Kravchenko, Vladislav V.; Moreira, Pablo E.; Porter, R. Michael Complete systems of Beltrami fields using complex quaternions and transmutation theory. (English) Zbl 1464.35004 Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 31, 21 p. (2021). MSC: 35A22 35C10 30G35 35Q60 PDFBibTeX XMLCite \textit{V. V. Kravchenko} et al., Adv. Appl. Clifford Algebr. 31, No. 3, Paper No. 31, 21 p. (2021; Zbl 1464.35004) Full Text: DOI
Delgado, Briceyda B.; Kravchenko, Vladislav V. A right inverse operator for \(\operatorname{curl}+\lambda \) and applications. (English) Zbl 1418.30047 Adv. Appl. Clifford Algebr. 29, No. 3, Paper No. 40, 15 p. (2019). MSC: 30G35 35Q60 PDFBibTeX XMLCite \textit{B. B. Delgado} and \textit{V. V. Kravchenko}, Adv. Appl. Clifford Algebr. 29, No. 3, Paper No. 40, 15 p. (2019; Zbl 1418.30047) Full Text: DOI arXiv
Campos, Hugo M.; Kravchenko, Vladislav V. Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients. (English) Zbl 1323.30067 Complex Anal. Oper. Theory 7, No. 2, 485-518 (2013). Reviewer: Linda R. Sons (DeKalb) MSC: 30G35 PDFBibTeX XMLCite \textit{H. M. Campos} and \textit{V. V. Kravchenko}, Complex Anal. Oper. Theory 7, No. 2, 485--518 (2013; Zbl 1323.30067) Full Text: DOI arXiv
Campos, Hugo M.; Kravchenko, Vladislav V.; Méndez, Luis M. Complete families of solutions for the Dirac equation using bicomplex function theory and transmutations. (English) Zbl 1257.30051 Adv. Appl. Clifford Algebr. 22, No. 3, 577-594 (2012). MSC: 30G20 30G35 81Q05 PDFBibTeX XMLCite \textit{H. M. Campos} et al., Adv. Appl. Clifford Algebr. 22, No. 3, 577--594 (2012; Zbl 1257.30051) Full Text: DOI arXiv
Kravchenko, Vladislav V.; Tremblay, Sébastien Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators. (English) Zbl 1242.30039 Math. Methods Appl. Sci. 34, No. 16, 1999-2010 (2011). Reviewer: Chuangan Hu (Palo Alto) MSC: 30G20 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{S. Tremblay}, Math. Methods Appl. Sci. 34, No. 16, 1999--2010 (2011; Zbl 1242.30039) Full Text: DOI arXiv
Kravchenko, Vladislav V.; Ramirez T., Marco P. On Bers generating functions for first order systems of mathematical physics. (English) Zbl 1244.30071 Adv. Appl. Clifford Algebr. 21, No. 3, 547-559 (2011). MSC: 30G35 30G20 35Q61 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{M. P. Ramirez T.}, Adv. Appl. Clifford Algebr. 21, No. 3, 547--559 (2011; Zbl 1244.30071) Full Text: DOI arXiv
Kravchenko, Vladislav V.; Oviedo, Héctor Time-dependent electromagnetic fields in chiral media. (English) Zbl 1203.78008 J. Phys. A, Math. Theor. 43, No. 45, Article ID 455213, 9 p. (2010). MSC: 78A25 78A48 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{H. Oviedo}, J. Phys. A, Math. Theor. 43, No. 45, Article ID 455213, 9 p. (2010; Zbl 1203.78008) Full Text: DOI
Kravchenko, Vladislav V. Applied pseudoanalytic function theory. (English) Zbl 1182.30002 Frontiers in Mathematics. Basel: Birkhäuser (ISBN 978-3-0346-0003-3/pbk; 978-3-0346-0004-0/ebook). xii, 184 p. (2009). Reviewer: Michael Reissig (Freiberg) MSC: 30-02 30G20 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, Applied pseudoanalytic function theory. Basel: Birkhäuser (2009; Zbl 1182.30002) Full Text: DOI Link
Khmelnytskaya, Kira V.; Kravchenko, Vladislav V. Biquaternions for analytic and numerical solution of equations of electrodynamics. (English) Zbl 1232.35162 Escassut, A. (ed.) et al., Some topics on value distribution and differentiability in complex and \(p\)-adic analysis. Beijing: Science Press (ISBN 978-7-03-020406-6). Mathematics Monograph Series 11, 301-322 (2008). MSC: 35Q61 30G35 78A25 35A08 35Q41 PDFBibTeX XMLCite \textit{K. V. Khmelnytskaya} and \textit{V. V. Kravchenko}, Math. Monogr. Ser. 11, 301--322 (2008; Zbl 1232.35162) Full Text: arXiv
