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## Advances in Applied Clifford Algebras

 Short Title: Adv. Appl. Clifford Algebr. Publisher: Springer (Birkhäuser), Basel ISSN: 0188-7009; 1661-4909/e Online: http://link.springer.com/journal/volumesAndIssues/6 Comments: Indexed cover-to-cover
 Documents Indexed: 1,440 Publications (since 1991) References Indexed: 1,031 Publications with 23,060 References.
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#### Latest Issues

 31, No. 4 (2021) 31, No. 3 (2021) 31, No. 2 (2021) 31, No. 1 (2021) 30, No. 5 (2020) 30, No. 4 (2020) 30, No. 3 (2020) 30, No. 2 (2020) 30, No. 1 (2020) 29, No. 5 (2019) 29, No. 4 (2019) 29, No. 3 (2019) 29, No. 2 (2019) 29, No. 1 (2019) 28, No. 5 (2018) 28, No. 4 (2018) 28, No. 3 (2018) 28, No. 2 (2018) 28, No. 1 (2018) 27, No. 4 (2017) 27, No. 3 (2017) 27, No. 2 (2017) 27, No. 1 (2017) 26, No. 4 (2016) 26, No. 3 (2016) 26, No. 2 (2016) 26, No. 1 (2016) 25, No. 4 (2015) 25, No. 3 (2015) 25, No. 2 (2015) 25, No. 1 (2015) 24, No. 4 (2014) 24, No. 3 (2014) 24, No. 2 (2014) 24, No. 1 (2014) 23, No. 4 (2013) 23, No. 3 (2013) 23, No. 2 (2013) 23, No. 1 (2013) 22, No. 4 (2012) 22, No. 3 (2012) 22, No. 2 (2012) 22, No. 1 (2012) 21, No. 4 (2011) 21, No. 3 (2011) 21, No. 2 (2011) 21, No. 1 (2011) 20, No. 3-4 (2010) 20, No. 2 (2010) 20, No. 1 (2010) 19, No. 3-4 (2009) 19, No. 2 (2009) 19, No. 1 (2009) 18, No. 3-4 (2008) 18, No. 2 (2008) 18, No. 1 (2008) 17, No. 4 (2007) 17, No. 3 (2007) 17, No. 2 (2007) 17, No. 1 (2007) 16, No. 2 (2006) 16, No. 1 (2006) 15, No. 2 (2005) 15, No. 1 (2005) 14, No. 2 (2004) 14, No. 1 (2004) 13, No. 2 (2003) 13, No. 1 (2003) 12, No. 2 (2002) 12, No. 1 (2002) 12, Suppl. 1 (2002) 11, No. 2 (2001) 11, No. 1 (2001) 11, Suppl. 2 (2001) 11, Suppl. 1 (2001) 10, No. 2 (2000) 10, No. 1 (2000) 9, No. 2 (1999) 9, No. 1 (1999) 8, No. 2 (1998) 8, No. 1 (1998) 7, No. 2 (1997) 7, No. 1 (1997) 7, Suppl. (1997) 6, No. 2 (1996) 6, No. 1 (1996) 5, No. 2 (1995) 5, No. 1 (1995) 4, No. 2 (1994) 4, No. 1 (1994) 3, No. 2 (1993) 3, No. 1 (1993) 2, No. 2 (1992) 2, No. 1 (1992) 1, No. 1 (1991)
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#### Authors

 34 Hitzer, Eckhard 31 Casanova, Gaston 26 Sommen, Franciscus 23 Keller, Jaime 20 Yayli, Yusuf 19 Helmstetter, Jacques 18 Rodrigues, Waldyr Alves jun. 17 Bory Reyes, Juan 14 Bayro-Corrochano, Eduardo 13 Abreu-Blaya, Ricardo 13 Eriksson, Sirkka-Liisa 13 Kähler, Uwe 13 Tosun, Murat 12 Abłamowicz, Rafał 12 Yamaleev, Robert M. 11 Catoni, Francesco 11 Gürlebeck, Klaus 11 Orelma, Heikki 10 Anglès, Pierre 10 Cerejeiras, Paula 10 Delanghe, Richard 10 Hildenbrand, Dietmar 10 Shirokov, Dmitry S. 10 Vaz, Jayme jun. 10 Wainer, Samuel Augusto 9 Brackx, Fred F. 9 Eelbode, David 9 Hestenes, David Orlin 9 Hrdina, Jaroslav 9 Leutwiler, Heinz 9 Ludkovsky, Sergey Victor 9 Návrat, Aleš 9 Ozdemir, Mustafa Kemal 9 Qian, Tao 9 Sprößig, Wolfgang 8 De Schepper, Hennie 8 Gal, Sorin Gheorghe 8 Kyrchei, Ivan I. 8 Sangwine, Stephen J. 8 Socolovsky, Miguel 8 Vašík, Petr 8 Yüce, Salim 7 Fauser, Bertfried 7 Flaut, Cristina 7 Gu, Yingqiu 7 Jadczyk, Arkadiusz 7 Lasenby, Anthony N. 7 Opfer, Gerhard 7 Shpakivskyi, Vitalii Stanislavovich 7 Soucek, Vladimir 7 Yu, Xuegang 6 Abramov, Viktor 6 Bernstein, Swanhild 6 Cannata, Roberto 6 Dinh, Doan Cong 6 Dvoeglazov, Valeri V. 6 El Kinani, El Hassan 6 Fernández Guasti, Manuel 6 Fuchs, Laurent 6 Gungor, Mehmet Ali 6 Jiang, Tongsong 6 Karakuş, Fatma 6 Lasenby, Joan 6 Lávička, Roman 6 Li, Xingmin 6 Luna-Elizarrarás, María Elena 6 Malonek, Helmuth Robert 6 Mann, Stephen 6 Qiao, Yuying 6 Sabadini, Irene 6 Schmeikal, Bernd 6 Shapiro, Michael V. 6 Suzuki, Osamu 6 Vanegas, Judith C. 6 Zampetti, Paolo 5 Bock, Sebastian 5 Budinich, Marco 5 da Rocha, Roldão Jun. 5 Dechant, Pierre-Philippe 5 Egeland, Olav 5 Falcão, Maria Irene 5 Giardino, Sergio 5 Gök, İsmail 5 Halıcı, Serpil 5 Kraußhar, Rolf Sören 5 Lavor, Carlile Campos 5 Ławrynowicz, Julian Mieczysław 5 Lee, Doohann 5 Li, Wuming 5 Lounesto, Pertti 5 Lu, Yu 5 Pavšič, Matej 5 Red’kov, Victor M. 5 Ren, Guangbin 5 Revoy, Philippe 5 Rochon, Dominic 5 Sobczyk, Garret E. 5 Song, Youngkwon 5 Vieira, Nelson 5 Yang, Heju ...and 1,128 more Authors
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#### Fields

