| Himachal Pradesh University Shimla, India

Dr. Rajesh Sharma

Name: Dr. Rajesh Sharma

Designation: Professor

Email: rajesh_hpu_math@yahoo.co.in

Contact: 9459193341

Qualifications: M.Phil., Ph.D in Mathematics from H.P. University Shimla and Postdoc. from IIT Mumbai.

Specialization/area of interest: Matrix Analysis and inequalities

Teaching and Research Experience: 24 years

Research Information:

Research Publications (total): 66

No. of Ph.D. guided: 13

No. of M. Phil guided: 30

Research Publications

1. R. Sharma, A. Sharma and R. Saini, “A note on variance bounds and location of eigenvalues” Journal Of Mathematical Inequalities, Volume 15, Number 1 (2021),67-80, Croatia.
2. R. Sharma, R. Kumar, R. Saini and P. Devi, Inequalities for central moments and spread of matrices, Annals of Functional Analysis, 2020, Iran.
3. R. Kumar, R. Sharma, Some inequalities involving positive linear maps under certain conditions, Operator and Matrices, 13, 3, 843-854, 2019, Croatia .
4. R. Sharma, A. Sharma, R. Saini, G. Kapoor, Means Moments and Newton’s Inequalities, Rocky Mountain J. Math. 49, 5, 1667-1677, 2019, USA.
5. R.Sharma, R. Kumar, R. Saini, G. Kapoor, Bounds on Spreads of Matrices Related to Fourth Central Moment, Bull. Malays. Sci. Soc. 41, 175-190, 2018, Malaysia.
6. R. Sharma, P. Devi, R. Kumari, A note on inequalities for Positive linear maps, Linear Algebra and Applications, 528, 62-75, 2017, USA.
7. R. Sharma, R. Kumari, Positive linear maps and perturbation bounds of matrices, Linear Algebra and Applications, 528,62-75, 2017, USA.
8. R. Sharma and R. Bhandari, Remark on variance bounds, J. of Combinatorics, Information & System Sciences, 41, 203-206, 2016, INDIA.
9. R. Sharma and R. Saini, An identity involving fourth central moment, The Mathematical Scientist, 41, 136-137, 2016, UK.
10. R. Sharma and R. Saini,On bounds for fourth central moment, J. of Combinatorics, Information & System Sciences, 41, 57-64, 2016, INDIA.
11. R. Sharma and R. Bhandari, Skewness, kurtosisandNewton’sinequality, Rocky Mountain Math. J.,45,1639-1643, 2015, USA.
12. R. Sharma and R. Kumar, Positive linear functional and Gersgorin disks of matrices, J. of Combinatorics, Information & System Sciences, 39, 13-19, 2014, INDIA.
13. R. Bhatia and R. Sharma, Positive linear maps and spread of matrices-II, Linear Algebra and Applications, 436, 1562–1571, 2015, USA.
14. R. Sharma, R.Kumar and S. Garge, On inequalities involving eigenvalues and traces of Hermitian matrices, Annals of Functional Analysis, 6, 78-90, 2015, Iran.
15. R. Sharma and R. Saini, Generalisation of Samuelson’ inequality and location of eigenvalues, Proc. Indian Acad. Sci. (Math. Sci.), 125, 103-111, 2015, INDIA.
16. R. Bhatia and R. Sharma, Positive linear maps and spread of matrices, Amer. Math. Monthly., 121, 619-624, 2014, USA.
17. R. Sharma and R. Bhandari, On variance upper bounds for unimodal dis-tributions, Communications in Statistics-Theory and Methods, 43, 4503-4513, 2014, UK.
18. R. Sharma and R. Bhandari, On bounds for moments of unimodal dis-tributions, Communications for Statistical Applications and Methods, 21, 201-212 ,2014, Korea.
19. R. Sharma and A. Thakur, A refinement of the gruss inequality for pos-itive linear functionals, J. of Combinatorics, Information & System Sci-ences, 38, 203-217, 2013, INDIA.
20. R. Sharma and R. Kumar, Remark on upper bounds for the spread of a matrix, Linear Algebra and Applications, 438 , 4359-4362, 2013, USA.
21. R. Sharma and A. Thakur, More inequalities for positive linear maps, Journal of Mathematical Inequalities, 7(1), 1-9, 2013, Croatia.
22. R. Sharma, R. Bhandari and M. Gupta, Inequalities related to the Cauchy-Schwarz inequality, Sankhya: The Indian Journal of Statistics, Series A, 74-A(1), 101-111, 2012, India.
