for all p-groups of order p^3 and p^4 and give results on p-groups of order p^5.
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Alnominy, Madai Obaid. "Monomial Progenitors and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/619.

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The main objective of this project is to find the original symmetric presentations of some very important finite groups and to give our constructions of some of these groups. We have found the Mathieu sporadic group M11, HS × D5, where HS is the sporadic group Higman-Sim group, the projective special unitary group U(3; 5) and the projective special linear group L2(149) as homomorphic images of the monomial progenitors 11*4 :m (5 :4), 5*6 :m S5 and 149*2 :m D37. We have also discovered 24 : S3 × C2, 24 : A5, (25 : S4), 25 : S3 × S3, 33 : S4 × C2, S6, 29: PGL(2,7), 22 • (S6 : S6), PGL(2,19), ((A5 : A5 × A5) : D6), 6 • (U4(3): 2), 2 • PGL(2,13), S7, PGL (2,8), PSL(2,19), 2 × PGL(2,81), 25 : (S6 × A5), 26 : S4 × D3, U(4,3), 34 : S4, 32 :D6, 2 • (PGL(2,7) :PSL(2,7), 22 : (S5 : S5) and 23 : (PSL3(4) : 2) as homomorphic images of the permutation progenitors 2*8 : (2 × 4 : 2), 2*16: (2 × 4 :C2 × C2), 2*9: (S3 × S3), 2*9: (S3 × A3), 2*9: (32 × 23) and 2*9: (33 × A3). We have also constructed 24: S3 × C2, 24 : A5, (25: S4), 25 : S3 × S3,: 33: S4 × C2, S6, M11 and U (3,5) by using the technique of double coset enumeration. We have determined the isomorphism types of the most of the images mentioned in this thesis. We demonstrate our work for the following examples: 34 : (32 * 23) × 2, 29 : PGL(2,7), 2•S6, (54 : (D4 × S3)), and 3: •PSL(2,19) ×2.
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Salt, Brittney M. "MONOID RINGS AND STRONGLY TWO-GENERATED IDEALS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/31.

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This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.
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Constable, Jonathan A. "Kronecker's Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares." UKnowledge, 2016. http://uknowledge.uky.edu/math_etds/35.

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In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence. In the second chapter we introduce the class number, proper class number and complete class number as well as two refinements, which facilitate the development of a connection with binary quadratic forms. Our third chapter is devoted to deriving several class number formulas in terms of divisors of the determinant. This chapter also contains lower bounds on the class number for bilinear forms and classifies when these bounds are attained. Lastly, we use the class number formulas to rigorously develop Kronecker's connection between binary bilinear forms and binary quadratic forms. We supply purely arithmetic proofs of five results stated but not proven in the original paper. We conclude by giving an application of this material to the number of representations of an integer as a sum of three squares and show the resulting formula is equivalent to the well-known result due to Gauss.
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Gopalan, Parikshit. "Computing with Polynomials over Composites." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/11564.

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In the last twenty years, algebraic techniques have been applied with great success to several areas in theoretical computer science. However, for many problems involving modular counting, there is a huge gap in our understanding depending on whether the modulus is prime or composite. A prime example is the problem of showing lower bounds for circuits with Mod gates in circuit complexity. Proof techniques that work well for primes break down over composites. Moreover, in some cases, the problem for composites turns out to be very different from the prime case. Making progress on these problems seems to require a better understanding of polynomials over composites. In this thesis, we address some such "prime vs. composite" problems from algorithms, complexity and combinatorics, and the surprising connections between them. We consider the complexity-theoretic problem of computing Boolean functions using polynomials modulo composites. We show that symmetric polynomials can viewed as simultaneous communication protocols. This equivalence allows us to use techniques from communication complexity and number theory to prove degree bounds. We use these to give the first tight degree bounds for a number of Boolean functions. We consider the combinatorial problem of explicit construction of Ramsey graphs. We present a simple construction of such graphs using polynomials modulo composites. This approach gives a unifying view of many known constructions,and explains why they all achieve the same bound.We show that certain approaches to this problem cannot give better bounds. Finally, we consider the algorithmic problem of interpolation for polynomials modulo composites. We present the first query-efficient algorithms for interpolation and learning under a distribution. These results rely on some new structural results about such polynomials.
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Munoz, Susana L. "A Fundamental Unit of O_K." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/133.

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In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.
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Fávaro, Eduardo Rogério [UNESP]. "Corpos cujo condutor é potência de primo: caracterização e reticulados ideais associados." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/100063.