 649 Linear and multilinear algebra; matrix theory (15-XX) 323 Functions of a complex variable (30-XX) 255 Quantum theory (81-XX) 175 Differential geometry (53-XX) 141 Number theory (11-XX) 126 Partial differential equations (35-XX) 119 Relativity and gravitational theory (83-XX) 100 Nonassociative rings and algebras (17-XX) 73 Associative rings and algebras (16-XX) 66 Geometry (51-XX) 58 Harmonic analysis on Euclidean spaces (42-XX) 58 Mechanics of particles and systems (70-XX) 56 Numerical analysis (65-XX) 53 Global analysis, analysis on manifolds (58-XX) 53 Computer science (68-XX) 49 Optics, electromagnetic theory (78-XX) 45 Functional analysis (46-XX) 43 Group theory and generalizations (20-XX) 41 Topological groups, Lie groups (22-XX) 41 Operator theory (47-XX) 38 Information and communication theory, circuits (94-XX) 33 Several complex variables and analytic spaces (32-XX) 26 Algebraic geometry (14-XX) 24 Combinatorics (05-XX) 23 Special functions (33-XX) 20 Potential theory (31-XX) 19 History and biography (01-XX) 19 Field theory and polynomials (12-XX) 15 Abstract harmonic analysis (43-XX) 14 Real functions (26-XX) 14 Integral transforms, operational calculus (44-XX) 12 Ordinary differential equations (34-XX) 11 General and overarching topics; collections (00-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Systems theory; control (93-XX) 10 Commutative algebra (13-XX) 10 Fluid mechanics (76-XX) 9 Difference and functional equations (39-XX) 8 Measure and integration (28-XX) 8 Integral equations (45-XX) 8 Probability theory and stochastic processes (60-XX) 8 Mechanics of deformable solids (74-XX) 7 Approximations and expansions (41-XX) 7 Manifolds and cell complexes (57-XX) 6 Algebraic topology (55-XX) 6 Biology and other natural sciences (92-XX) 5 Convex and discrete geometry (52-XX) 5 Statistics (62-XX) 4 Mathematical logic and foundations (03-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Category theory; homological algebra (18-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Astronomy and astrophysics (85-XX) 1 General algebraic systems (08-XX) 1 $$K$$-theory (19-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

886 Publications have been cited 3,712 times in 1,872 Documents Cited by Year
Quaternion Fourier transform on quaternion fields and generalizations. Zbl 1143.42006
Hitzer, Eckhard M. S.
2007
The Hermitian Clifford analysis toolbox. Zbl 1177.30064
Brackx, Fred; De Schepper, Hennie; Sommen, Frank
2008
On Fibonacci quaternions. Zbl 1329.11016
Halici, Serpil
2012
Clifford Fourier transform on multivector fields and uncertainty principles for dimensions $$n=2\pmod 4$$ and $$n=3\pmod 4$$. Zbl 1177.15029
Hitzer, Eckhard M. S.; Mawardi, Bahri
2008
Directional uncertainty principle for quaternion Fourier transform. Zbl 1198.42006
Hitzer, Eckhard M. S.
2010
Models for irreducible representations of Spin$$(m)$$. Zbl 1221.22016
van Lancker, P.; Sommen, Frank; Constales, D.
2001
On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions. Zbl 1330.11009
Flaut, Cristina; Shpakivskyi, Vitalii
2013
Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra $$\mathrm{Cl}_{3,0}$$. Zbl 1133.42305
Mawardi, Bahri; Hitzer, Eckhard S. M.
2006
The octonionic eigenvalue problem. Zbl 0927.15007
Dray, Tevian; Manogue, Corinne A.
1998
Applications of Clifford’s geometric algebra. Zbl 1269.15022
Hitzer, Eckhard; Nitta, Tohru; Kuroe, Yasuaki
2013
Matrix representations of octonions and their applications. Zbl 0974.15012
Tian, Yongge
2000
Holomorphic Cliffordian functions. Zbl 0940.30028
1998
Bicomplex quantum mechanics. II: The Hilbert space. Zbl 1142.81010
Rochon, D.; Tremblay, S.
2006
Discrete Dirac operators in Clifford analysis. Zbl 1208.30046
Faustino, Nelson; Kähler, Uwe; Sommen, Frank
2007
Fibonacci generalized quaternions. Zbl 1321.11020
Akyiğit, Mahmut; Hüda Kösal, Hidayet; Tosun, Murat
2014
Determinantal representations of solutions to systems of quaternion matrix equations. Zbl 1391.15057
Kyrchei, Ivan
2018
ELKO, flagpole and flag-dipole spinor fields, and the instanton Hopf fibration. Zbl 1202.81237
da Rocha, R.; Hoff da Silva, J. M.
2010
Quaternionic formulation of the classical fields. Zbl 0943.35092
Majerník, V.
1999
Unitary spaces on Clifford algebras. Zbl 1156.15015
Marchuk, N. G.; Shirokov, D. S.
2008
On Appell sets and the Fueter-Sce mapping. Zbl 1170.30023
Gürlebeck, Norman
2009
Bicomplex quantum mechanics. I: The generalized Schrödinger equation. Zbl 1169.81339
Rochon, D.; Tremblay, S.