23. R. Bhatia and R. Sharma, Some more inequalities for positive linear maps, Linear Algebra and Applications, 436, 1562–1571, 2012, USA.
24. P.L. Sharma, R. Sharma and A. Thakur, A note on inequalities involving moments of a discrete random variable, International J. of Math. Sci. & Engg. Appls., 6(2): 133-143,2012, India.
25. R. Sharma and P.L. Sharma, On optimization problems and inequalities involving three moments. Int. J. of Mathematical Sciences and Applica-tions, 2(1):245-249, 2012, India.
26. R. Sharma and P.L. Sharma, Some optimization problems involving mo-ments of discrete random variables, International Journal of Theoretical and Applied Science, 3(2): 88-90, 2011, India.
27. R. Sharma and P.L. Sharma, Some optimization problems related with inequalities between the moments, Bulletin of pure and applied sciences, 30(1):135-144, 2011, India.
28. R. Sharma and A. Thakur, On Inequalities involving first three moments, International Journal of Mathematics and Scientific Computing, 1(1): 43-47, 2011, India.
29. R. Sharma and A. Thakur, Inequalities related to variance of complex numbers, Journal of inequalities and special functions, 2(1):8-15, 2011, Kosovo.
30. R. Sharma, On Jensen’s inequality for positive linear functionals, International J. of Math. Sci. & Engg. Appls.,5(5): 263-271, 2011, India.
31. R. Sharma, R.G. Shandil and G. Kapoor, A note on Karl Pearson’s Co-efficient of Dispersion, Journal of H.P. University, 1(1): 147-149, 2011, India.
32. R. Sharma, R. Bhandari and A. Thakur, Some bounds for integrals with re…nements of the gruss inequality, Indian journal of pure and applied mathematics, 42(3): 187-202, 2011, India.
33. R. Sharma A. Thakur and R. Bhandari, On covariance bounds related to discrete gruss type inequalities, International J. of Math. Sci. & Engg. Appls., 5(2): 287–301,2011, India.
34. R. Sharma and R. Bhandari, On inequalities involving positive definite matrices and its extreme eigenvalues,Recent advances in continuum mechanics & algebra. Regal publication-New-Delhi, 2011, India.
35. R. Sharma and M. Gupta,On some inequalities involving harmonic mean and moments, Recent advances in continum mechanics & algebra. Regal publication-New-Delhi, 2011, India.
36. R. Sharma and P.L. Sharma, A note on inequalities between the moments, International Journal of theoretical and applied sciences, 2(2): 30-33, 2010, India.
37. R. Sharma and R. Bhandari, On Some Kantorovich Type Inequalities and their Applications, Journal of Combinatorics, Information & System Sci-ences, 35(3-4): 459-470, 2010, India.
38. R. Sharma and M. Gupta, Stress strain distribution and elastic moduli: multiphase composite bodies, International J. of Math. Sci. & Engg. Ap-pls., 4(4): 405-411, 2010, India.
39. R. Sharma, G. Kapoor and M. Gupta, Some better bounds on the vari-ance with applications, Journal of Mathematical inequalities, 4(3), 355-363, 2010, Croatia.
40. R. Sharma, S. Devi, G. Kapoor, S. Ram and N.S. Barnett, A brief note on some bounds connecting lower order moments for random variables defined on a finite interval, International Journal of theoretical and applied sciences, 1(2): 83-85, 2009, India.
41. R. Sharma, S. Ram and S. Devi, Some inequalities for the ratio and di¤ er-ence of moments, International journal of theoretical and applied sciences, 1(1): 103-110, 2009, India.
42. R. Sharma, A. Kaura, M. Gupta and S. Ram, Some bounds on sample parameters with re…nements of Samuelson and Brunk inequalities, Journal of mathematical inequalities, 3(1): 99-106, 2009, Croatia.
43. R. Sharma, R.G. Shandil, G. Kapoor, S. Devi and N.S. Barnett, Some bounds on the sample variance in terms of the mean and extreme values, Advances in inequalities from probability theory and statistics, Edited by N.S.Barnett and S.S. Dragomir and published by “Nova Publication”, (2008), Australia.