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Made available in DSpace on 2014-06-11T19:30:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-08-02Bitstream added on 2014-06-13T18:40:35Z : No. of bitstreams: 1 favaro_er_dr_sjrp.pdf: 449730 bytes, checksum: 66f6b6e8876e035dcd2e6aa8db337bbd (MD5)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Este trabalho esta relacionado com a Teoria Algébrica dos Números e aplicações em Reticulados Ideais. Descrevemos os corp os cujo condutor e potência de primo. Quando o primo e dois, descrevemos tamb em o anel de inteiros. Quando o primo e mpar calculamos o discriminante de um modo alternativo ao existente na literatura. Neste caso, e quando o corpo tem como grau o pr oprio primo mpar, descrevemos o anel de inteiros com uma base integral e a forma traço associada, além do mínimo euclidiano. Com isso, obtemos uma família de reticulados ideais de dimensão prima ímpar
This work is relate to Algebric Number Theory and applications in Ideal Lattices. We describ e numb er elds with p ower prime conductor. In the case prime two, we showed the ring of integers. For o dd prime, we give a new pro of for formula of discrimanate. In the case that the the degree of the eld is the o dd prime, we describ e the ring of integers, the trace form asso ciated and the Euclidean minimum. With this, we have a family of ideal lattices in odd prime dimension
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Shaughnessy, John F. "Finding Zeros of Rational Quadratic Forms." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/cmc_theses/849.

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In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.
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Samson, Duncan Alistair. "An analysis of the influence of question design on pupils' approaches to number pattern generalisation tasks." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1003302.

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This study is based on a qualitative investigation framed within an interpretive paradigm, and aims to investigate the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil and paper exercises based on linear generalisation tasks set in both numeric and 2-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. The method or strategy adopted was carefully analysed and classified into one of seven categories. A meta-analysis focused on the formula derived for the nth term in conjunction with its justification. The process of justification proved to be a critical factor in being able to accurately interpret the origin of the sub-structure evident in many of these responses. From a theoretical perspective, the central role of justification/proof within the context of this study is seen as communication of mathematical understanding, and the process of justification/proof proved to be highly successful in providing a window of understanding into each pupil’s cognitive reasoning. The results of this study strongly support the notion that question design can play a critical role in influencing pupils’ choice of strategy and level of attainment when solving pattern generalisation tasks. Furthermore, this study identified a diverse range of visually motivated strategies and mechanisms of visualisation. An awareness and appreciation for such a diversity of visualisation strategies, as well as an understanding of the importance of appropriate question design, has direct pedagogical application within the context of the mathematics classroom.
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Books on the topic "010101 Algebra and Number Theory"

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Frey, Gerhard, and Jürgen Ritter, eds. Algebra and Number Theory. Berlin, New York: DE GRUYTER, 1994. http://dx.doi.org/10.1515/9783110878103.

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Tandon, Rajat, ed. Algebra and Number Theory. Gurgaon: Hindustan Book Agency, 2005. http://dx.doi.org/10.1007/978-93-86279-23-1.

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Zimmer, Horst G., ed. Group Theory, Algebra, and Number Theory. Berlin, New York: DE GRUYTER, 1996. http://dx.doi.org/10.1515/9783110811957.

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Bosma, Wieb. Computational Algebra and Number Theory. Dordrecht: Springer Netherlands, 1995.

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Bosma, Wieb, and Alf van der Poorten, eds. Computational Algebra and Number Theory. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-017-1108-1.

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Larcher, Gerhard, Friedrich Pillichshammer, Arne Winterhof, and Chaoping Xing, eds. Applied Algebra and Number Theory. Cambridge: Cambridge University Press, 2014. http://dx.doi.org/10.1017/cbo9781139696456.

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Matzat, B. Heinrich, Gert-Martin Greuel, and Gerhard Hiss, eds. Algorithmic Algebra and Number Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-59932-3.

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Number theory in function fields. New York: Springer, 2001.

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R, Sivaramakrishnan. Certain Number-Theoretic Episodes In Algebra. Hoboken: CRC Press, 2006.

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Galois Theory. New York, NY: Springer New York, 2001.

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Book chapters on the topic "010101 Algebra and Number Theory"

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Lawson, Mark V. "Number Theory." In Algebra & Geometry, 131–70. 2nd ed. Second edition. | Boca Raton : Chapman & Hall/CRC Press, 2021.: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003098072-7.

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Gårding, Lars, and Torbjörn Tambour. "Number theory." In Algebra for Computer Science, 1–20. New York, NY: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-8797-8_1.

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Mignotte, Maurice. "Number Theory, Complements." In Mathematics for Computer Algebra, 53–83. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4613-9171-5_2.

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Knapp, Anthony W. "Transition to Modern Number Theory." In Advanced Algebra, 1–75. Boston, MA: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4613-4_1.

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Delfs, Hans, and Helmut Knebl. "Algebra and Number Theory." In Information Security and Cryptography, 245–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-87126-9_11.

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Gårding, Lars, and Torbjörn Tambour. "Number theory and computing." In Algebra for Computer Science, 21–33. New York, NY: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-8797-8_2.

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Knapp, Anthony W. "Three Theorems in Algebraic Number Theory." In Advanced Algebra, 262–312. Boston, MA: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4613-4_5.

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Knapp, Anthony W. "The Number Theory of Algebraic Curves." In Advanced Algebra, 520–57. Boston, MA: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4613-4_9.

