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Journal articles on the topic 'Application de base de Gröbner'

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Published: 25 May 2024

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1

Bokut, L. A., Yuqun Chen, and Zerui Zhang. "Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras." Journal of Algebra and Its Applications 16, no. 01 (January 2017): 1750001. http://dx.doi.org/10.1142/s0219498817500013.

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We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.

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2

Steiner, Matthias Johann. "Solving Degree Bounds for Iterated Polynomial Systems." IACR Transactions on Symmetric Cryptology 2024, no. 1 (March 1, 2024): 357–411. http://dx.doi.org/10.46586/tosc.v2024.i1.357-411.

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For Arithmetization-Oriented ciphers and hash functions Gröbner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gröbner basis algorithms is only understood for special cases, and it is needless to say that these cases do not apply to most cryptographic polynomial systems. Therefore, cryptographers have to resort to experiments, extrapolations and hypotheses to assess the security of their designs. One established measure to quantify the complexity of linear algebra-based Gröbner basis algorithms is the so-called solving degree. Caminata & Gorla revealed that under a certain genericity condition on a polynomial system the solving degree is always upper bounded by the Castelnuovo-Mumford regularity and henceforth by the Macaulay bound, which only takes the degrees and number of variables of the input polynomials into account. In this paper we extend their framework to iterated polynomial systems, the standard polynomial model for symmetric ciphers and hash functions. In particular, we prove solving degree bounds for various attacks on MiMC, Feistel-MiMC, Feistel-MiMC-Hash, Hades and GMiMC. Our bounds fall in line with the hypothesized complexity of Gröbner basis attacks on these designs, and to the best of our knowledge this is the first time that a mathematical proof for these complexities is provided. Moreover, by studying polynomials with degree falls we can prove lower bounds on the Castelnuovo-Mumford regularity for attacks on MiMC, Feistel-MiMC and Feistel-MiMCHash provided that only a few solutions of the corresponding iterated polynomial system originate from the base field. Hence, regularity-based solving degree estimations can never surpass a certain threshold, a desirable property for cryptographic polynomial systems.

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3

Xia, Shengxiang, and Gaoxiang Xia. "AN APPLICATION OF GRÖBNER BASES." Mathematics Enthusiast 6, no. 3 (July 1, 2009): 381–94. http://dx.doi.org/10.54870/1551-3440.1159.

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4

BORISOV, A. V., A. V. BOSOV, and A. V. IVANOV. "APPLICATION OF COMPUTER SIMULATION TO THE ANONYMIZATION OF PERSONAL DATA: STATE-OF-THE-ART AND KEY POINTS." Программирование, no. 4 (July 1, 2023): 58–74. http://dx.doi.org/10.31857/s0132347423040040.

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A new version of GInv (Gröbner Involutive) for computing involutive Gröbner bases is presented as a library in C++11. GInv uses object-oriented memory reallocation for dynamic data structures, such as lists, red-black trees, binary trees, and GMP libraries for arbitrary-precision integer calculations. The interface of the package is designed as a Python3 module.

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5

Çelik, Ercan, and Mustafa Bayram. "Application of Gröbner basis techniques to enzyme kinetics." Applied Mathematics and Computation 153, no. 1 (May 2004): 97–109. http://dx.doi.org/10.1016/s0096-3003(03)00612-x.

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6

HASHEMI, AMIR, and PARISA ALVANDI. "APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS." Journal of Algebra and Its Applications 12, no. 07 (May 16, 2013): 1350034. http://dx.doi.org/10.1142/s0219498813500345.

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Norton and Sălăgean [Strong Gröbner bases and cyclic codes over a finite-chain ring, in Proc. Workshop on Coding and Cryptography, Paris, Electronic Notes in Discrete Mathematics, Vol. 6 (Elsevier Science, 2001), pp. 391–401] have presented an algorithm for computing Gröbner bases over finite-chain rings. Byrne and Fitzpatrick [Gröbner bases over Galois rings with an application to decoding alternant codes, J. Symbolic Comput.31 (2001) 565–584] have simultaneously proposed a similar algorithm for computing Gröbner bases over Galois rings (a special kind of finite-chain rings). However, they have not incorporated Buchberger's criteria into their algorithms to avoid unnecessary reductions. In this paper, we propose the adapted version of these criteria for polynomials over finite-chain rings and we show how to apply them on Norton–Sălăgean algorithm. The described algorithm has been implemented in Maple and experimented with a number of examples for the Galois rings.