Kravchenko, Vladislav V. On a factorization of second-order elliptic operators and applications. (English) Zbl 1106.30028 J. Phys. A, Math. Gen. 39, No. 40, 12407-12425 (2006). MSC: 30G20 30G35 35J10 35J15 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, J. Phys. A, Math. Gen. 39, No. 40, 12407--12425 (2006; Zbl 1106.30028) Full Text: DOI arXiv
Kravchenko, Vladislav V. On force free magnetic fields. Quaternionic approach. (English) Zbl 1141.76480 Math. Methods Appl. Sci. 28, No. 4, 379-386 (2005). MSC: 76W05 78A25 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, Math. Methods Appl. Sci. 28, No. 4, 379--386 (2005; Zbl 1141.76480) Full Text: DOI
Kravchenko, Vladislav V. On Beltrami fields with nonconstant proportionality factor. (English) Zbl 1039.35027 J. Phys. A, Math. Gen. 36, No. 5, 1515-1522 (2003). MSC: 35F05 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, J. Phys. A, Math. Gen. 36, No. 5, 1515--1522 (2003; Zbl 1039.35027) Full Text: DOI
Kravchenko, V. V.; Oviedo, H. On a quaternionic reformulation of Maxwell’s equations for chiral media and its applications. (English) Zbl 1060.30063 Z. Anal. Anwend. 22, No. 3, 569-589 (2003). MSC: 30G35 78A25 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{H. Oviedo}, Z. Anal. Anwend. 22, No. 3, 569--589 (2003; Zbl 1060.30063) Full Text: DOI
Khmelnytskaya, K. V.; Kravchenko, V. V.; Rabinovich, V. S. Quaternionic fundamental solutions for electromagnetic scattering problems and application. (English) Zbl 1076.30052 Z. Anal. Anwend. 22, No. 1, 147-166 (2003). Reviewer: Wolfgang Sprößig (Freiberg) MSC: 30G35 PDFBibTeX XMLCite \textit{K. V. Khmelnytskaya} et al., Z. Anal. Anwend. 22, No. 1, 147--166 (2003; Zbl 1076.30052) Full Text: DOI
Kravchenko, Vladislav V.; Castillo P., Raúl An analogue of the Sommerfeld radiation condition for the Dirac operator. (English) Zbl 1058.30047 Math. Methods Appl. Sci. 25, No. 16-18, 1383-1394 (2002). Reviewer: Klaus Habetha (Aachen) MSC: 30G35 35Q40 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{R. Castillo P.}, Math. Methods Appl. Sci. 25, No. 16--18, 1383--1394 (2002; Zbl 1058.30047) Full Text: DOI arXiv
Kravchenko, V. V. Quaternionic reformulation of Maxwell equations for inhomogeneous media and new solutions. (English) Zbl 0999.30033 Z. Anal. Anwend. 21, No. 1, 21-26 (2002). Reviewer: M.Kracht (Düsseldorf) MSC: 30G35 35Q60 78A25 78A30 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, Z. Anal. Anwend. 21, No. 1, 21--26 (2002; Zbl 0999.30033) Full Text: DOI arXiv
Khmelnytskaya, Kira V.; Kravchenko, Vladislav V.; Rabinovich, Vladimir S. Quaternionic fundamental solutions for the numerical analysis of electromagnetic scattering problems. arXiv:math-ph/0206013 Preprint, arXiv:math-ph/0206013 [math-ph] (2002). MSC: 30G35 65N35 78M25 BibTeX Cite \textit{K. V. Khmelnytskaya} et al., ``Quaternionic fundamental solutions for the numerical analysis of electromagnetic scattering problems'', Preprint, arXiv:math-ph/0206013 [math-ph] (2002) Full Text: arXiv
