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Journal articles on the topic 'Clifford analysis'

To see the other types of publications on this topic, follow the link: Clifford analysis.

Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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1

Leutwiler, Heinz. "Modified clifford analysis." Complex Variables, Theory and Application: An International Journal 17, no. 3-4 (February 1992): 153–71. http://dx.doi.org/10.1080/17476939208814508.

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2

Ryan, John. "Duality in complex Clifford analysis." Journal of Functional Analysis 61, no. 2 (April 1985): 117–35. http://dx.doi.org/10.1016/0022-1236(85)90031-x.

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3

Eriksson-Bique, Sirkka-Liisa. "On modified clifford analysis." Complex Variables, Theory and Application: An International Journal 45, no. 1 (July 2001): 11–33. http://dx.doi.org/10.1080/17476930108815366.

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4

Ren, Guangbin, Haiyan Wang, and Lin Chen. "Paracomplex Hermitean Clifford Analysis." Complex Analysis and Operator Theory 8, no. 6 (November 23, 2013): 1367–82. http://dx.doi.org/10.1007/s11785-013-0341-3.

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5

Chen, Lin, Guangbin Ren, and Haiyan Wang. "Bicomplex Hermitian Clifford analysis." Frontiers of Mathematics in China 10, no. 3 (February 2, 2015): 523–46. http://dx.doi.org/10.1007/s11464-015-0410-1.

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6

Sommen, F., and W. Sprößig. "Introduction to Clifford analysis." Mathematical Methods in the Applied Sciences 25, no. 16-18 (November 10, 2002): 1337–42. http://dx.doi.org/10.1002/mma.373.

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7

Timorin, V. A. "Circles and Clifford Algebras." Functional Analysis and Its Applications 38, no. 1 (January 2004): 45–51. http://dx.doi.org/10.1023/b:faia.0000024867.02438.e3.

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8

Vasilescu, Florian-Horia. "Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions." Concrete Operators 8, no. 1 (January 1, 2021): 90–113. http://dx.doi.org/10.1515/conop-2020-0115.

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Abstract The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a spectrum defined in the complex plane, and also certain stem functions, analytic in neighborhoods of such a spectrum. The replacement of the slice regular functions, having values in a Clifford algebra, by analytic stem functions becomes possible because of an isomorphism induced by a Cauchy type transform, whose existence is proved in the first part of this work.

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9

Ren, Guangbin, Lin Chen, and Haiyan Wang. "Split-quaternionic Hermitian Clifford analysis." Complex Variables and Elliptic Equations 60, no. 3 (August 26, 2014): 333–53. http://dx.doi.org/10.1080/17476933.2014.936861.

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10

Krausshar, Rolf Sören. "Automorphic Forms in Clifford Analysis." Complex Variables, Theory and Application: An International Journal 47, no. 5 (May 2002): 417–40. http://dx.doi.org/10.1080/02781070290013758.

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11

Delanghe, Richard. "Clifford Analysis: History and Perspective." Computational Methods and Function Theory 1, no. 1 (September 2001): 107–53. http://dx.doi.org/10.1007/bf03320981.

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12

Swanhild, Bernstein. "Inverse scattering and Clifford analysis." Advances in Applied Clifford Algebras 11, S2 (June 2001): 21–30. http://dx.doi.org/10.1007/bf03219119.

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13

De Ridder, H., T. Raeymaekers, and F. Sommen. "Rotations in discrete Clifford analysis." Applied Mathematics and Computation 285 (July 2016): 114–40. http://dx.doi.org/10.1016/j.amc.2016.03.027.

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14

Brackx, Fred, Hennie De Schepper, and Frank Sommen. "The Hermitian Clifford Analysis Toolbox." Advances in Applied Clifford Algebras 18, no. 3-4 (April 28, 2008): 451–87. http://dx.doi.org/10.1007/s00006-008-0081-z.