2004
Correct rules for Clifford calculus on superspace. Zbl 1129.30034
De Bie, Hendrik; Sommen, Frank
2007
The spacetime algebra approach to massive classical electrodynamics with magnetic monopoles. Zbl 1113.78003
Cafaro, C.; Ali, S. A.
2007
Split Fibonacci quaternions. Zbl 1328.11016
Akyiǧit, Mahmut; Kösal, Hidayet Hüda; Tosun, Murat
2013
On Pell quaternions and Pell-Lucas quaternions. Zbl 1344.11022
Çimen, Cennet Bolat; İpek, Ahmet
2016
The Pell quaternions and the Pell octonions. Zbl 1344.11027
Szynal-Liana, Anetta; Włoch, Iwona
2016
Cramer’s rules for Sylvester quaternion matrix equation and its special cases. Zbl 1404.15013
Kyrchei, Ivan
2018
On complex Fibonacci quaternions. Zbl 1270.11012
Halici, Serpil
2013
On eigenvalues of split quaternion matrices. Zbl 1296.15005
Erdoğdu, Melek; Özdemir, Mustafa
2013
$$p$$-Dirac operators. Zbl 1170.53028
Nolder, Craig A.; Ryan, John
2009
Hyperbolic calculus. Zbl 0922.30035
Motter, A. E.; Rosa, M. A. F.
1998
On the Riemann Hilbert type problems in Clifford analysis. Zbl 1061.30033
Abreu Blaya, Ricardo; Bory Reyes, Juan
2001
Nonlinear $$A$$-Dirac equations. Zbl 1253.30073
Nolder, Craig A.
2011
On Hermitian solutions of the split quaternion matrix equation $$AXB+CXD=E$$. Zbl 1386.15036
Yuan, Shi-Fang; Wang, Qing-Wen; Yu, Yi-Bin; Tian, Yong
2017
Mathematics of Clifford – a Maple package for Clifford and Graßmann algebras. Zbl 1099.65520
Ablamowicz, Rafal; Fauser, Bertfried
2005
Special monogenic polynomials and $$L_2$$-approximation. Zbl 1221.30100
Cação, I.; Gürlebeck, K.; Malonek, H.
2001
Clifford algebra and the discretizable molecular distance geometry problem. Zbl 1327.15052
Lavor, Carlile; Alves, Rafael; Figueiredo, Weber; Petraglia, Antonio; Maculan, Nelson
2015
Biquaternion (complexified quaternion) roots of $$- 1$$. Zbl 1107.30038
Sangwine, Stephen J.
2006
Clifford Cauchy type integrals on Ahlfors-David regular surfaces in $$\mathbb R^{m+1}$$. Zbl 1100.30032
Abreu Blaya, Ricardo; Peña Peña, Dixan; Bory Reyes, Juan
2003
An improved Cauchy formula for hypermonogenic functions. Zbl 1172.30027
Eriksson, Sirkka-Liisa; Leutwiler, Heinz
2009
The Howe duality for the Dunkl version of the Dirac operator. Zbl 1404.17018
Ørsted, Bent; Somberg, Petr; Souček, Vladimír
2009
Hyperbolic quaternion formulation of electromagnetism. Zbl 1203.78005
Demir, Süleyman; Tanışlı, Murat; Candemir, Nuray
2010
Interactive 3D space group visualization with CLUCalc and the Clifford geometric algebra description of space groups. Zbl 1242.20060
Hitzer, Eckhard; Perwass, Christian
2010
An introduction to commutative quaternions. Zbl 1207.30073
Catoni, Francesco; Cannata, Roberto; Zampetti, Paolo
2006
A general geometric Fourier transform convolution theorem. Zbl 1263.15021
Bujack, Roxana; Scheuermann, Gerik; Hitzer, Eckhard
2013
Clifford multivector toolbox (for MATLAB). Zbl 1407.68566
Sangwine, Stephen J.; Hitzer, Eckhard
2017
Finite-dimensional bicomplex Hilbert spaces. Zbl 1237.46009
Gervais Lavoie, Raphaël; Marchildon, Louis; Rochon, Dominic
2011
An algorithm for coneigenvalues and coneigenvectors of quaternion matrices. Zbl 1318.15005
Ling, Sitao; Cheng, Xuehan; Jiang, Tongsong
2015
Some algebraic and analytical properties of coquaternion algebra. Zbl 1186.37053
Pogoruy, Anatoliy A.; Rodríguez-Dagnino, Ramón M.
2010
Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers. Zbl 1052.83004
2001
Boundary value problems for quaternionic monogenic functions on non-smooth surfaces. Zbl 0948.30047
Abreu Blaya, Ricardo; Bory Reyes, Juan
1999
On the integral representation of spherical $$k$$-regular functions in Clifford analysis. Zbl 1167.35327
Min, Ku; Jinyuan, Du
2009
Riemann boundary value problems on the sphere in Clifford analysis. Zbl 1262.30056
Ku, Min; Kähler, Uwe; Wang, Daoshun
2012
A new adjacency matrix for finite graphs. Zbl 1194.05099
Staples, George Stacey
2008
The Balian-Low theorem for the windowed quaternionic Fourier transform. Zbl 1256.42044
Fu, Yingxiong; Kähler, Uwe; Cerejeiras, Paula
2012
Hypermonogenic functions and Möbius transformations. Zbl 1221.30105
Eriksson-Bique, Sirkka-Liisa; Leutwiler, Heinz
2001
On finite difference Dirac operators and their fundamental solutions. Zbl 1221.30107
Gürlebeck, Klaus; Hommel, Angela
2001
The Laurent series on the octonions. Zbl 1221.30112
Li, Xingmin; Zhao, Kai; Peng, Lizhong
2001
Real matrix representations for the complex quaternions. Zbl 1290.15020
Flaut, Cristina; Shpakivskyi, Vitalii
2013
On monogenic series expansions with applications to linear elasticity. Zbl 1310.33007
Bock, Sebastian
2014
The Fibonacci octonions. Zbl 1375.11015
Keçilioğlu, Osman; Akkus, Ilker
2015
Geometric algebra to model uncertainties in the discretizable molecular distance geometry problem. Zbl 1373.92148
Alves, Rafael; Lavor, Carlile
2017
The modified Pell and the modified $$k$$-Pell quaternions and octonions. Zbl 1380.11010
Catarino, Paula
2016
Geometric roots of $$-1$$ in Clifford algebras $$C \ell_{p,q}$$ with $$p + q \leq 4$$. Zbl 1216.15019
Hitzer, Eckhard; Abłamowicz, Rafał
2011
Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like. Zbl 1187.15026
Hitzer, Eckhard; Tachibana, Kanta; Buchholz, Sven; Yu, Isseki
2009
Cayley formula, Euler parameters and rotations in 3-dimensional Lorentzian space. Zbl 1197.15015
Özkaldı, Sıddıka; Gündoğan, Halit
2010
Albert Crumeyrolle’s work on Clifford algebras and spinors. Zbl 0842.01017
Lounesto, P.