Kravchenko, Vladislav V. On a new approach for solving Dirac equations with some potentials and Maxwell’s system in inhomogeneous media. (English) Zbl 1006.30030 Elschner, J. (ed.) et al., Problems and methods in mathematical physics. The Siegfried Prössdorf memorial volume. Proceedings of the 11th TMP conference, Chemnitz, Germany, March 25-28, 1999. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 121, 278-306 (2001). Reviewer: Li Mingzhong (Shanghai) MSC: 30G35 81Q05 78A25 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, in: Problems and methods in mathematical physics. The Siegfried Prössdorf memorial volume. Proceedings of the 11th TMP conference, Chemnitz, Germany, March 25--28, 1999. Basel: Birkhäuser. 278--306 (2001; Zbl 1006.30030)
Kravchenko, V. V. Applied quaternionic analysis. Maxwell’s system and Dirac’s equation. (English) Zbl 1027.30070 Florian, H. (ed.) et al., Functional-analytic and complex methods, their interactions, and applications to partial differential equations. Proceedings of the international Graz workshop, Graz, Austria, February 12-16, 2001. Singapore: World Scientific. 143-160 (2001). MSC: 30G35 35Q60 35Q40 78A25 81R25 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, in: Functional-analytic and complex methods, their interactions, and applications to partial differential equations. Proceedings of the international Graz workshop, Graz, Austria, February 12--16, 2001. Singapore: World Scientific. 143--160 (2001; Zbl 1027.30070)
Kravchenko, Viktor; Kravchenko, Vladisłav; Williams, Benjamin A quaternionic generalization of the Riccati differential equation. (English) Zbl 1038.30021 Brackx, F. (ed.) et al., Clifford analysis and its applications. Proceedings of the NATO advanced research workshop, Prague, Czech Republic, October 30–November 3, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-7044-9/hbk; 0-7923-7045-7/pbk). NATO Sci. Ser. II, Math. Phys. Chem. 25, 143-154 (2001). Reviewer: Li Mingzhong (Shanghai) MSC: 30G35 35J60 PDFBibTeX XMLCite \textit{V. Kravchenko} et al., NATO Sci. Ser. II, Math. Phys. Chem. 25, 143--154 (2001; Zbl 1038.30021) Full Text: arXiv
Kravchenko, Vladislav; Oviedo, Hector Representaciones integrales para el campo electromagnetico en medios chirales. arXiv:math-ph/0101023 Preprint, arXiv:math-ph/0101023 [math-ph] (2001). MSC: 30G35 78A25 BibTeX Cite \textit{V. Kravchenko} and \textit{H. Oviedo}, ``Representaciones integrales para el campo electromagnetico en medios chirales'', Preprint, arXiv:math-ph/0101023 [math-ph] (2001) Full Text: arXiv
Kravchenko, V. V. A new approach for describing electromagnetic wave propagation in inhomogeneous media. (English) Zbl 1030.30040 Z. Anal. Anwend. 19, No. 4, 903-912 (2000). MSC: 30G35 78A40 78M35 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, Z. Anal. Anwend. 19, No. 4, 903--912 (2000; Zbl 1030.30040) Full Text: DOI
Kravchenko, V. V. A new method for obtaining solutions of the Dirac equation. (English) Zbl 0977.30029 Z. Anal. Anwend. 19, No. 3, 655-676 (2000). Reviewer: M.Reissig (Freiberg) MSC: 30G35 81Q05 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, Z. Anal. Anwend. 19, No. 3, 655--676 (2000; Zbl 0977.30029) Full Text: DOI EuDML
Kravchenko, Vladislav V.; Ramirez T., Marco P. New exact solutions of the massive Dirac equation with electric or scalar potential. (English) Zbl 1032.81511 Math. Methods Appl. Sci. 23, No. 9, 769-776 (2000). MSC: 81Q05 20G35 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{M. P. Ramirez T.}, Math. Methods Appl. Sci. 23, No. 9, 769--776 (2000; Zbl 1032.81511)
