Journal articles: 'Dual basis'

1

Lewanowicz, Stanisław, and Paweł Woźny. "Dual generalized Bernstein basis." Journal of Approximation Theory 138, no. 2 (February 2006): 129–50. http://dx.doi.org/10.1016/j.jat.2005.10.005.

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2

Zhang, Li, Hongyi Wu, and Jieqing Tan. "Dual bases for Wang–Bézier basis and their applications." Applied Mathematics and Computation 214, no. 1 (August 2009): 218–27. http://dx.doi.org/10.1016/j.amc.2009.03.079.

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3

Dong-Bing, Wu. "Dual bases of a Bernstein polynomial basis on simplices." Computer Aided Geometric Design 10, no. 6 (December 1993): 483–89. http://dx.doi.org/10.1016/0167-8396(93)90025-x.

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4

Nikitin, V. S. "Dual technologies – basis for development." TRANSACTIONS OF THE KRYLOV STATE RESEARCH CENTRE 2, no. 380 (June 1, 2017): 5–8. http://dx.doi.org/10.24937/2542-2324-2017-2-380-5-8.

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5

Woźniak, J. J. "Systolic dual basis serial multiplier." IEE Proceedings - Computers and Digital Techniques 145, no. 3 (1998): 237. http://dx.doi.org/10.1049/ip-cdt:19981938.

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6

Huapeng Wu and M. A. Hasan. "Efficient exponentiation using weakly dual basis." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 9, no. 6 (December 2001): 874–79. http://dx.doi.org/10.1109/92.974900.

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7

Zhang, Li, Hongyi Wu, and Jieqing Tan. "Dual basis functions for the NS-power basis and their applications." Applied Mathematics and Computation 207, no. 2 (January 2009): 434–41. http://dx.doi.org/10.1016/j.amc.2008.10.048.

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8

Irwansyah, Intan Muchtadi-Alamsyah, Aleams Barra, and Ahmad Muchlis. "Self-Dual Normal Basis of a Galois Ring." Journal of Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/258187.

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LetR′=GR(ps,psml)andR=GR(ps,psm)be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis forR′overR, whereR′is considered as a free module overR. Moreover, we explain a way to construct self-dual normal basis using particular system of polynomials. Finally, we show the connection between self-dual normal basis forR′overRand the set of all invertible, circulant, and orthogonal matrices overR.

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9

Gilbert, M. J., R. Akis, and D. K. Ferry. "Dual computational basis qubit in semiconductor heterostructures." Applied Physics Letters 83, no. 7 (August 18, 2003): 1453–55. http://dx.doi.org/10.1063/1.1599633.

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10

Ibrahim, M. K., and A. Aggoun. "Dual basis digit serial GF(2m) multiplier." International Journal of Electronics 89, no. 7 (July 2002): 517–23. http://dx.doi.org/10.1080/0020721021000044304.

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11

Fenn, S. T. J., M. Benaissa, and D. Taylor. "Dual basis systolic multipliers for GF(2m)." IEE Proceedings - Computers and Digital Techniques 144, no. 1 (1997): 43. http://dx.doi.org/10.1049/ip-cdt:19970660.

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12

Ksiazek, Agnieszka, and Krzysztof Wolinski. "Molecular properties with dual basis set methods." Molecular Physics 106, no. 6 (March 20, 2008): 769–86. http://dx.doi.org/10.1080/00268970801961013.

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13

Kimura, Yoshiyuki. "Quantum unipotent subgroup and dual canonical basis." Kyoto Journal of Mathematics 52, no. 2 (2012): 277–331. http://dx.doi.org/10.1215/21562261-1550976.

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14

Kersey, Scott N. "A DUAL BASIS FOR DISCRETE POLYNOMIAL BLENDING." International Journal of Numerical Methods and Applications 15, no. 4 (January 25, 2017): 267–303. http://dx.doi.org/10.17654/nm015040267.

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15

Fenn, S. T. J., M. Benaissa, and D. Taylor. "Finite field inversion over the dual basis." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 4, no. 1 (March 1996): 134–37. http://dx.doi.org/10.1109/92.486087.

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16

Yla-Oijala, Pasi, Sami P. Kiminki, and Seppo Jarvenpaa. "Solving IBC-CFIE With Dual Basis Functions." IEEE Transactions on Antennas and Propagation 58, no. 12 (December 2010): 3997–4004. http://dx.doi.org/10.1109/tap.2010.2078473.