1992
Similarity and consimilarity of elements in the real Cayley-Dickson algebras. Zbl 1043.17500
Tian, Yongge
1999
Complete families of solutions for the Dirac equation using bicomplex function theory and transmutations. Zbl 1257.30051
Campos, Hugo M.; Kravchenko, Vladislav V.; Méndez, Luis M.
2012
Fischer decomposition for difference Dirac operators. Zbl 1116.15023
Faustino, N.; Kähler, U.
2007
On a quaternionic analogue of the cross-ratio. Zbl 1257.15014
Gwynne, Ewain; Libine, Matvei
2012
On dual Fibonacci octonions. Zbl 1354.11014
Halici, Serpil
2015
Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson form. Zbl 1223.16005
Sangwine, Stephen J.; Le Bihan, Nicolas
2010
Canal surfaces with quaternions. Zbl 1339.53018
Aslan, Selahattin; Yaylı, Yusuf
2016
On generalization of Martinelli-Bochner integral formula using Clifford analysis. Zbl 1206.30069
Ku, Min; Du, Jinyuan; Wang, Daoshun
2010
$$n$$-dimensional hyperbolic complex numbers. Zbl 0937.30029
1998
Octonions and triality. Zbl 1046.15035
Lounesto, Pertti
2001
Feynman’s operational calculi for noncommuting operators: The monogenic calculus. Zbl 1096.47501
Jefferies, B.; Johnson, G. W.
2001
A constraint system of generalized Sylvester quaternion matrix equations. Zbl 1386.15035
2017
$$\sigma$$-PBW extensions of skew Armendariz rings. Zbl 1392.16021
Reyes, Armando; Suárez, Héctor
2017
Computations with Clifford and Grassmann algebras. Zbl 1182.65068
Abłamowicz, Rafał
2009
Super 3-Lie algebras induced by super Lie algebras. Zbl 1419.17005
Abramov, Viktor
2017
On the quaternionic $$B _{2}$$-slant helices in the Euclidean space $$E ^{4}$$. Zbl 1239.53002
Gök, İsmail; Okuyucu, O. Zeki; Kahraman, Ferdağ; Hacisalihoğlu, H. Hilmi
2011
A Clifford algebraic framework for $$\mathfrak{sp}(m)$$-invariant differential operators. Zbl 1127.58035
Eelbode, David
2007
Fundamental representations and algebraic properties of biquaternions or complexified quaternions. Zbl 1272.15016
Sangwine, Stephen J.; Ell, Todd A.; Le Bihan, Nicolas
2011
Split Fibonacci and Lucas octonions. Zbl 1320.11012
Akkus, Ilker; Keçilioğlu, Osman
2015
On complex split quaternion matrices. Zbl 1292.15032
Erdoğdu, Melek; Özdemir, Mustafa
2013
$$R(4, 4)$$ as a computational framework for 3-dimensional computer graphics. Zbl 1312.65020
Goldman, Ron; Mann, Stephen
2015
Solution of initial value problems with monogenic initial functions in Banach spaces with $$L_p$$-norm. Zbl 1190.35055
Yüksel, Uğur
2010
Integral formula of isotonic functions over unbounded domain in Clifford analysis. Zbl 1191.30018
Min, Ku
2010
Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving $$\phi$$-skew-Hermicity. Zbl 1409.15017
He, Zhuo-Heng
2019
Clifford algebras of polynomials, generalized Grassmann algebras and $$q$$-deformed Heisenberg algebras. Zbl 0841.15023
Rausch de Traubenberg, M.
1994
Universal similarity factorization equalities over real Clifford algebras. Zbl 0926.15026
Tian, Yongge
1998
Lie symmetries of inviscid Burgers’ equation. Zbl 1173.35699
2009
Hyperbolic extensions of integral formulas. Zbl 1203.30053
Eriksson, Sirkka-Liisa
2010
Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups. Zbl 1273.15021
Dechant, Pierre-Philippe
2013
Complex algebras on $$n$$-order polynomials and generalizations of trigonometry, oscillator model and Hamilton dynamics. Zbl 1098.13504
Yamaleev, Robert M.
2005
A modified uncertainty principle for two-sided quaternion Fourier transform. Zbl 1342.42009
Bahri, Mawardi
2016
The generalized Clifford-Hermite continuous wavelet transform. Zbl 1221.42058
Brackx, F.; Sommen, Frank
2001
On octonionic polynomials. Zbl 1160.17003
Serôdio, Rogério
2007
The existence of Cauchy kernels of Kravchenko-generalized Dirac operators. Zbl 1456.30088
Dinh, Doan Cong
2021
Solvability of new constrained quaternion matrix approximation problems based on core-EP inverses. Zbl 1456.15014
Kyrchei, Ivan; Mosić, Dijana; Stanimirović, Predrag S.
2021
Wavelet transform of Dini Lipschitz functions on the quaternion algebra. Zbl 1457.42049
Bouhlal, A.; Safouane, N.; Achak, A.; Daher, R.
2021
Ternary Clifford algebras. Zbl 1461.30115
Cerejeiras, P.; Vajiac, M.