44. R. Sharma, Some More Inequalities for Arithmetic Mean, Harmonic Mean and Variance, Journal of Mathematical Inequalities, 2(1): 109-114, 2008, Croatia.
45. R. Sharma, S. Ranta and A. Ranjan, On Inverse Mixture Rule of Multi-phase Composite Bodies, Journal of Reinforced Plastics and Composites, 24(7): 2005, USA.
46. R. Sharma, R.G. Shandil, S. Devi, and M. Dutta, Some Inequalities be-tween Moments of Probability Distributions, Journal of Inequalities in Pure and Applied Mathematics, 5(4): 1-12, 2004, Australia.
47. R. Sharma and S. Ranta, On Simplified Composite Micromechanics Equa-tion and Mixture Rule, Journal of Reinforced Plastics and Composites, 23(14): 1465-1472, 2004, USA.
48. R. Sharma, S. Ranta and A. Ranjan, Bounds on Elastic Modulus of a Mul-tiphase Composite Bodies, Journal of Reinforced Plastics and Composites, 23(3): 317-325, 2004, USA.
49. R. Sharma and A. Ranjan, Bounds on Longitudinal and Transverse Mod-ulus of a Multiphase Composite: Journal of Reinforced Plastics and Com-posites, 22(11): 1017-1027, 2003, USA.
50. R. Sharma and A. Ranjan, Bounds on Transverse Modulus of a Multiphase Composite, Journal of Reinforced Plastics and Composites, 21(16): 1467-1476, 2002, USA.
51. R. Sharma and A. Ranjan, Elastic Properties of Reinforced Solid: Analo-gus of Mohr Circle Diagram-II, Journal of Reinforced Plastics and Com-posites, 21(14): 1319-1336, 2002, USA.
52. R. Sharma and A. Ranjan, Elastic Properties of Reinforced Solids: Ana-logus of Mohr Circle Diagram, Journal of Reinforced Plastics and Com-posites, 19(14): 1147-1158, 2000, USA.
53. R. Sharma, J.S. Dhiman and M.S. Pattanayak, On Reducing Banerjee-Shandil Semi-Circle, Ganita, Vol. 50(1): 5-8, 1999, India.
54. R. Sharma and K.S.Parihar, Young’s Modulus and Poisson’s Ratio of An n-Phase Composite Body Reinforced with Inclined Inclusions, Journal of Reinforced Plastics and Composites, , 16 (2): 167-181, 1997, USA.
55. R. Sharma, Distribution of Body Stresses in an n-Phase Composite Body:Prior to Outside Loading, Journal of Reinforced Plastics and Composites, 14( 12): 1307-1316, 1995, USA.
56. B.B.Sharma and R. Sharma, Elastic Constants for a two phase Isotropic Composite, Journal of Reinforced Plastics and Composites, Vol. 14(11): 1144-1149, 1995, USA.
57. R. Sharma and Anupam Sharma, Young’s modulus of A Composite: Rein-forced with (n-1) Di¤ erent Inclusions, Journal of Reinforced Plastics and Composites, 12(6): 670-676, 1993, USA.
58. B.B.Sharma and R. Sharma, Young’s modulus of Reinforced Compos-ite, Advanced Composite Materials, 2(4): 277-288, 1992, Japan.
59. B.B. Sharma, R. Sharma and Rajinder Gupta, Continuum Damage Me-chanics and Heterogeneity of Reinforced Composites, Journal of Reinforced Plastics and Composites, 11(10): 1103-1110, 1992, USA.
60. B.B. Sharma, R. Sharma and Rajinder Gupta, On the Rupture Properties of Reinforced Solids, Journal of Reinforced Plastics and Composites, 2(1): 1-6, 1992, Japan.
61. B.B. Sharma and R. Sharma, A Study on the Elastic Properties of Rein-forced Solids, Journal of Reinforced Plastics and Composites, 11(9): 860-967, 1992, USA.
62. B.B. Sharma, R. Sharma and Rajinder Gupta, A Statistical Study on the Rupture of Composite Materials, Acta Ciencia India, 17(3): 433-442, 1991, India.
63. B.B. Sharma, R. Sharma and Rajinder Gupta, Conditions on the time of Rupture of Reinforced Materials, Acta Ciencia India, 17(3): 440-456, 1991, India.
64. B.B. Sharma, R. Sharma and Rajinder Gupta, A Study on Rupture and Economy of Composite Material, Advanced Composite Materials, 1(3): 169-179, 1991, Japan.
65. B.B. Sharma, R. Sharma and Rajinder Gupta, A Study on the Damage of Reinforced Material, Journal of Reinforced Plastics and Composites, 10(6): 585-593, November, 1991, USA.
66. B.B. Sharma, R. Sharma and Rajinder Gupta, A Condition on the time of Rupture of Reinforced Materials, Journal of Reinforced Plastics and Composites, 9(4): 362-368, 1990, USA.