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7

Yunus, Gulshadam, Zhenzhen Gao, and Abdukadir Obul. "Gröbner-Shirshov Basis of Quantum Groups." Algebra Colloquium 22, no. 03 (July 14, 2015): 495–516. http://dx.doi.org/10.1142/s1005386715000449.

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In this paper, by using the Ringel-Hall algebra method, we prove that the set of the skew-commutator relations of quantum root vectors forms a minimal Gröbner-Shirshov basis for the quantum groups of Dynkin type. As an application, we give an explicit basis for the types E7 and Dn.

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8

Kolesnikov, P. S. "Gröbner–Shirshov Bases for Replicated Algebras." Algebra Colloquium 24, no. 04 (November 15, 2017): 563–76. http://dx.doi.org/10.1142/s1005386717000372.

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We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Gröbner–Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincaré–Birkhoff–Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD!-algebra).

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9

Li, Huishi. "The General PBW Property." Algebra Colloquium 14, no. 04 (December 2007): 541–54. http://dx.doi.org/10.1142/s1005386707000508.

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For ungraded quotients of an arbitrary ℤ-graded ring, we define the general PBW property, that covers the classical PBW property and the N-type PBW property studied via the N-Koszulity by several authors (see [2–4]). In view of the noncommutative Gröbner basis theory, we conclude that every ungraded quotient of a path algebra (or a free algebra) has the general PBW property. We remark that an earlier result of Golod [5] concerning Gröbner bases can be used to give a homological characterization of the general PBW property in terms of Shafarevich complex. Examples of application are given.

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10

Chaharbashloo, Mohammad Saleh, Abdolali Basiri, Sajjad Rahmany, and Saber Zarrinkamar. "An Application of Gröbner Basis in Differential Equations of Physics." Zeitschrift für Naturforschung A 68, no. 10-11 (November 1, 2013): 646–50. http://dx.doi.org/10.5560/zna.2013-0044.

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We apply the Gröbner basis to the ansatz method in quantum mechanics to obtain the energy eigenvalues and the wave functions in a very simple manner. There are important physical potentials such as the Cornell interaction which play significant roles in particle physics and can be treated via this technique. As a typical example, the algorithm is applied to the semi-relativistic spinless Salpeter equation under the Cornell interaction. Many other applications of the idea in a wide range of physical fields are listed as well.

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11

Qiu, Jianjun, and Yuqun Chen. "Free Lie differential Rota–Baxter algebras and Gröbner–Shirshov bases." International Journal of Algebra and Computation 27, no. 08 (December 2017): 1041–60. http://dx.doi.org/10.1142/s0218196717500485.

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12

Conca, A., E. De Negri, and E. Gorla. "Universal Gröbner Bases and Cartwright–Sturmfels Ideals." International Mathematics Research Notices 2020, no. 7 (April 25, 2018): 1979–91. http://dx.doi.org/10.1093/imrn/rny075.

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Abstract The main theoretical contribution of the paper is the description of two classes of multigraded ideals named after Cartwright and Sturmfels and the study of their surprising properties. Among other things we prove that these classes of ideals have very special multigraded generic initial ideals and are closed under several operations including arbitrary multigraded hyperplane sections. As a main application we describe the universal Gröbner basis of the ideal of maximal minors and the ideal of 2-minors of a multigraded matrix of linear forms generalizing earlier results of various authors including Bernstein, Sturmfels, Zelevinsky, and Boocher.

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13

Matsuda, Kazunori, Hidefumi Ohsugi, and Kazuki Shibata. "Toric Rings and Ideals of Stable Set Polytopes." Mathematics 7, no. 7 (July 10, 2019): 613. http://dx.doi.org/10.3390/math7070613.

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In the present paper, we study the normality of the toric rings of stable set polytopes, generators of toric ideals of stable set polytopes, and their Gröbner bases via the notion of edge polytopes of finite nonsimple graphs and the results on their toric ideals. In particular, we give a criterion for the normality of the toric ring of the stable set polytope and a graph-theoretical characterization of the set of generators of the toric ideal of the stable set polytope for a graph of stability number two. As an application, we provide an infinite family of stable set polytopes whose toric ideal is generated by quadratic binomials and has no quadratic Gröbner bases.