2021
Quaternion Fourier transform and generalized Lipschitz classes. Zbl 1457.42019
Loualid, El Mehdi; Elgargati, Abdelghani; Daher, Radouan
2021
Dual hyperquaternion Poincaré groups. Zbl 07330642
Girard, Patrick R.; Clarysse, Patrick; Pujol, Romaric; Goutte, Robert; Delachartre, Philippe
2021
BiHom-Lie superalgebra structures and BiHom-Yang-Baxter equations. Zbl 07213861
Wang, Shengxiang; Guo, Shuangjian
2020
Spectrums of functions associated to the fractional Clifford-Fourier transform. Zbl 1433.42006
Li, Shanshan; Leng, Jinsong; Fei, Minggang
2020
Generalized Hadamard product bases of special monogenic polynomials. Zbl 1435.30145
Zayed, Mohra
2020
Projection factors and generalized real and complex Pythagorean theorems. Zbl 1453.15010
Mandolesi, André L. G.
2020
The tangential $$k$$-Cauchy-Fueter operator and $$k$$-CF functions over the Heisenberg group. Zbl 1431.22011
Ren, Guangzhen; Shi, Yun; Wang, Wei
2020
Quadratic split quaternion polynomials: factorization and geometry. Zbl 1448.12001
Scharler, Daniel F.; Siegele, Johannes; Schröcker, Hans-Peter
2020
Heisenberg’s and Hardy’s uncertainty principles for special relativistic space-time Fourier transformation. Zbl 1454.15017
El Haoui, Youssef; Hitzer, Eckhard; Fahlaoui, Said
2020
Conformal mappings revisited in the octonions and Clifford algebras of arbitrary dimension. Zbl 1441.30075
Kraußhar, Rolf Sören
2020
Time series, hidden variables and spatio-temporal ordinality networks. Zbl 1444.37064
Thiruvengadam, Sudharsan; Tan, Jei Shian; Miller, Karol
2020
Drinfeld double for infinitesimal BiHom-bialgebras. Zbl 07239334
Ma, Tianshui; Yang, Haiyan
2020
3-Hom-Lie algebras based on $$\sigma$$-derivation and involution. Zbl 07239337
Abramov, Viktor; Silvestrov, Sergei
2020
Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense. Zbl 1448.30006
Teodoro, A. Di; Ferreira, M.; Vieira, N.
2020
The Riemann curvature tensor and Higgs scalar field within CAM theory. Zbl 1437.81141
Wolk, Brian Jonathan
2020
Quaternion windowed linear canonical transform of two-dimensional signals. Zbl 1435.30140
Gao, Wen-Biao; Li, Bing-Zhao
2020
A geometric algebra based higher dimensional approximation method for statics and kinematics of robotic manipulators. Zbl 1448.70008
2020
A Cauchy integral formula for infrapolymonogenic functions in Clifford analysis. Zbl 1435.30136
Abreu Blaya, Ricardo; Bory Reyes, Juan; Moreno García, Arsenio; Moreno García, Tania
2020
The unified standard model. Zbl 07261280
Gording, Brage; Schmidt-May, Angnis
2020
Generalized $$(k_i)$$-monogenic functions. Zbl 1451.30004
Dinh, Doan Cong
2020
Polynomial approximation in quaternionic Bloch and Besov spaces. Zbl 1455.30039
2020
The Moore-Penrose inverse and singular value decomposition of split quaternions. Zbl 1444.15004
Abłamowicz, Rafał
2020
Brauer-Clifford group of $$(S,\mathcal{G},H)$$-Azumaya algebras. Zbl 1454.16026
Guédénon, Thomas
2020
Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving $$\phi$$-skew-Hermicity. Zbl 1409.15017
He, Zhuo-Heng
2019
A system of coupled quaternion matrix equations with seven unknowns and its applications. Zbl 1414.15021
He, Zhuo-Heng
2019
Donoho-Stark’s uncertainty principles in real Clifford algebras. Zbl 1428.43004
El Haoui, Youssef; Fahlaoui, Said
2019
Determinantal representations of the quaternion core inverse and its generalizations. Zbl 1436.15004
Kyrchei, Ivan
2019
Consistency of split quaternion matrix equations $$AX^{\star }-XB=CY+D$$ and $$X-AX^\star B=CY+D$$. Zbl 1420.15013
Liu, Xin; Zhang, Yang
2019
Drinfeld codoubles of Hom-Hopf algebras. Zbl 1454.17010
Zhang, Xiaohui; Guo, Shuangjian; Wang, Shengxiang
2019
Uncertainty principles for the continuous quaternion shearlet transform. Zbl 1431.42017
Brahim, Kamel; Nefzi, Bochra; Tefjeni, Emna
2019
Cramer’s rules of $$\eta$$-(skew-)Hermitian solutions to the quaternion Sylvester-type matrix equations. Zbl 1415.15016
Kyrchei, Ivan
2019
Oriented conformal geometric algebra and the molecular distance geometry problem. Zbl 1410.92086
Lavor, Carlile; Alves, Rafael
2019
Garamon: a geometric algebra library generator. Zbl 1422.68329
Breuils, Stéphane; Nozick, Vincent; Fuchs, Laurent
2019
Geometric algebra to describe the exact discretizable molecular distance geometry problem for an arbitrary dimension. Zbl 1430.68361
Camargo, Valter S.; Castelani, Emerson V.; Fernandes, Leandro A. F.; Fidalgo, Felipe
2019
On the structure of octonion regular functions. Zbl 1427.30079
Kauhanen, Janne; Orelma, Heikki
2019
Direct linear interpolation of geometric objects in conformal geometric algebra. Zbl 07111360
2019
Cramer’s rule for the general solution to a restricted system of quaternion matrix equations. Zbl 1439.15006
Song, Guang-Jing; Yu, Shao-Wen
2019
On hom-Lie superalgebras. Zbl 1440.17017
Guan, Baoling; Chen, Liangyun; Sun, Bing
2019
Zeros of zeon polynomials and the zeon quadratic formula. Zbl 1442.15040
Haake, Erin; Staples, G. Stacey
2019
Finding $$n$$-th roots of a $$2\times 2$$ real matrix using de Moivre’s formula. Zbl 1403.15005
Özdemir, Mustafa
2019
On $$\mathbf{C} \otimes \mathbf{H} \otimes \mathbf{O}$$-valued gravity, sedenions, Hermitian matrix geometry and nonsymmetric Kaluza-Klein theory. Zbl 1429.83071
Perelman, Carlos Castro
2019
More on modified spherical harmonics. Zbl 1427.30080
Leutwiler, Heinz
2019
Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms. Zbl 1427.30076
Ghanmi, Allal; Zine, Khalil
2019
Some constructions of multiplicative $$n$$-ary Hom-Nambu algebras. Zbl 1435.17030
Ben Hassine, Abdelkader; Mabrouk, Sami; Ncib, Othmen
2019
Uncertainty principles for the quaternion linear canonical transform. Zbl 1426.42004
Achak, A.; Abouelaz, A.; Daher, R.; Safouane, N.