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15

Laville, Guy. "Some Topics in Clifford Analysis." Advances in Applied Clifford Algebras 19, no. 3-4 (November 20, 2009): 721–75. http://dx.doi.org/10.1007/s00006-009-0193-0.

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16

Bolívar, Yanett, Licet Lezama, Luis Gerardo Mármol, and Judith Vanegas. "Associated Spaces in Clifford Analysis." Advances in Applied Clifford Algebras 25, no. 3 (February 14, 2015): 539–51. http://dx.doi.org/10.1007/s00006-015-0528-y.

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17

Souček, Vladimír. "Invariant operators and clifford analysis." Advances in Applied Clifford Algebras 11, S1 (February 2001): 37–52. http://dx.doi.org/10.1007/bf03042208.

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18

Sommen, F. "Clifford analysis on super-space." Advances in Applied Clifford Algebras 11, S1 (February 2001): 291–304. http://dx.doi.org/10.1007/bf03042224.

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19

Dubinskii, Julii, and Michael Reissig. "Variational problems in Clifford analysis." Mathematical Methods in the Applied Sciences 25, no. 14 (2002): 1161–76. http://dx.doi.org/10.1002/mma.270.

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20

Sabadini, Irene, and Frank Sommen. "Hermitian Clifford analysis and resolutions." Mathematical Methods in the Applied Sciences 25, no. 16-18 (2002): 1395–413. http://dx.doi.org/10.1002/mma.378.

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21

Gürlebeck, Klaus, Uwe Kähler, John Ryan, and Wolfgang Sprößig. "Clifford Analysis over Unbounded Domains." Advances in Applied Mathematics 19, no. 2 (August 1997): 216–39. http://dx.doi.org/10.1006/aama.1997.0541.

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22

Pu, Li Juan, Wen Ming Cao, and Xao Jiang Liang. "Clifford Sensor Network Connected Coverage Energy Analysis." Advanced Materials Research 204-210 (February 2011): 1225–30. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.1225.

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IN a Clifford Wireless Sensor Network, We aimed to extend network lifetime while maintaining a high quality of service. In this paper we researched the Geometric algebra capacity theorem of the connection map of the 3-D Clifford sensor network model on the basis of ref [1]. Then we proposed Clifford Sensor Network Connectivity-Coverage Energy Consumption Algorithm (CSNCCECA) under the principle of nearest direction. This algorithm can efficiently utilize energy by building an efficient connection map of the WSN. Finally we tested and verified the rationality of the algorithm. The experiment results show that SDECA based on Shortest-Distance is exceeded by CSNCCECA as demonstrated in fig. 4.

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23

Carey, A. L., and D. E. Evans. "Algebras almost commuting with Clifford algebras." Journal of Functional Analysis 88, no. 2 (February 1990): 279–98. http://dx.doi.org/10.1016/0022-1236(90)90107-v.

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24

Franssens, Ghislain R. "Fundamental Theorems for Clifford Algebra-Valued Distributions in Elliptic Clifford Analysis." Advances in Applied Clifford Algebras 21, no. 4 (March 16, 2011): 697–705. http://dx.doi.org/10.1007/s00006-011-0283-7.

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25

Abreu-Blaya, R., J. Bory-Reyes, T. Moreno-García, and D. Peña-Peña. "Weighted Cauchy transforms in Clifford analysis." Complex Variables and Elliptic Equations 51, no. 5-6 (May 2006): 397–406. http://dx.doi.org/10.1080/17476930500481251.

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26

Cerejeiras, P., U. Kähler, and G. Ren. "Clifford analysis for finite reflection groups." Complex Variables and Elliptic Equations 51, no. 5-6 (May 2006): 487–95. http://dx.doi.org/10.1080/17476930500482499.

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27

Begehr, Heinrich, Zhang Zhongxiang, and Vu Thi Ngoc Ha. "Generalized integral representations in Clifford analysis." Complex Variables and Elliptic Equations 51, no. 8-11 (August 2006): 745–62. http://dx.doi.org/10.1080/17476930600672940.