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17

Ye, ZhiJian, Qi Gao, HongPing Wang, RunJie Wei, and JinJun Wang. "Dual-basis reconstruction techniques for tomographic PIV." Science China Technological Sciences 58, no. 11 (August 19, 2015): 1963–70. http://dx.doi.org/10.1007/s11431-015-5909-x.

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18

Park, Sun-Mi. "Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis." Integration 45, no. 2 (March 2012): 205–10. http://dx.doi.org/10.1016/j.vlsi.2011.07.005.

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19

Steele, Ryan P., Robert A. DiStasio, and Martin Head-Gordon. "Non-Covalent Interactions with Dual-Basis Methods: Pairings for Augmented Basis Sets." Journal of Chemical Theory and Computation 5, no. 6 (April 30, 2009): 1560–72. http://dx.doi.org/10.1021/ct900058p.

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20

Othman, W. A. M., and R. N. Goldman. "The dual basis functions for the generalized Ball basis of odd degree." Computer Aided Geometric Design 14, no. 6 (August 1997): 571–82. http://dx.doi.org/10.1016/s0167-8396(96)00047-7.

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21

Paulsen, Vern I., and Fred Shultz. "Complete positivity of the map from a basis to its dual basis." Journal of Mathematical Physics 54, no. 7 (July 2013): 072201. http://dx.doi.org/10.1063/1.4812329.

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22

Mishra, Alok, Rajendra Kumar Sharma, and Wagish Shukla. "On the Complexity of the Dual Bases of the Gaussian Normal Bases." Algebra Colloquium 22, spec01 (November 6, 2015): 909–22. http://dx.doi.org/10.1142/s1005386715000760.

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In this paper, we study the complexity of the dual bases of the Gaussian normal bases of type (n, t), for all n and t = 3, 4, 5, 6, of 𝔽qn over 𝔽q and provide conditions under which the complexity of the Gaussian normal basis of type (n, t) is equal to the complexity of the dual basis over any finite field.

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23

Goryachev, V., and A. Chuprin. "DUAL PWM IN BASIS OF OR-NOT ELEMENTS." LastMile, no. 5 (2017): 64–71. http://dx.doi.org/10.22184/2070-8963.2017.66.5.64.71.

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24

Zhao, Kang. "Global Linear Independence and Finitely Supported Dual Basis." SIAM Journal on Mathematical Analysis 23, no. 5 (September 1992): 1352–55. http://dx.doi.org/10.1137/0523077.

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25

Coleman, Brian. "A dual first-postulate basis for special relativity." European Journal of Physics 24, no. 3 (April 10, 2003): 301–13. http://dx.doi.org/10.1088/0143-0807/24/3/311.

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26

Coleman, B. "A dual first-postulate basis for special relativity." European Journal of Physics 24, no. 4 (July 8, 2003): 493. http://dx.doi.org/10.1088/0143-0807/24/4/501.

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27

Calmels, Claire, Mégane Erblang, Malika Machtoune, and Cornelis Stam. "Neural basis of errors when performing dual tasks." Neurophysiologie Clinique/Clinical Neurophysiology 46, no. 2 (April 2016): 97. http://dx.doi.org/10.1016/j.neucli.2016.05.005.

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28

Novelli, Jean-Christophe, Jean-Yves Thibon, and Frédéric Toumazet. "Noncommutative Bell polynomials and the dual immaculate basis." Algebraic Combinatorics 1, no. 5 (2018): 653–76. http://dx.doi.org/10.5802/alco.28.

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29

Jurgens-Lutovsky, Robin, and Jan Almlöf. "Dual basis sets in calculations of electron correlation." Chemical Physics Letters 178, no. 5-6 (April 1991): 451–54. http://dx.doi.org/10.1016/0009-2614(91)87001-r.

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30

Stefanus, Lim Yohanes. "De Boor-Fix dual functionals for transformation from polynomial basis to convolution basis." ACM Communications in Computer Algebra 42, no. 3 (February 6, 2009): 146–48. http://dx.doi.org/10.1145/1504347.1504360.

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31

Aktaş, Buşra, Olgun Durmaz, and Halit Gündoğan. "ON THE BASIC STRUCTURES OF DUAL SPACE." Facta Universitatis, Series: Mathematics and Informatics 35, no. 1 (April 6, 2020): 253. http://dx.doi.org/10.22190/fumi2001253a.

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Topology studies the properties of spaces that are invariant under any con-tinuous deformation. Topology is needed to examine the properties of the space. Funda-mentally, the most basic structure required to do math in the space is topology. There exists little information on the expression of the basis and topology on dual space. The main point of the research is to explain how to deﬁne the basis and topology on dual space Dⁿ. Then, we will study the geometric constructions corresponding to the open balls in D and D², respectively.