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14

Gao, Xing, and Tianjie Zhang. "Averaging algebras, rewriting systems and Gröbner–Shirshov bases." Journal of Algebra and Its Applications 17, no. 07 (June 13, 2018): 1850130. http://dx.doi.org/10.1142/s021949881850130x.

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In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain a sufficient and necessary condition for the confluence. We supply the relationship between rewriting systems and Gröbner–Shirshov bases based on bracketed polynomials. As an application, we give a basis of the free unitary averaging algebra on a nonempty set.

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15

Sawada, Hiroyuki, and Xiu-Tian Yan. "Application of Gröbner bases and quantifier elimination for insightful engineering design." Mathematics and Computers in Simulation 67, no. 1-2 (September 2004): 135–48. http://dx.doi.org/10.1016/j.matcom.2004.05.014.

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16

Ioakimidis, N. I., and E. G. Anastasselou. "Application of Gröbner bases to problems of movement of a particle." Computers & Mathematics with Applications 27, no. 3 (February 1994): 51–57. http://dx.doi.org/10.1016/0898-1221(94)90046-9.

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17

Dargys, Adolfas, and Artūras Acus. "Application of Gröbner basis in calculation of wave functions in nanostructures." Lithuanian Journal of Physics 51, no. 4 (2011): 335–40. http://dx.doi.org/10.3952/lithjphys.51408.

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18

Mao, Lingling, and Jingqian Wang. "Gröbner-Shirshov Basis and Minimal Projective Resolution of Uq+(B2)." Algebra Colloquium 25, no. 04 (December 2018): 713–20. http://dx.doi.org/10.1142/s1005386718000500.

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In this paper, by using the Anick resolution and Gröbner-Shirshov basis for quantized enveloping algebra of type B2, we compute the minimal projective resolution of the trivial module of [Formula: see text], and as an application we compute the global dimension of [Formula: see text].

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19

Ohsugi, Hidefumi, and Takayuki Hibi. "Prestable ideals and Sagbi bases." MATHEMATICA SCANDINAVICA 96, no. 1 (March 1, 2005): 22. http://dx.doi.org/10.7146/math.scand.a-14942.

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In order to find a reasonable class of squarefree monomial ideals $I$ for which the toric ideal of the Rees algebra of $I$ has a quadratic Gröbner basis, the concept of prestable ideals will be introduced. Prestable ideals arising from finite pure posets together with their application to Sagbi bases will be discussed.

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20

Price, Kenneth L. "Generic Lie colour algebras." Bulletin of the Australian Mathematical Society 71, no. 2 (April 2005): 327–35. http://dx.doi.org/10.1017/s0004972700038284.

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We describe a type of Lie colour algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Gröbner basis methods can be used to study universal enveloping algebras of factors of generic Lie colour algebras.

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21

Byrne, Eimear, and Patrick Fitzpatrick. "Gröbner Bases over Galois Rings with an Application to Decoding Alternant Codes." Journal of Symbolic Computation 31, no. 5 (May 2001): 565–84. http://dx.doi.org/10.1006/jsco.2001.0442.

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22

BOKUT, L. A., and A. A. KLEIN. "SERRE RELATIONS AND GRÖBNER-SHIRSHOV BASES FOR SIMPLE LIE ALGEBRAS II." International Journal of Algebra and Computation 06, no. 04 (August 1996): 401–12. http://dx.doi.org/10.1142/s0218196796000234.

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Gröbner-Shirshov bases for the Lie algebras Bn, Cn, Dn, abstractly defined by generators and the Serre relations for the corresponding Cartan matrices over a field of characteristic ≠2, 3, are constructed. As an application, we obtain that each of the previous algebras is isomorphic to a classical simple Lie algebra so2n+1(k), sp2n(k), so2nk respectively.

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23

Georg, Klein, and Zargeh Chia. "Operadic approach to HNN-extensions of Leibniz algebras." Quasigroups and Related Systems 30, no. 1(47) (May 2022): 101–14. http://dx.doi.org/10.56415/qrs.v30.08.

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We construct HNN-extensions of Lie di-algebras in the variety of di-algebras and provide a presentation for the replicated HNN-extension of a Lie di-algebras. Then, by applying the method of Gröbner-Shirshov bases for replicated algebras, we obtain a linear basis. As an application of HNN-extensions, we prove that Lie di-algebras are embedded in their HNNextension.