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28

Gong, yanfang. "Some integral properties in Clifford analysis." Complex Variables and Elliptic Equations 52, no. 10-11 (October 2007): 1039–46. http://dx.doi.org/10.1080/17476930701470194.

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29

Common, A. K. "Axial monogenic Clifford-Padé approximants." Journal of Approximation Theory 68, no. 2 (February 1992): 206–22. http://dx.doi.org/10.1016/0021-9045(92)90093-4.

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30

Sabadini, Irene, and Daniele C. Struppa. "Computational algebraic analysis methods in Clifford analysis." Mathematical Methods in the Applied Sciences 25, no. 16-18 (2002): 1415–27. http://dx.doi.org/10.1002/mma.379.

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31

Ryan, John. "Conformally Covariant Operators in Clifford Analysis." Zeitschrift für Analysis und ihre Anwendungen 14, no. 4 (1995): 677–704. http://dx.doi.org/10.4171/zaa/647.

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32

Begehr, Heinrich. "Iterated Integral Operators in Clifford Analysis." Zeitschrift für Analysis und ihre Anwendungen 18, no. 2 (1999): 361–77. http://dx.doi.org/10.4171/zaa/887.

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33

Bureš, J., F. Sommen, V. Souček, and P. Van Lancker. "Rarita–Schwinger Type Operators in Clifford Analysis." Journal of Functional Analysis 185, no. 2 (October 2001): 425–55. http://dx.doi.org/10.1006/jfan.2001.3781.

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34

Li, Pingrun, and Lixia Cao. "Linear BVPs and SIEs for Generalized Regular Functions in Clifford Analysis." Journal of Function Spaces 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/6967149.

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We study some properties of a regular function in Clifford analysis and generalize Liouville theorem and Plemelj formula with values in Clifford algebra An(R). By means of the classical Riemann boundary value problem and of the theory of a regular function, we discuss some boundary value problems and singular integral equations in Clifford analysis and obtain the explicit solutions and the conditions of solvability. Thus, the results in this paper will be of great significance for the study of improving and developing complex analysis, integral equation, and boundary value theory.

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35

Nekovar, Ya. "Maslov index and Clifford algebras." Functional Analysis and Its Applications 24, no. 3 (1991): 196–204. http://dx.doi.org/10.1007/bf01077960.

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36

Brackx, Fred, Nele De Schepper, and Frank Sommen. "The Clifford-Fourier Transform." Journal of Fourier Analysis and Applications 11, no. 6 (November 1, 2005): 669–81. http://dx.doi.org/10.1007/s00041-005-4079-9.

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37

Peels, Rik. "De scheepseigenaar en de gelovige: William Clifford over God, bewijs en doxastische verantwoordelijkheid." NTT Journal for Theology and the Study of Religion 61, no. 2 (May 18, 2007): 89–108. http://dx.doi.org/10.5117/ntt2007.61.089.peel.

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At the end of the nineteenth century, in his famous essay ‘The Ethics of Belief’ the well-known mathematician and philosopher William Kingdon Clifford offered a powerful argument against religious beliefs. This article first gives an extensive analysis of Clifford’s evidentialist argument by placing it against the background of his evidentialist epistemology. Second, some arguments of William James, Clifford’s most famous critic, are expounded and criticised. Although there is some plausibility to these arguments, they are insufficient to refute Clifford’s evidentialism. Third, the author presents some problems for Clifford’s evidentialism, having to do with evidentialism as a moral thesis and with doxastic involuntarism, and offers some new arguments against Clifford’s evidentialist argument. Clifford’s argument against belief in God, as it stands, turns out to be untenable.

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38

Abul-Ez, Mahmoud, Mohamed Abdalla, and Aidah Al-Ahmadi. "On the representation of monogenic functions by the product bases of polynomials." Filomat 34, no. 4 (2020): 1209–22. http://dx.doi.org/10.2298/fil2004209a.