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Gray, Jeremy. "Algebraic Number Theory: Cyclotomy." In A History of Abstract Algebra, 189–93. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94773-0_16.

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Gray, Jeremy. "Kronecker’s Algebraic Number Theory." In A History of Abstract Algebra, 217–29. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94773-0_20.

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Conference papers on the topic "010101 Algebra and Number Theory"

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Erkoç, Temha. "Preface to Algebra and Number Theory." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136226.

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KOLODNYTSKY, M., A. KOVALCHUK, S. KURYATA, and V. LEVITSKY. "THE MATHEMATICAL SOFTWARE IMPLEMENTATION FOR COMPUTATIONAL ALGEBRA AND NUMBER THEORY." In Proceedings of the Fourth Asian Symposium (ASCM 2000). WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812791962_0039.

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Gajdos, A., J. Hanc, and M. Hancova. "Interactive Jupyter Notebooks with SageMath in Number Theory, Algebra, Calculus, and Numerical Methods." In 2022 20th International Conference on Emerging eLearning Technologies and Applications (ICETA). IEEE, 2022. http://dx.doi.org/10.1109/iceta57911.2022.9974868.

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HILTON, PETER, JEAN PEDERSEN, and BYRON WALDEN. "PAPER-FOLDING, POLYGONS, COMPLETE SYMBOLS, AND THE EULER TOTIENT FUNCTION: AN ONGOING SAGA CONNECTING GEOMETRY, ALGEBRA, AND NUMBER THEORY." In Proceedings of the Second International Congress in Algebra and Combinatorics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790019_0010.

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A. N., Rybalov. "GENERIC COMPLEXITY OF ALGORITHMIC PROBLEMS." In Mechanical Science and Technology Update. Omsk State Technical University, 2022. http://dx.doi.org/10.25206/978-5-8149-3453-6-2022-10-14.

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Generic approach is one of the approaches to the study of algorithmic problems for almost all inputs, born at the intersection of computational algebra and computer science. Within the framework of this approach, algorithms are studied that solve a problem for almost all inputs, and for the remaining rare inputs give an undefined answer. This review reflects two areas of research of generic complexity of algorithmic problems in algebra, mathematical logic, number theory, and theoretical computer science. The first direction is devoted to the construction of generic algorithms for problems that are unsolvable and hard in the classical sense. In the second direction, algorithmic problems are sought that remain unsolvable or hard even in the generic sense. Such problems are important in cryptography.
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Ciblak, Namik, and Harvey Lipkin. "Synthesis of Stiffnesses by Springs." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5879.

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Abstract A new, systematic approach to the synthesis of stiffness by springs is presented using screw (spatial vector) algebra. The space of solutions is fully characterized for all stiffnesses realizable by springs. The main result shows that a rank r stiffness can always be synthesized by r springs. Further, a stiffness can be synthesized by an arbitrarily large number of springs greater than r. Algorithms and numerical results support the theory.
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Huang, Chintien, and Bernard Roth. "Position-Force Synthesis of Closed-Loop Linkages." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0303.

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Abstract The dimensional synthesis of spatial closed-loop linkages to match both force and position specifications is investigated. An efficient means of formulating force equations is introduced through the application of linear algebra to screw theory. The synthesis of spatial four-bar linkages is discussed in detail; it is shown that the maximum number of allowable design positions is not decreased after force constraints are imposed on classical position synthesis problems.
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Aguilera, Daniel, Jose´ Mari´a Rico, and Jaime Gallardo. "Computer Implementation of an Improved Kutzbach-Gru¨bler Mobility Criterion." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dac-34093.

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Recent results have shown that the application of group theory to the Euclidean group, E(3), and its subgroups yields a new and improved mobility criterion. Unlike the well known Kutzbach-Gru¨bler criterion, this improved mobility criterion yields correct results for both trivial and exceptional linkages. Unfortunately, this improved mobility criterion requires a little bit more than counting links and kinematic pairs. An important advance was made when it was proved that the improved mobility criterion, originally stated in a language of group theory and subsets and subgroups of the Euclidean group, E(3), can be translated into a language of the Lie algebra, e(3), of the Euclidean group, E(3), and its vector subspaces and its subalgebras. The language of the Lie algebra, e(3), is far simpler than the nonlinear language of the Euclidean group, E(3). Still, the computations required for the improved mobility criterion are more involved than those required for the Kutzbach-Gru¨bler criterion, and it might preclude the employment of the improved mobility criterion in prospective tasks such as the number synthesis of parallel and modular manipulators. This contribution dispels these doubts by showing that the improved criterion can be easily implemented by a simple computer program. Several examples are included.
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Reports on the topic "010101 Algebra and Number Theory"

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Sultanov, S. R. Electronic textbook " Algebra and number theory. Part 2 "direction of training 02.03.03" Mathematical support and administration of information systems". OFERNIO, June 2018. http://dx.doi.org/10.12731/ofernio.2018.23685.

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