2019
Calculating the rotor between conformal objects. Zbl 1430.53041
Lasenby, J.; Hadfield, H.; Lasenby, A.
2019
Clifford wavelet transform and the uncertainty principle. Zbl 1430.30024
Banouh, Hicham; Mabrouk, Anouar Ben; Kesri, Mhamed
2019
Differential calculus of zeon functions. Zbl 1466.15026
Staples, G. Stacey
2019
Characteristic polynomials in Clifford algebras and in more general algebras. Zbl 1428.15008
Helmstetter, Jacques
2019
$$2\times 2$$ matrix representation forms and inner relationships of split quaternions. Zbl 1414.15015
Ni, Qiu-Ying; Ding, Jin-Kou; Cheng, Xue-Han; Jiao, Ying-Nan
2019
Boolean combination of circular arcs using orthogonal spheres. Zbl 1417.51014
Dorst, Leo
2019
Product of three octonions. Zbl 1410.11124
Kharinov, Mikhail
2019
Clifford algebra approach of 3D Ising model. Zbl 1412.82015
Zhang, Zhidong; Suzuki, Osamu; March, Norman H.
2019
Norm inequalities in zeon algebras. Zbl 1410.15047
Lindell, Theresa; Staples, G. Stacey
2019
$$\mathbb{R} \otimes \mathbb{C}\otimes \mathbb{H}\otimes \mathbb{O}$$-valued gravity as a grand unified field theory. Zbl 1410.81034
Castro Perelman, Carlos
2019
Clifford algebras, multipartite systems and gauge theory gravity. Zbl 1408.83010
Trindade, Marco A. S.; Pinto, Eric; Floquet, Sergio
2019
Screw theory in Lorentzian space. Zbl 1404.70004
Karakuş, Sıddıka Özkaldı
2019
An unified CGA-based formal expression of spatio-temporal topological relations for Computation and analysis of geographic objects. Zbl 1423.86003
Wang, Yingzhi; Zhang, Feng
2019
Zeon and idem-Clifford formulations of Boolean satisfiability. Zbl 1456.68123
Davis, Amanda; Staples, G. Stacey
2019
Cohomology and 1-parameter formal deformations of Hom-$$\delta$$-Lie Triple systems. Zbl 07111338
Chen, Liangyun; Yi, Yang; Chen, Ming; Tang, Yuling
2019
REFORM: rotor estimation from object resampling and matching. Zbl 1422.68246
Hadfield, H.; Lasenby, J.; Ramage, M.; Doran, C.
2019
Hypermonogenic plane wave solutions of the Dirac equation in superspace. Zbl 1427.30072
Adán, Alí Guzmán; Orelma, Heikki; Sommen, Frank
2019
Geometric algebra, gravity and gravitational waves. Zbl 1429.83017
Lasenby, Anthony N.
2019
Split octonionic Cauchy integral formula. Zbl 1435.17008
Prather, Benjamin
2019
Hyperbolic function theory in the skew-field of quaternions. Zbl 1430.30027
Eriksson, Sirkka-Liisa; Orelma, Heikki
2019
Modified spherical harmonics in several dimensions. Zbl 1446.30079
Leutwiler, Heinz
2019
$$(m,h)$$-monogenic functions related to axially symmetric Helmholtz equations. Zbl 1435.30139
Dinh, Doan Cong
2019
Solutions of inhomogeneous generalized Moisil-Teodorescu systems in Euclidean space. Zbl 1429.30038
Bory-Reyes, Juan; Pérez-de la Rosa, Marco Antonio
2019
On paravectors and their associated algebras. Zbl 1411.15014
Vaz, Jayme jun.
2019
Characterization of the principal 3D slices related to the multicomplex Mandelbrot set. Zbl 1418.37080
Brouillette, Guillaume; Rochon, Dominic
2019
A right inverse operator for $$\operatorname{curl}+\lambda$$ and applications. Zbl 1418.30047
2019
Three-dimensional quadrics in conformal geometric algebras and their versor transformations. Zbl 1416.15019
Hitzer, Eckhard
2019
$$GL_{r,s}(n)$$-covariant differential calculi on the quantum $$n$$-space. Zbl 07068749
Fakhri, Hossein; Laheghi, Samaneh
2019
Bicomplex modules with indefinite inner product. Zbl 1418.30043
Banerjee, A.; Deb, R.