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24

Shany, Yaron, and Amit Berman. "A Gröbner-Bases Approach to Syndrome-Based Fast Chase Decoding of Reed–Solomon Codes." IEEE Transactions on Information Theory 68, no. 4 (April 2022): 2300–2318. http://dx.doi.org/10.1109/tit.2022.3140678.

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25

Ioakimidis, N. I., and E. G. Anastasselou. "Computer-based manipulation of systems of equations in elasticity problems with Gröbner bases." Computer Methods in Applied Mechanics and Engineering 110, no. 1-2 (December 1993): 103–11. http://dx.doi.org/10.1016/0045-7825(93)90022-p.

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26

BOKUT, L. A., and A. A. KLEIN. "SERRE RELATIONS AND GRÖBNER-SHIRSHOV BASES FOR SIMPLE LIE ALGEBRAS I." International Journal of Algebra and Computation 06, no. 04 (August 1996): 389–400. http://dx.doi.org/10.1142/s0218196796000222.

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A Gröbner-Shirshov basis for the Lie algebra An, abstractly defined by generators hi, xi, yi, i=1,..., n and the Serre relations for the Cartan matrix An, over a field k of characteristic ≠2 is constructed. It consists of the Serre relations for An together with the following relations: [Formula: see text] with j≥1, i≥2, i+j≤n and the same relations for y1,…, yn, where by [z1z2…zm] we mean [z1[z2… zm]]. As an application we get a direct proof that An, as defined, is isomorphic to sℓn+1(k).

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27

Mora, Teo, and Massimiliano Sala. "On the Gröbner bases of some symmetric systems and their application to coding theory." Journal of Symbolic Computation 35, no. 2 (February 2003): 177–94. http://dx.doi.org/10.1016/s0747-7171(02)00131-1.

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28

Scheicher, Martin. "Gröbner bases and their application to the Cauchy problem on finitely generated affine monoids." Journal of Symbolic Computation 80 (May 2017): 416–50. http://dx.doi.org/10.1016/j.jsc.2016.07.002.

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29

Chou, Shang-Ching, William F. Schelter, and Jin-Gen Yang. "An algorithm for constructing gröbner bases from characteristic sets and its application to geometry." Algorithmica 5, no. 1-4 (June 1990): 147–54. http://dx.doi.org/10.1007/bf01840382.

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30

PAUER, FRANZ, and SANDRO ZAMPIERI. "Gröbner Bases with Respect to Generalized Term Orders and their Application to the Modelling Problem." Journal of Symbolic Computation 21, no. 2 (February 1996): 155–68. http://dx.doi.org/10.1006/jsco.1996.0007.

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31

BRUNO, A. D., A. B. BATKHIN, and Z. Kh KHAIDAROV. "COMPUTING LEVEL LINES OF A POLYNOMIAL ON THE PLANE." Программирование, no. 2 (March 1, 2023): 13–30. http://dx.doi.org/10.31857/s0132347423020073.

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Application of the method of computing the location of all types of level lines of a real polynomial on the real plane is demonstrated. The theory underlying this method is based on methods of local and global analysis by the means of power geometry and computer algebra. Three nontrivial examples of computing level lines of real polynomials on the real plane are discussed in detail. The following computer algebra algorithms are used: factorization of polynomials, computation of the Gröbner basis, construction of the Newton polygon, and representation of an algebraic curve on a plane. It is shown how computational difficulties can be overcome.

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32

Pauer, Franz, and Andreas Unterkircher. "Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations." Applicable Algebra in Engineering, Communication and Computing 9, no. 4 (February 1, 1999): 271–91. http://dx.doi.org/10.1007/s002000050108.

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33

Jha, Ranjan, Damien Chablat, and Luc Baron. "Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot." Transactions of the Canadian Society for Mechanical Engineering 42, no. 1 (March 1, 2018): 30–37. http://dx.doi.org/10.1139/tcsme-2017-0011.