Kravchenko, Vladislav V.; Malonek, Helmuth R.; Santana, Gustavo Biquaternionic integral representations for massive Dirac spinors in a magnetic field and generalized biquaternionic differentiability. (English) Zbl 1075.35546 Math. Methods Appl. Sci. 19, No. 17, 1415-1431 (1996). MSC: 35Q40 30G35 35C15 81V10 PDFBibTeX XMLCite \textit{V. V. Kravchenko} et al., Math. Methods Appl. Sci. 19, No. 17, 1415--1431 (1996; Zbl 1075.35546) Full Text: DOI
Kravchenko, V. V.; Shapiro, Michael V. Integral representations for spatial models of mathematical physics. (English) Zbl 0872.35001 Pitman Research Notes in Mathematics Series. 351. Harlow: Longman. 247 p (1996). Reviewer: N.L.Vasilevskij (Mexico) MSC: 35-02 30G35 35C15 78A25 81V05 81Q05 11R52 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{M. V. Shapiro}, Integral representations for spatial models of mathematical physics. Harlow: Longman (1996; Zbl 0872.35001)
Kravchenko, Vladislav V.; Santana, Gustavo On singular integral operators associated with the vector Helmholtz equation. (English) Zbl 0973.35065 J. Nat. Geom. 10, No. 2, 119-136 (1996). MSC: 35J05 30G35 47G10 78A25 83C22 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{G. Santana}, J. Nat. Geom. 10, No. 2, 119--136 (1996; Zbl 0973.35065)
Kravchenko, Vladislav V.; Shapiro, Michael V. Quaternionic time-harmonic Maxwell operator. (English) Zbl 0869.35099 J. Phys. A, Math. Gen. 28, No. 17, 5017-5031 (1995). MSC: 35Q60 78A25 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{M. V. Shapiro}, J. Phys. A, Math. Gen. 28, No. 17, 5017--5031 (1995; Zbl 0869.35099) Full Text: DOI
Kravchenko, V. V. Quaternion-valued integral representations of the harmonic electromagnetic and spinor fields. (English. Russian original) Zbl 0945.30037 Dokl. Math. 51, No. 2, 287-289 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 341, No. 5, 603-605 (1995). Reviewer: Marin Marinov (Sofia) MSC: 30G35 35Q40 35Q80 35C15 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, Dokl. Math. 51, No. 2, 287--289 (1995; Zbl 0945.30037); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 341, No. 5, 603--605 (1995)
Kravchenko, V. V.; Shapiro, M. V. Helmholtz operator with a quaternionic wave number and associated function theory. (English) Zbl 0831.30030 Ławrynowicz, Julian (ed.), Deformations of mathematical structures 2: Hurwitz-type structures and applications to surface physics. Selected papers from the seminar on deformations, Łódź-Malinka, Poland, 1988-1992. Dordrecht: Kluwer Academic Publishers Group. 101-128 (1994). Reviewer: G.Laville (Caen) MSC: 30G35 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{M. V. Shapiro}, in: Deformations of mathematical structures 2: Hurwitz-type structures and applications to surface physics. Selected papers from the seminar on deformations, Łódź-Malinka, Poland, 1988-1992. Dordrecht: Kluwer Academic Publishers Group. 101--128 (1994; Zbl 0831.30030)
Kravchenko, V. V. Generalized holomorphic vectors and \(\alpha\)-hyperholomorphic function theory. (English) Zbl 0806.30028 J. Nat. Geom. 6, No. 2, 125-132 (1994). Reviewer: J.Cnops (Gent) MSC: 30G35 47G10 78A25 PDFBibTeX XMLCite \textit{V. V. Kravchenko}, J. Nat. Geom. 6, No. 2, 125--132 (1994; Zbl 0806.30028)
Kravchenko, V. V.; Shapiro, M. V. Helmholtz operator with a quaternionic wave number and associated function theory. II: Integral representations. (English) Zbl 0790.30039 Acta Appl. Math. 32, No. 3, 243-265 (1993). Reviewer: K.Habetha (Aachen) MSC: 30G35 35J05 30E20 83C22 PDFBibTeX XMLCite \textit{V. V. Kravchenko} and \textit{M. V. Shapiro}, Acta Appl. Math. 32, No. 3, 243--265 (1993; Zbl 0790.30039) Full Text: DOI