List of publications

Scientific papers

1. Sharipov R. A. Finite-gap analogs of N-multiplet solutions of KdV equation, Uspehi Mat. Nauk, 41(1986), No. 5, 203-204.
2. Sharipov R. A. Soliton multiplets of Korteweg-de Vries equation, Dokladi AN SSSR, 292(1987), No. 6, 1356-1359.
3. Sharipov R. A. Multiplet solutions of Kadomtsev-Petviashvili equation on a finite-gap background, Uspehi Mat. Nauk, 42(1987), No. 5, 221-222.

4. Bikbaev R. F. & Sharipov R. A. Magnetization waves in Landau-Lifshits model, Physics Letters A, 134(1988), No. 2, 105-108.
5. Bikbaev R. F. & Sharipov R. A. Assymptotics as t → ∞ for the solution of Cauchy problem for the Korteweg-de Vries equation in the class of potentials with finite-gap behaviour as x → ± ∞, TMF, 78(1989), No. 3, 345-356.

6. Sharipov R. A. On the integration of Bogoyavlensky chains, Mat. zametki, 47(1990), No. 1, 157-160.

7. Cherdantsev I. Yu. & Sharipov R. A. Finite-gap solutions of Bullough-Dodd-Jiber-Shabat equation, TMF, 82(1990), No. 1, 155-160.
8. Cherdantsev I. Yu. & Sharipov R. A. Solitons on a finite-gap background in Bullough-Dodd-Jiber-Shabat model, International. Journ. of Modern Physics A, 5(1990), No. 5, 3021-3027.

9. Sharipov R. A. & Yamilov R. I. Backlund transformations and the construction of the integrable boundary value problem for the equation uxt=eu-e-2u, in book "Some problems of mathematical physics and asymptotics of its solutions", Institute of mathematics BNC UrO AN SSSR, 1991, 66-77.
10. Sharipov R. A. Minimal tori in five-dimensional sphere in $C^3$, TMF, 87(1991), No. 1, 48-56.
11. Safin S. S. & Sharipov R. A. Backlund autotransformation for the equation uxt=eu-e-2u, TMF, 95(1993), No. 1, 146-159.
12. Boldin A. Yu. & Safin S. S. & Sharipov R. A. On an old paper of Tzitzeika and the inverse scattering method, Journal of Mathematical Physics, 34(1993), No. 12, 5801-5809.

13. Boldin A. Yu. & Sharipov R. A. Dynamical systems, accepting the normal shift, TMF, 97(1993), No. 3, 386-395.
14. Boldin A. Yu. & Sharipov R. A. Dynamical systems, accepting the normal shift, Dokladi RAN, 334(1994), No. 2, 165-167.
15. Boldin A. Yu. & Sharipov R. A. Multidimensional dynamical systems, accepting the normal shift, TMF, 100(1994), No. 2, 264-269.
16. Sharipov R. A. Problem of metrizability for the dynamical systems, accepting the normal shift, TMF, 101(1994), No. 1, 85-93.
17. Sharipov R. A. Dynamical systems, accepting the normal shift, Uspehi Mat. Nauk, 49(1994), No. 4, 105.
18. Boldin A. Yu. & Dmitrieva V. V. & Safin S. S. & Sharipov R. A. Dynamical systems accepting the normal shift on an arbitrary Riemannian manifold, in book: "Dynamical systems accepting the normal shift", Bashkir State University, 1994, 4-19; see also TMF, 103(1995), No. 2, 256-266.
19. Boldin A. Yu. & Bronnikov A. A. & Dmitrieva V. V. & Sharipov R. A. Complete normality conditions for the dynamical systems on Riemannian manifolds, in book: "Dynamical systems accepting the normal shift", Bashkir State University, 1994, 20-30; see also TMF, 103(1995), No. 2, 267-275.
20. Sharipov R. A. Higher dynamical systems accepting the normal shift, in book: "Dynamical systems accepting the normal shift", Bashkir State University, 1994, 41-65.

21. Pavlov M. V. & Svinolupov S. I. & Sharipov R. A. Invariant criterion of integrability for the system of equations of hydrodynamical type, in book: "Integrability in dynamical systems", Inst. of Math. UrO RAN, Ufa, 1994, 27-48; see also Funk. Anal. i Pril., 30(1996), No. 1, 18-29.