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This paper presents variations in the workspace, singularities, and joint space with respect to design parameter k, which is the ratio of the dimensions of the mobile platform to the dimensions of the base of a 3-RPS parallel manipulator. The influence of the design parameters on parasitic motion, which is important when selecting a manipulator for a desired task, is also studied. The cylindrical algebraic decomposition method and Gröbner-based computations are used to model the workspace and joint space with parallel singularities in 2R1T (two rotational and one translational) and 3T (three translational) projection spaces, where the orientation of the mobile platform is represented using quaternions. These computations are useful in selecting the optimum value for the design parameter k such that the parasitic motions can be limited to specific values. Three designs of the 3-RPS parallel robot, based on different values of k, are analyzed.

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34

Zhang, Shenggui, Zhaolin Jiang, and Sanyang Liu. "An application of the Gröbner basis in computation for the minimal polynomials and inverses of block circulant matrices." Linear Algebra and its Applications 347, no. 1-3 (May 2002): 101–14. http://dx.doi.org/10.1016/s0024-3795(01)00529-8.

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35

Jangisarakul, P., and C. Charoenlarpnopparut. "Algebraic decoder of multidimensional convolutional code: constructive algorithms for determining syndrome decoder and decoder matrix based on Gröbner basis." Multidimensional Systems and Signal Processing 22, no. 1-3 (October 22, 2010): 67–81. http://dx.doi.org/10.1007/s11045-010-0139-7.

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36

Riff, Eduardo J. "APPLICATION OF A MEDICAL DATA BASE." Southern Medical Journal 86, Supplement (September 1993): 137. http://dx.doi.org/10.1097/00007611-199309001-00395.

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37

Yang, Bei, Li Yang, and Jia Chen. "Development and Application of Base Editors." CRISPR Journal 2, no. 2 (April 2019): 91–104. http://dx.doi.org/10.1089/crispr.2019.0001.

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38

Kendall, Wilfrid S. "A diffusion model for bookstein triangle shape." Advances in Applied Probability 30, no. 2 (June 1998): 317–34. http://dx.doi.org/10.1239/aap/1035228071.

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A stochastic dynamical context is developed for Bookstein's shape theory. It is shown how Bookstein's shape space for planar triangles arises naturally when the landmarks are moved around by a special Brownian motion on the general linear group of invertible (2×2) real matrices. Asymptotics for the Brownian transition density are used to suggest an exponential family of distributions, which is analogous to the von Mises-Fisher spherical distribution and which has already been studied by J. K. Jensen. The computer algebra implementation Itovsn3 (W. S. Kendall) of stochastic calculus is used to perform the calculations (some of which actually date back to work by Dyson on eigenvalues of random matrices and by Dynkin on Brownian motion on ellipsoids). An interesting feature of these calculations is that they include the first application (to the author's knowledge) of the Gröbner basis algorithm in a stochastic calculus context.

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39

Kendall, Wilfrid S. "A diffusion model for bookstein triangle shape." Advances in Applied Probability 30, no. 02 (June 1998): 317–34. http://dx.doi.org/10.1017/s0001867800047303.

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A stochastic dynamical context is developed for Bookstein's shape theory. It is shown how Bookstein's shape space for planar triangles arises naturally when the landmarks are moved around by a special Brownian motion on the general linear group of invertible (2×2) real matrices. Asymptotics for the Brownian transition density are used to suggest an exponential family of distributions, which is analogous to the von Mises-Fisher spherical distribution and which has already been studied by J. K. Jensen. The computer algebra implementationItovsn3(W. S. Kendall) of stochastic calculus is used to perform the calculations (some of which actually date back to work by Dyson on eigenvalues of random matrices and by Dynkin on Brownian motion on ellipsoids). An interesting feature of these calculations is that they include the first application (to the author's knowledge) of the Gröbner basis algorithm in a stochastic calculus context.

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40

Yildirim, Necmettin, Nurullah Ankaralioglu, Derya Yildrim, and Fatih Akcay. "Application of Gröbner Bases theory to derive rate equations for enzyme catalysed reactions with two or more substrates or products." Applied Mathematics and Computation 137, no. 1 (May 2003): 67–76. http://dx.doi.org/10.1016/s0096-3003(02)00084-x.

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41

Yoshida, Hiroshi. "A model for analyzing phenomena in multicellular organisms with multivariable polynomials: Polynomial life." International Journal of Biomathematics 11, no. 01 (January 2018): 1850007. http://dx.doi.org/10.1142/s1793524518500079.