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32

PICKETT, ERIK JARL. "CONSTRUCTION OF SELF-DUAL INTEGRAL NORMAL BASES IN ABELIAN EXTENSIONS OF FINITE AND LOCAL FIELDS." International Journal of Number Theory 06, no. 07 (November 2010): 1565–88. http://dx.doi.org/10.1142/s1793042110003654.

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Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that Tr F/E(g(x), h(x)) = δg, h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char (E) ≠ 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char (E) = 2, then F admits a self-dual normal basis if and only if the exponent of Γ is not divisible by 4. In this paper, we construct self-dual normal basis generators for finite extensions of finite fields whenever they exist. Now let K be a finite extension of ℚp, let L/K be a finite abelian Galois extension of odd degree and let [Formula: see text] be the valuation ring of L. We define AL/K to be the unique fractional [Formula: see text]-ideal with square equal to the inverse different of L/K. It is known that a self-dual integral normal basis exists for AL/K if and only if L/K is weakly ramified. Assuming p ≠ 2, we construct such bases whenever they exist.

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33

Noll, Thomas. "Consistent Pitch Height Forms: A commentary on Daniel Muzzulini's contribution Isaac Newton's Microtonal Approach to Just Intonation." Empirical Musicology Review 15, no. 3-4 (June 28, 2021): 268–72. http://dx.doi.org/10.18061/emr.v15i3-4.8243.

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This text revisits selected aspects of Muzzulini's article and reformulates them on the basis of a three-dimensional interval space E and its dual E*. The pitch height of just intonation is conceived as an element h of the dual space. From octave-fifth-third coordinates it becomes transformed into chromatic coordinates. The dual chromatic basis is spanned by the duals a* of a minor second a and the duals b* and c* of two kinds of augmented primes b and c. Then for every natural number n a modified pitch height form hn is derived from h by augmenting its coordinates with the factor n, followed by rounding to nearest integers. Of particular interest are the octave-consitent forms hn mapping the octave to the value n. The three forms hn for n = 612, 118, 53 (yielding smallest deviations from the respective values of n h) form the Muzzulini basis of E*. The respective transformation matrix T* between the coordinate representations of linear forms in the Muzzulini basis and the dual chromatic basis is unimodular and a Pisot matrix with the dominant eigen-co-vector very close to h. Certain selections of the linear forms hn are displayed in Muzzuli coordinates as ball-like point clouds within a suitable cuboid containing the origin. As an open problem remains the estimation of the musical relevance of Newton's chromatic mode, and chromatic modes in general. As a possible direction of further investigation it is proposed to study the exo-mode of Newton's chromatic mode

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34

Wan, Zhe-Xian, and Kai Zhou. "On the complexity of the dual basis of a type I optimal normal basis." Finite Fields and Their Applications 13, no. 2 (April 2007): 411–17. http://dx.doi.org/10.1016/j.ffa.2005.10.007.

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35

Sugimoto, Koichi. "On the Bases of Wrench Spaces for the Kinematic and Dynamic Analysis of Mechanisms." Journal of Mechanical Design 125, no. 3 (September 1, 2003): 552–56. http://dx.doi.org/10.1115/1.1588345.

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The aim of this paper is to find out a computational procedure for the kinematic and dynamic analysis of a mechanism with multiple loops having motion spaces of a Lie algebra or Lie algebras. The basis of a motion space of the loop is determined such that it consists of passive joints axes in a loop, and a basis of a wrench space is determined to be its dual basis. The analysis of a closed loop mechanism can be done by selecting loop-cut-joints and computing values of wrenches acting on these joints from the condition that virtual works of passive joints are zero. By expressing these wrenches in the coordinate vectors on the dual bases, the concise analysis procedure can be obtained. Because a formulation for the analysis is developed based on the bases consisting of passive joint axes and their dual bases, the computational procedure can be applied to a mechanism with any Lie algebras.

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36

Chlewicki, Lukasz K., C. Alejandro Velikovsky, Vamsi Balakrishnan, Roy A. Mariuzza, and Vinay Kumar. "Molecular Basis of the Dual Functions of 2B4 (CD244)." Journal of Immunology 180, no. 12 (June 3, 2008): 8159–67. http://dx.doi.org/10.4049/jimmunol.180.12.8159.