22. Bronnikov A. A. & Sharipov R. A. Axially symmetric dynamical systems accepting the normal shift in $R^n$, in book: "Integrability in dynamical systems", Inst. of Math. UrO RAN, Ufa, 1994, 62-69.
23. Sharipov R. A. Metrizability by means of conformally equivalent metric for the dynamical systems, in book: "Integrability in dynamical systems", Inst. of Math. UrO RAN, Ufa, 1994, 80-90; see also TMF, 103(1995), No. 2, 276-282.

24. Sharipov R. A. & Sukhov A. B. On CR-mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions, Trans. of American Math. Society, 348(1996), No. 2, 767�780; see also Dokladi RAN, 350(1996), No. 4, 453-454.
25. Sharipov R. A. & Tsyganov E. N. On the separate algebraicity along the families of algebraic curves, Preprint of Baskir State University, Ufa, 1996, 1-7; see also Mat. Zametki, 68(2000), No. 2, 294-302.

26. Ferapontov E. V. & Sharipov R. A. On conservation laws of first order for the system of equations of hydrodynamical type, TMF, 108(1996), No. 1, 109-128.

27. Boldin A. Yu. & Sharipov R. A. On the solution of normality equations for the dimension n ≥ 3. Electronic archive http://arXiv.org, 1996, solv-int/9610006, 1-17; see also Algebra i Analiz, 10(1998), No. 4, 31-61.

28. Dmitrieva V. V. & Sharipov R. A. On the point transformations for the second order differential equations, Electronic archive http://arXiv.org, 1997, solv-int/9703003, 1-14.
29. Sharipov R. A. On the point transformations for the equation $y''=P+ 3Qy'+3Ry'^2+Sy'^3$, Electronic archive http://arXiv.org, 1997, solv-int/9706003, 1-35; see also Vestnik BashGU, 1998, No. 1(I), 5-8.
30. Mikhailov O. N. & Sharipov R. A. On the point expansion for certain class of differential equations of second order, Electronic archive http://arXiv.org, 1997, solv-int/9712001, 1-8; Diff. Uravneniya, 36(2000), No. 10, 1331-1335.
31. Sharipov R. A. Effective procedure of point-classification for the equation $y'' = P + 3Qy' + 3Ry'^2 + Sy'^3$, Electronic archive http://arXiv.org, 1998, math.DG/9802027, 1-35.

32. Dmitrieva V. V. & Gladkov A. V. & Sharipov R. A. On some equations that can be brought to the equations of diffusion type. Electronic archive http://arXiv.org, 1999, math.DG/9904080, 1-13; see also TMF, 123(2000), No. 1, 26-37.
33. Dmitrieva V. V. & Neufeld E. G. & Sharipov R. A. & Tsaregorodtsev A. A. On a point symmetry analysis for generalized diffusion type equations. Electronic archive at LANL, 1999, math.AP/9907130, 1-52.

34. Sharipov R. A. Dynamical systems admitting the normal shift, Thesis for the degree of Doctor of Sciences in Russia, Electronic archive http://arXiv.org, 2000, math.DG/0002202, 1-219.

35. Sharipov R. A. Newtonian normal shift in multidimensional Riemannian geometry, Electronic archive http://arXiv.org, 2000, math.DG/0006125,1-38; see also Mat. Sbornik, 192(2001), No. 6, 105-144.
36. Sharipov R. A. Newtonian dynamical systems admitting normal blow-up of points, Electronic archive http://arXiv.org, 2000, math.DG/0008081, 1-16; see also Zap. semin. POMI, 280(2001), 278-298.

37. Sharipov R. A. Orthogonal matrices with rational components in composing tests for High School students, Electronic archive http://arXiv.org, 2000, math.GM/0006230, 1-10.
38. Sharipov R. A. On rational extension of Heisenberg algebra, Electronic archive http://arXiv.org, 2000, math.RA/0009194, 1-12.