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Most of life maintains itself through turnover, namely cell proliferation, movement and elimination. Hydra’s cells, for example, disappear continuously from the ends of tentacles, but these cells are replenished by cell proliferation within the body. Inspired by such a biological fact, and together with various operations of polynomials, I here propose polynomial-life model toward analysis of some phenomena in multicellular organisms. Polynomial life consists of multicells that are expressed as multivariable polynomials. A cell is expressed as a term of polynomial, in which point [Formula: see text] is described as a term [Formula: see text] and the condition is described as its coefficient. Starting with a single term and following reductions by set of polynomials, I simulate the development from a cell to a multicell. In order to confirm uniqueness of the eventual multicell-pattern, Gröbner base can be used, which has been conventionally used to ensure uniqueness of normal form in the mathematical context. In this framework, I present various patterns through the polynomial-life model and discuss patterns maintained through turnover. Cell elimination seems to play an important role in turnover, which may shed some light on cancer or regenerative medicine.

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42

Kim, Jae-Hoon. "Korean Base-Noun Extraction and its Application." KIPS Transactions:PartB 15B, no. 6 (December 31, 2008): 613–20. http://dx.doi.org/10.3745/kipstb.2008.15-b.6.613.

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43

NI, Zhi-wei, Li-ping NI, and Zhong-xiao YANGGE. "Application of fractal in case base maintenance." Journal of Computer Applications 29, no. 6 (December 4, 2009): 1598–600. http://dx.doi.org/10.3724/sp.j.1087.2009.01598.

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44

Zhao, Yu Xin. "Intelligent Household Application Base on Mobile Phone." Applied Mechanics and Materials 155-156 (February 2012): 464–69. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.464.

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With life level constantly and the quality of life improved, paying more attention to the quality of life, people are eager to wander in a safe, effective, convenient and comfortable living environment.Networking technology is used in intelligent household, which rolls out of the wireless network based on intelligent household products, such as the realization of household security, information release, multimedia, household appliances, intelligent control and IP telephoneand other functions.We can use intelligent terminal, computer, mobile phone to control the home of the electrical equipment for remote monitoring and remote management, which let people enjoy comfort and convenience that high-tech brings.The author mainly introduces the application of mobile phone in intelligent household.

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45

Tanabe, K. "Industrial application of solid acid–base catalysts." Applied Catalysis A: General 181, no. 2 (May 17, 1999): 399–434. http://dx.doi.org/10.1016/s0926-860x(98)00397-4.

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46

Chung, Myoung-Beom, and Il-Ju Ko. "Mobile Donation Application of User Participation Base." Journal of the Korea Society of Computer and Information 16, no. 11 (November 30, 2011): 113–22. http://dx.doi.org/10.9708/jksci.2011.16.11.113.

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47

Preece, Alun D., and Rajjan Shinghal. "Foundation and application of knowledge base verification." International Journal of Intelligent Systems 9, no. 8 (1994): 683–701. http://dx.doi.org/10.1002/int.4550090804.

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48

Xu, Ben Sheng, Can Wang, and Yan Ru Zhong. "Research on Knowledge Base System of Straightness Verification Base on Ontology." Applied Mechanics and Materials 278-280 (January 2013): 1814–17. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.1814.

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Abstract:

To realize the management and reuse of the knowledge of straightness verification, the ontology theory is applied in the knowledge base system of straightness verification. The system is divided into three layers: domain layer, inference layer and application layer. The ontology of the straightness verification is established for formal description of the conceptions of straightness verification and the relationship among these conceptions. Related axioms, rules of straightness measurement are given out according to related standard documents. Finally, an application platform is provided for the digitized realization of the straightness verification.

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49

Khalil, R. A., A. H. Jalil, and A. Y. Abd-Alrazzak. "Application of a Schiff base derived from sulfanilamide as an acid-base indicator." Journal of the Iranian Chemical Society 6, no. 2 (June 2009): 345–52. http://dx.doi.org/10.1007/bf03245844.

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50

Ikeda, Hikaru, Takanori Iwahashi, Toshiko Osada, and Hideshi Miura. "Application of MIM Process for Nickel Base Superalloy." Journal of the Japan Society of Powder and Powder Metallurgy 58, no. 1 (2011): 33–37. http://dx.doi.org/10.2497/jjspm.58.33.

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