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37

Jensen, Ole, and John E. Lisman. "Dual oscillations as the physiological basis for capacity limits." Behavioral and Brain Sciences 24, no. 1 (February 2001): 126. http://dx.doi.org/10.1017/s0140525x01333927.

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A physiological model for short-term memory (STM) based on dual theta (5–10 Hz) and gamma (20–60 Hz) oscillation was proposed by Lisman and Idiart (1995). In this model a memory is represented by groups of neurons that fire in the same gamma cycle. According to this model, capacity is determined by the number of gamma cycles that occur within the slower theta cycle. We will discuss here the implications of recent reports on theta oscillations recorded in humans performing the Sternberg task. Assuming that the oscillatory memory models are correct, these findings can help determine STM capacity.

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38

Park, Chun-Myoung. "Design of the Efficient Multiplier based on Dual Basis." Journal of the Institute of Electronics and Information Engineers 51, no. 6 (June 25, 2014): 117–23. http://dx.doi.org/10.5573/ieie.2014.51.6.117.

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39

Kersey, Scott N. "Dual basis functions in subspaces of inner product spaces." Applied Mathematics and Computation 219, no. 19 (June 2013): 10012–24. http://dx.doi.org/10.1016/j.amc.2013.04.015.

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40

Imai, S., M. Osawa, K. Takeuchi, and I. Shimada. "Structural basis underlying the dual gate properties of KcsA." Proceedings of the National Academy of Sciences 107, no. 14 (March 8, 2010): 6216–21. http://dx.doi.org/10.1073/pnas.0911270107.

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41

Moro, Federico, and Massimo Guarnieri. "Efficient 3-D Domain Decomposition With Dual Basis Functions." IEEE Transactions on Magnetics 51, no. 3 (March 2015): 1–4. http://dx.doi.org/10.1109/tmag.2014.2352034.

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42

Chen, C. S., C. A. Brebbia, and H. Power. "Dual reciprocity method using compactly supported radial basis functions." Communications in Numerical Methods in Engineering 15, no. 2 (February 1999): 137–50. http://dx.doi.org/10.1002/(sici)1099-0887(199902)15:2<137::aid-cnm233>3.0.co;2-9.

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43

Kelly, David, and R. Padmanabhan. "Another independent self-dual basis for the trivial variety." Algebra universalis 57, no. 4 (November 21, 2007): 497–99. http://dx.doi.org/10.1007/s00012-007-2048-7.

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44

Rababah, Abedallah, and Mohammad Al-Natour. "Weighted dual functions for Bernstein basis satisfying boundary constraints." Applied Mathematics and Computation 199, no. 2 (June 2008): 456–63. http://dx.doi.org/10.1016/j.amc.2007.10.006.

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45

Steele, Ryan P., Martin Head-Gordon, and John C. Tully. "Ab Initio Molecular Dynamics with Dual Basis Set Methods." Journal of Physical Chemistry A 114, no. 43 (November 4, 2010): 11853–60. http://dx.doi.org/10.1021/jp107342g.

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46

Chwee, T. S., G. S. Lim, W. Y. Fan, and M. B. Sullivan. "Computational study of molecular properties with dual basis sets." Physical Chemistry Chemical Physics 15, no. 39 (2013): 16566. http://dx.doi.org/10.1039/c3cp51055g.

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47

Steele, Ryan P., Yihan Shao, Robert A. DiStasio,, and Martin Head-Gordon. "Dual-Basis Analytic Gradients. 1. Self-Consistent Field Theory." Journal of Physical Chemistry A 110, no. 51 (December 2006): 13915–22. http://dx.doi.org/10.1021/jp065444h.

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48

Hamel, A. M., L. F. McAven, H. J. Ross, and P. H. Butler. "Transformation between the Young - Yamanouchi basis and its dual." Journal of Physics A: Mathematical and General 29, no. 18 (September 21, 1996): 5935–44. http://dx.doi.org/10.1088/0305-4470/29/18/022.

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49

Wolinski, Krzysztof, and Peter Pulay. "Second-order Møller–Plesset calculations with dual basis sets." Journal of Chemical Physics 118, no. 21 (June 2003): 9497–503. http://dx.doi.org/10.1063/1.1562606.

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50

Mo, Jia, Zhaofeng Ma, Yixian Yang, and Xinxin Niu. "A Quantum Watermarking Protocol Based on Bell Dual Basis." International Journal of Theoretical Physics 52, no. 11 (June 19, 2013): 3813–19. http://dx.doi.org/10.1007/s10773-013-1687-z.

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Journal articles on the topic 'Dual basis'

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