39. Sharipov R. A. On the solutions of weak normality equations in multidimensional case, Electronic archive http://arXiv.org, 2000, math.DG/0012110, 1-16.
40. Sharipov R. A. First problem of globalization in the theory of dynamical systems admitting the normal shift of hypersurfaces, Electronic archive at LANL, 2001, math.DG/0101150, 1-14; see also Global geometric structures associated with dynamical systems admitting normal shift of hypersurfaces in Riemannian manifolds, International Journal of Mathematics and Mathematical Sciences, 30(2002) No. 9, 541-557.
41. Sharipov R. A. Second problem of globalization in the theory of dynamical systems admitting the normal shift of hypersurfaces, Electronic archive http://arXiv.org, 2001, math.DG/0102141, 1-21.
42. Sharipov R. A. A note on Newtonian, Lagrangian, and Hamiltonian dynamical systems in Riemannian manifolds, Electronic archive http://arXiv.org, 2001, math.DG/0107212, 1-21.
43. Sharipov R. A. Dynamical systems admitting normal shift and wave equations, Electronic archive http://arXiv.org, 2001, math.DG/0108158, 1-16; see also TMF, 131(2002), No. 2, 244-260.
44. Sharipov R. A. Normal shift in general Lagrangian dynamics, Electronic archive http://arXiv.org, 2001, math.DG/0112089, 1-27.

45. Sharipov R. A. Algorithm for generating orthogonal matrices with rational elements, Electronic archive http://arXiv.org, 2002, cs.MS/0201007, 1-7.

46. Sharipov R. A. Comparative analysis for pair of dynamical systems, one of which is Lagrangian, Electronic archive http://arXiv.org, 2002, math.DG/0204161, 1-40.
47. Sharipov R. A. On the concept of normal shift in non-metric geometry, Electronic archive http://arXiv.org, 2002, math.DG/0208029, 1-47.
48. Sharipov R. A. V-representation for normality equations in geometry of generalized Legendre transformation, Electronic archive http://arXiv.org, 2002, math.DG/0210216, 1-32.
49. Sharipov R. A. On the subset of normality equations describing generalized Legendre transformation, Electronic archive http://arXiv.org, 2002, math.DG/0212059,1-19.

50. Lyuksyutov S. F. & Sharipov R. A. Note on kinematics, dynamics, and thermodynamics of plastic glassy media, Electronic archive http://arXiv.org, 2003, cond-mat/0304190, 1-19.
51. Lyuksyutov S. F. & Sharipov R. A. & Sigalov G. & Paramonov P. B. Exact analytical solution for electrostatic field produced by biased atomic force microscope tip dwelling above dielectric-conductor bilayer, Electronic archive http://arXiv.org, 2004, cond-mat/0408247, 1-6.
52. Lyuksyutov S. F. & Sharipov R. A. Separation of plastic deformations in polymers based on elements of general nonlinear theory, Electronic archive http://arXiv.org, 2004, cond-mat/0408433, 1-4.
53. Comer J. & Sharipov R. A. A note on the kinematics of dislocations in crystals, Electronic archive http://arXiv.org, 2004, math-ph/0410006, 1-15.
54. Sharipov R. A. Gauge or not gauge? Electronic archive http://arXiv.org, 2004, cond-mat/0410552, 1-12.
55. Sharipov R. A. Burgers space versus real space in the nonlinear theory of dislocations, Electronic archive http://arXiv.org, 2004, cond-mat/0411148, 1-10.
56. Comer J. & Sharipov R. A. On the geometry of a dislocated medium, Electronic archive http://arXiv.org, 2005, math-ph/0502007, 1-17.

57. Sharipov R. A. Tensor functions of tensors and the concept of extended tensor fields, Electronic archive http://arXiv.org, 2005, math.DG/0503332, 1-43.

58. Sharipov R. A. A note on the dynamics and thermodynamics of dislocated crystals, Electronic archive http://arXiv.org, 2005, cond-mat/0504180, 1-18.