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The main purpose of this paper is to study questions concerning representations of Clifford valued functions by the product bases of Clifford polynomials. By the way we generalize several results from complex analysis to the setting of Clifford analysis.

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39

Abul-Ez, Mahmoud, Mohamed Abdalla, and Aidah Al-Ahmadi. "On the representation of monogenic functions by the product bases of polynomials." Filomat 34, no. 4 (2020): 1209–22. http://dx.doi.org/10.2298/fil2004209a.

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The main purpose of this paper is to study questions concerning representations of Clifford valued functions by the product bases of Clifford polynomials. By the way we generalize several results from complex analysis to the setting of Clifford analysis.

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40

CASTRO, CARLOS. "POLYVECTOR SUPER-POINCARÉ ALGEBRAS, M, F THEORY ALGEBRAS AND GENERALIZED SUPERSYMMETRY IN CLIFFORD-SPACES." International Journal of Modern Physics A 21, no. 10 (April 20, 2006): 2149–72. http://dx.doi.org/10.1142/s0217751x06028916.

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Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic supersymmetric point-particle action in Clifford-space backgrounds. The relativistic supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector super-Poincaré and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our final analysis of the novel Clifford-superspace realizations of generalized supersymmetries in Clifford spaces.

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41

Jefferies, Brian, and Alan McIntosh. "The Weyl calculus and Clifford analysis." Bulletin of the Australian Mathematical Society 57, no. 2 (April 1998): 329–41. http://dx.doi.org/10.1017/s0004972700031695.

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42

Zhongxiang, Z. "Some properties of operators in Clifford analysis." Complex Variables and Elliptic Equations 52, no. 6 (June 2007): 455–73. http://dx.doi.org/10.1080/17476930701200666.

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43

Xie, Yonghong, Heju Yang, and Yuying Qiao. "Complexk-hypermonogenic functions in complex Clifford analysis." Complex Variables and Elliptic Equations 58, no. 10 (October 2013): 1467–79. http://dx.doi.org/10.1080/17476933.2012.686496.

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44

Cerejeiras, P., N. Faustino, and N. Vieira. "Numerical Clifford analysis for nonlinear Schrödinger problem." Numerical Methods for Partial Differential Equations 24, no. 4 (2008): 1181–202. http://dx.doi.org/10.1002/num.20312.

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45

Lim, Su Jin, and Kwang Ho Shon. "SPLIT HYPERHOLOMORPHIC FUNCTION IN CLIFFORD ANALYSIS." Pure and Applied Mathematics 22, no. 1 (February 28, 2015): 57–63. http://dx.doi.org/10.7468/jksmeb.2015.22.1.57.

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46

BRACKX, F., and H. DE SCHEPPER. "HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS." Chinese Annals of Mathematics 26, no. 01 (January 2005): 1–14. http://dx.doi.org/10.1142/s0252959905000026.

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47

Krausshar, Rolf Sören. "Monogenic muitiperiodic functions in clifford analysis." Complex Variables, Theory and Application: An International Journal 46, no. 4 (November 2001): 337–68. http://dx.doi.org/10.1080/17476930108815421.

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48

Peetre, Jaak, and Per S. Sjölin. "Three-line theorems and clifford analysis." Complex Variables, Theory and Application: An International Journal 19, no. 3 (August 1992): 92–124. http://dx.doi.org/10.1080/17476939208814568.

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49

Brackx, F., F. Sommen, and N. Van Acker. "Reproducing bergman kernels in clifford analysis." Complex Variables, Theory and Application: An International Journal 24, no. 3-4 (March 1994): 191–204. http://dx.doi.org/10.1080/17476939408814711.

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50

El-Sayed Ahmed, A., and Saleh Omran. "On Bergman spaces in Clifford analysis." Applied Mathematical Sciences 7 (2013): 4203–11. http://dx.doi.org/10.12988/ams.2013.34208.

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