2019
Determinantal representations of solutions to systems of quaternion matrix equations. Zbl 1391.15057
Kyrchei, Ivan
2018
Cramer’s rules for Sylvester quaternion matrix equation and its special cases. Zbl 1404.15013
Kyrchei, Ivan
2018
Leptons, quarks, and gauge from the complex Clifford algebra $$\mathbb {C}\ell _6$$. Zbl 1403.81072
Stoica, Ovidiu Cristinel
2018
Introduction to hybrid numbers. Zbl 1394.11024
Özdemir, Mustafa
2018
Novel uncertainty principles for two-sided quaternion linear canonical transform. Zbl 1392.81164
Zhang, Yan-Na; Li, Bing-Zhao
2018
Quadric conformal geometric algebra of $${\mathbb {R}}^{9,6}$$. Zbl 1397.15019
Breuils, Stéphane; Nozick, Vincent; Sugimoto, Akihiro; Hitzer, Eckhard
2018
A classification of Clifford algebras as images of group algebras of Salingaros vee groups. Zbl 1394.15016
Abłamowicz, Rafał; Varahagiri, Manisha; Walley, Anne Marie
2018
Cauchy-Riemann operators in octonionic analysis. Zbl 1394.30035
Kauhanen, Janne; Orelma, Heikki
2018
Generalization of superalgebras to color superalgebras and their representations. Zbl 1418.17065
Aizawa, Naruhiko
2018
Geometric algebra for conics. Zbl 1398.51045
Hrdina, Jaroslav; Návrat, Aleš; Vašík, Petr
2018
Elementary functions and factorizations of zeons. Zbl 1393.05305
Staples, G. Stacey; Weygandt, Alexander
2018
Non-anti-Hermitian quaternionic quantum mechanics. Zbl 1392.81147
Giardino, Sergio
2018
Extreme points and some quaternion valued functions in the unit ball of $${\mathbb {R}}^3$$. Zbl 1401.46015
El-Sayed Ahmed, Ahmed; Omran, Saleh
2018
Mvtree for hierarchical network representation based on geometric algebra subspace. Zbl 1403.90216
Zhu, Shuai; Yuan, Shuai; Li, Dongshuang; Luo, Wen; Yuan, Linwang; Yu, Zhaoyuan
2018
Subalgebras of the split octonions. Zbl 1430.11154
Bentz, Lida; Dray, Tevian
2018
First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators. Zbl 1397.30037
Ferreira, M.; Rodrigues, M. M.; Vieira, N.
2018
Modified spherical harmonics in four dimensions. Zbl 1396.33027
Leutwiler, Heinz
2018
Covariantly constant solutions of the Yang-Mills equations. Zbl 1393.70044
Shirokov, Dmitry
2018
$$p$$-trigonometric approach to elliptic biquaternions. Zbl 1410.11125
Özen, Kahraman Esen; Tosun, Murat
2018
Hyperquaternions: a new tool for physics. Zbl 1402.15018
Girard, Patrick R.; Clarysse, Patrick; Pujol, Romaric; Goutte, Robert; Delachartre, Philippe
2018
Resolution of the $${k}$$-Dirac operator. Zbl 1397.58008
Salač, Tomáš
2018
Quantum super Nambu bracket of cubic supermatrices and 3-Lie superalgebra. Zbl 1459.17005
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2018
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#### Cited by 1,633 Authors

 64 Sommen, Franciscus 52 Bory Reyes, Juan 41 Abreu-Blaya, Ricardo 41 De Schepper, Hennie 36 Brackx, Fred F. 32 Eelbode, David 30 Kähler, Uwe 28 Hitzer, Eckhard 22 Soucek, Vladimir 21 Kyrchei, Ivan I. 20 Lávička, Roman 19 Cerejeiras, Paula 18 Ku, Min 17 Bahri, Mawardi 17 Kraußhar, Rolf Sören 17 Orelma, Heikki 17 Shirokov, Dmitry S. 16 Eriksson, Sirkka-Liisa 16 Lavor, Carlile Campos 16 Peña Peña, Dixan 16 Sabadini, Irene 16 Yayli, Yusuf 15 Kravchenko, Vladislav V. 15 Qiao, Yuying 14 De Bie, Hendrik 14 Gürlebeck, Klaus 14 Tosun, Murat 14 Vieira, Nelson 13 Abłamowicz, Rafał 13 Adán, Alí Guzmán 13 Bock, Sebastian 13 Helmstetter, Jacques 13 Morais, João Pedro 13 Qian, Tao 12 Falcão, Maria Irene 12 Vaz, Jayme jun. 11 Demir, Süleyman 11 Fabbri, Luca 11 Gök, İsmail 11 Kou, Kit-Ian 11 Raeymaekers, Tim 11 Rodrigues, Waldyr Alves jun. 11 Vanegas, Judith C. 10 Ashino, Ryuichi 10 Colombo, Fabrizio 10 He, ZhuoHeng 10 Hrdina, Jaroslav 10 Leutwiler, Heinz 10 Návrat, Aleš 10 Ozdemir, Mustafa Kemal 10 Ren, Guangbin 10 Van Lancker, Peter 9 Cação, Isabel 9 da Rocha, Roldão Jun. 9 Fauser, Bertfried 9 Flaut, Cristina 9 Iglewska-Nowak, Ilona 9 Jiang, Tongsong 9 Keller, Jaime 9 Li, Xingmin 9 Lian, Pan 9 Ludkovsky, Sergey Victor 9 Marchuk, Nikolaĭ Gur’evich 9 Mironov, Sergey V. 9 Mironov, Victor L. 9 Nielsen, Lance 9 Reyes, Armando 9 Sangwine, Stephen J. 9 Shapiro, Michael V. 9 Struppa, Daniele Carlo 9 Tanişli, Murat 9 Vašík, Petr 9 Yamaleev, Robert M. 9 Yang, Heju 9 Yuan, Hongfen 9 Yüce, Salim 8 Abramov, Viktor 8 De Ridder, Hilde 8 Dechant, Pierre-Philippe 8 He, Fuli 8 Luna-Elizarrarás, María Elena 8 Malonek, Helmuth Robert 8 Pérez-de La Rosa, Marco Antonio 8 Shpakivskyi, Vitalii Stanislavovich 8 Zhang, Binlin 7 Bekar, Murat 7 Cerda-Morales, Gamaliel Cerda 7 Chanyal, Bhupesh Chandra 7 Di Teodoro, Antonio Nicola 7 Faustino, Nelson José Rodrigues 7 Fernández Guasti, Manuel 7 Gu, Yingqiu 7 Gungor, Mehmet Ali 7 Kisil, Vladimir V. 7 Liberti, Leo 7 Lu, Yu 7 Moreno García, Tania 7 Song, Youngkwon 7 Staples, George Stacey 7 Szynal-Liana, Anetta ...and 1,533 more Authors
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#### Cited in 309 Journals