59. Sharipov R. A. Spinor functions of spinors and the concept of extended spinor fields, Electronic archive http://arXiv.org, 2005, math.DG/0511350, 1-56.
60. Sharipov R. A. Commutation relationships and curvature spin-tensors for extended spinor connections, Electronic archive http://arXiv.org, 2005, math.DG/0512396, 1-22.
61. Sharipov R. A. A note on Dirac spinors in a non-flat space-time of general relativity, Electronic archive http://arXiv.org, 2006, math.DG/0601262, 1-22.
62. Sharipov R. A. A note on metric connections for chiral and Dirac spinors, Electronic archive http://arXiv.org, 2006, math.DG/0602359, 1-40.
63. Sharipov R. A. On the Dirac equation in a gravitation field and the secondary quantization, Electronic archive http://arXiv.org, 2006, math.DG/0603367, 1-10.
64. Sharipov R. A. The electro-weak and color bundles for the Standard Model in a gravitation field, Electronic archive http://arXiv.org, 2006, math.DG/0603611, 1-8.
65.Sharipov R. A. A note on connections of the Standard Model in a gravitation field, Electronic archive http://arXiv.org, 2006, math.DG/0604145, 1-11.
66.Sharipov R. A. A note on the Standard Model in a gravitation field, Electronic archive http://arXiv.org, 2006, math.DG/0605709, 1-36.

67. Lyuksyutov S. F. & Paramonov P. B. & Sharipov R. A. & Sigalov G. Induced nanoscale deformations in polymers using atomic force microscopy, Phys. Rev. B 70, 174110 (2004); see also cond-mat/0408247 (paper 51 above in this list)

68. Sharipov R. A. The Higgs field can be expressed through the lepton and quark fields, Electronic archive http://arXiv.org, 2007, hep-ph/0703001, 1-4.

69. Sharipov R. A. Algorithms for laying points optimally on a plane and a circle, Electronic archive http://arXiv.org, 2007, 0705.0350 [cs.CG], 1-6.

70. Sharipov R. A. Comparison of two formulas for metric connections in the bundle of Dirac spinors, Electronic archive http://arXiv.org, 2007, 0707.0482 [math.DG], 1-16.
71. Sharipov R. A. On the spinor structure of the homogeneous and isotropic universe in closed model, Electronic archive http://arXiv.org, 2007, 0708.1171 [math.DG], 1-25.
72. Sharipov R. A. On Killing vector fields of a homogeneous and isotropic universe in closed model, Electronic archive http://arXiv.org, 2007, 0708.2508 [math.DG], 1-19.
73. Sharipov R. A. On deformations of metrics and their associated spinor structures, Electronic archive http://arXiv.org, 2007, 0709.1460 [math.DG], 1-22.

74. Sharipov R. A. A note on pairs of metrics in a two-dimensional linear vector space, Electronic archive http://arXiv.org, 2007, 0710.3949 [math.MG], 1-9.
75. Sharipov R. A. A note on pairs of metrics in a three-dimensional linear vector space, Electronic archive http://arXiv.org, 2007, 0711.0555 [math.MG], 1-17.

76. Sharipov R. A. A cubic identity for the Infeld-van der Waerden field and its application, Electronic archive http://arXiv.org, 2008, 0801.0008 [math.DG], 1-18.
77. Sharipov R. A. A note on Kosmann-Lie derivatives of Weyl spinors, Electronic archive http://arXiv.org, 2008, 0801.0622 [math.DG], 1-22.
78. Sharipov R. A. On operator fields in the bundle of Dirac spinors, Electronic archive http://arXiv.org, 2008, 0802.1491 [math.DG], 1-14.

79. Sharipov R. A. Transfinite normal and composition series of groups, Electronic archive http://arXiv.org, 2009, 0908.2257 [math.GR], 1-12.
80. Sharipov R. A. Transfinite normal and composition series of modules, Electronic archive http://arXiv.org, 2009,0909.2068 [math.RT], 1-7.

Books.

This resource was initially placed at
http://www.geocities.com/r-sharipov/e4-b.htm

1. Sharipov R. A. Theory of representations of finite groups, Bash-NII-Stroy, Ufa, 1995 (both English and Russian versions are now available on-line).
2. Sharipov R. A. Course of linear algebra and multidimensional geometry, Bashkir State University, Ufa, 1996, (both English and Russian versions of the book are now available on-line).
3. Sharipov R. A. Course of differential geometry, Bashkir State University, Ufa, 1996 (both English and Russian versions of the book are now available on-line).
4. Sharipov R. A. Classical electrodynamics and theory of relativity, Bashkir State University, Ufa, 1996 (both English and Russian versions of the book are now available on-line).
5. Sharipov R. A. Foundations of geometry for university students and high-school students, Bashkir State University, 1998 (both English and Russian versions of the book are now available on-line).
6. Sharipov R. A. Quick introduction to tensor analysis, free on-line textbook, 2004 (both English and Russian versions are now available).