 634 Advances in Applied Clifford Algebras 61 Complex Variables and Elliptic Equations 57 Complex Analysis and Operator Theory 53 Journal of Mathematical Physics 51 Mathematical Methods in the Applied Sciences 43 Journal of Mathematical Analysis and Applications 41 International Journal of Theoretical Physics 28 Applied Mathematics and Computation 26 International Journal of Geometric Methods in Modern Physics 18 Linear and Multilinear Algebra 16 Journal of Geometry and Physics 16 Linear Algebra and its Applications 16 Computational Methods and Function Theory 14 Communications in Algebra 14 Integral Transforms and Special Functions 14 Abstract and Applied Analysis 12 Reports on Mathematical Physics 12 Results in Mathematics 11 Chaos, Solitons and Fractals 11 Foundations of Physics 11 Boundary Value Problems 10 International Journal of Modern Physics A 10 General Relativity and Gravitation 10 Mediterranean Journal of Mathematics 9 Mathematical Problems in Engineering 9 Advances in Mathematical Physics 8 Journal of Algebra 8 Acta Applicandae Mathematicae 8 Annals of Global Analysis and Geometry 8 Journal of Algebra and its Applications 7 Computers & Mathematics with Applications 7 Physics Letters. B 7 Geometriae Dedicata 7 Proceedings of the American Mathematical Society 7 International Journal of Modern Physics D 7 Applied and Computational Harmonic Analysis 7 Journal of Inequalities and Applications 7 Russian Physics Journal 7 International Journal of Wavelets, Multiresolution and Information Processing 7 Advances in Difference Equations 7 Asian-European Journal of Mathematics 7 Symmetry 7 Journal of Mathematics 6 Journal of Mathematical Sciences (New York) 6 Mathematical Physics, Analysis and Geometry 6 Journal of High Energy Physics 6 International Electronic Journal of Geometry 6 Analysis and Mathematical Physics 6 International Journal of Applied and Computational Mathematics 5 Beiträge zur Algebra und Geometrie 5 Journal of Geometry 5 Journal of Global Optimization 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 The Journal of Fourier Analysis and Applications 5 Acta Mathematica Sinica. English Series 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 5 Quantum Information Processing 5 Journal of Function Spaces 4 Discrete Applied Mathematics 4 Israel Journal of Mathematics 4 Physics Letters. A 4 Theoretical and Mathematical Physics 4 Ukrainian Mathematical Journal 4 Advances in Mathematics 4 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 4 Mathematische Nachrichten 4 Transactions of the American Mathematical Society 4 International Journal of Algebra and Computation 4 Journal of Mathematical Imaging and Vision 4 Computational and Applied Mathematics 4 Complexity 4 Journal of Mathematical Chemistry 4 Nonlinear Dynamics 4 Honam Mathematical Journal 4 Journal of Nonlinear Mathematical Physics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Science China. Mathematics 4 Journal of Pseudo-Differential Operators and Applications 4 Palestine Journal of Mathematics 3 Journal of the Franklin Institute 3 Letters in Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Approximation Theory 3 Journal of Functional Analysis 3 Mathematische Zeitschrift 3 Zeitschrift für Analysis und ihre Anwendungen 3 Neural Computation 3 The Journal of Geometric Analysis 3 Russian Journal of Mathematical Physics 3 Fractals 3 Journal of Difference Equations and Applications 3 Boletín de la Sociedad Matemática Mexicana. Third Series 3 Doklady Mathematics 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Journal of Integer Sequences 3 Journal of Applied Mathematics 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM ...and 209 more Journals
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#### Cited in 61 Fields

 544 Linear and multilinear algebra; matrix theory (15-XX) 529 Functions of a complex variable (30-XX) 295 Quantum theory (81-XX) 217 Number theory (11-XX) 182 Differential geometry (53-XX) 174 Partial differential equations (35-XX) 143 Harmonic analysis on Euclidean spaces (42-XX) 135 Nonassociative rings and algebras (17-XX) 127 Relativity and gravitational theory (83-XX) 86 Associative rings and algebras (16-XX) 74 Numerical analysis (65-XX) 71 Geometry (51-XX) 68 Mechanics of particles and systems (70-XX) 64 Global analysis, analysis on manifolds (58-XX) 63 Functional analysis (46-XX) 61 Computer science (68-XX) 61 Information and communication theory, circuits (94-XX) 59 Operator theory (47-XX) 50 Several complex variables and analytic spaces (32-XX) 49 Combinatorics (05-XX) 49 Group theory and generalizations (20-XX) 48 Special functions (33-XX) 46 Optics, electromagnetic theory (78-XX) 44 Topological groups, Lie groups (22-XX) 42 Ordinary differential equations (34-XX) 35 Integral transforms, operational calculus (44-XX) 33 Potential theory (31-XX) 29 Algebraic geometry (14-XX) 29 Abstract harmonic analysis (43-XX) 26 Dynamical systems and ergodic theory (37-XX) 25 Approximations and expansions (41-XX) 24 Statistical mechanics, structure of matter (82-XX) 21 Biology and other natural sciences (92-XX) 20 Probability theory and stochastic processes (60-XX) 19 Systems theory; control (93-XX) 18 Difference and functional equations (39-XX) 16 Field theory and polynomials (12-XX) 16 Real functions (26-XX) 16 Measure and integration (28-XX) 16 Integral equations (45-XX) 14 Fluid mechanics (76-XX) 14 Operations research, mathematical programming (90-XX) 13 Manifolds and cell complexes (57-XX) 12 Commutative algebra (13-XX) 11 Convex and discrete geometry (52-XX) 11 Statistics (62-XX) 10 Category theory; homological algebra (18-XX) 10 Mechanics of deformable solids (74-XX) 7 History and biography (01-XX) 7 Astronomy and astrophysics (85-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Algebraic topology (55-XX) 5 Geophysics (86-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 $$K$$-theory (19-XX) 2 General topology (54-XX) 2 Mathematics education (97-XX) 1 Mathematical logic and foundations (03-XX) 1 Sequences, series, summability (40-XX)