Dr. Rajesh Sharma

Name: Dr. Rajesh Sharma

Designation: Professor

Email: rajesh_hpu_math@yahoo.co.in

Contact: 9459193341

Qualifications: M.Phil., Ph.D in Mathematics from H.P. University Shimla and Postdoc. from IIT Mumbai.

Specialization/area of interest: Matrix Analysis and inequalities

Teaching and Research Experience: 24 years

Research Information:

Research Publications (total): 66

No. of Ph.D. guided: 13

No. of M. Phil guided: 30

Research Publications

1. R. Sharma, A. Sharma and R. Saini, “A note on variance bounds and location of eigenvalues” Journal Of Mathematical Inequalities, Volume 15, Number 1 (2021),67-80, Croatia.

2. R. Sharma, R. Kumar, R. Saini and P. Devi, Inequalities for central moments and spread of matrices, Annals of Functional Analysis, 2020, Iran.

3. R. Kumar, R. Sharma, Some inequalities involving positive linear maps under certain conditions, Operator and Matrices, 13, 3, 843-854, 2019, Croatia .

4. R. Sharma, A. Sharma, R. Saini, G. Kapoor, Means Moments and Newton’s Inequalities, Rocky Mountain J. Math. 49, 5, 1667-1677, 2019, USA.

5. R.Sharma, R. Kumar, R. Saini, G. Kapoor, Bounds on Spreads of Matrices Related to Fourth Central Moment, Bull. Malays. Sci. Soc. 41, 175-190, 2018, Malaysia.

6. R. Sharma, P. Devi, R. Kumari, A note on inequalities for Positive linear maps, Linear Algebra and Applications, 528, 62-75, 2017, USA.

7. R. Sharma, R. Kumari, Positive linear maps and perturbation bounds of matrices, Linear Algebra and Applications, 528,62-75, 2017, USA.

8. R. Sharma and R. Bhandari, Remark on variance bounds, J. of Combinatorics, Information & System Sciences, 41, 203-206, 2016, INDIA.

9. R. Sharma and R. Saini, An identity involving fourth central moment, The Mathematical Scientist, 41, 136-137, 2016, UK.

10. R. Sharma and R. Saini,On bounds for fourth central moment, J. of Combinatorics, Information & System Sciences, 41, 57-64, 2016, INDIA.

11. R. Sharma and R. Bhandari, Skewness, kurtosisandNewton’sinequality, Rocky Mountain Math. J.,45,1639-1643, 2015, USA.

12. R. Sharma and R. Kumar, Positive linear functional and Gersgorin disks of matrices, J. of Combinatorics, Information & System Sciences, 39, 13-19, 2014, INDIA.

13. R. Bhatia and R. Sharma, Positive linear maps and spread of matrices-II, Linear Algebra and Applications, 436, 1562–1571, 2015, USA.

14. R. Sharma, R.Kumar and S. Garge, On inequalities involving eigenvalues and traces of Hermitian matrices, Annals of Functional Analysis, 6, 78-90, 2015, Iran.

15. R. Sharma and R. Saini, Generalisation of Samuelson’ inequality and location of eigenvalues, Proc. Indian Acad. Sci. (Math. Sci.), 125, 103-111, 2015, INDIA.

16. R. Bhatia and R. Sharma, Positive linear maps and spread of matrices, Amer. Math. Monthly., 121, 619-624, 2014, USA.

17. R. Sharma and R. Bhandari, On variance upper bounds for unimodal dis-tributions, Communications in Statistics-Theory and Methods, 43, 4503-4513, 2014, UK.

18. R. Sharma and R. Bhandari, On bounds for moments of unimodal dis-tributions, Communications for Statistical Applications and Methods, 21, 201-212 ,2014, Korea.

19. R. Sharma and A. Thakur, A refinement of the gruss inequality for pos-itive linear functionals, J. of Combinatorics, Information & System Sci-ences, 38, 203-217, 2013, INDIA.

20. R. Sharma and R. Kumar, Remark on upper bounds for the spread of a matrix, Linear Algebra and Applications, 438 , 4359-4362, 2013, USA.

21. R. Sharma and A. Thakur, More inequalities for positive linear maps, Journal of Mathematical Inequalities, 7(1), 1-9, 2013, Croatia.

22. R. Sharma, R. Bhandari and M. Gupta, Inequalities related to the Cauchy-Schwarz inequality, Sankhya: The Indian Journal of Statistics, Series A, 74-A(1), 101-111, 2012, India.

23. R. Bhatia and R. Sharma, Some more inequalities for positive linear maps, Linear Algebra and Applications, 436, 1562–1571, 2012, USA.

24. P.L. Sharma, R. Sharma and A. Thakur, A note on inequalities involving moments of a discrete random variable, International J. of Math. Sci. & Engg. Appls., 6(2): 133-143,2012, India.

25. R. Sharma and P.L. Sharma, On optimization problems and inequalities involving three moments. Int. J. of Mathematical Sciences and Applica-tions, 2(1):245-249, 2012, India.

26. R. Sharma and P.L. Sharma, Some optimization problems involving mo-ments of discrete random variables, International Journal of Theoretical and Applied Science, 3(2): 88-90, 2011, India.

27. R. Sharma and P.L. Sharma, Some optimization problems related with inequalities between the moments, Bulletin of pure and applied sciences, 30(1):135-144, 2011, India.

28. R. Sharma and A. Thakur, On Inequalities involving first three moments, International Journal of Mathematics and Scientific Computing, 1(1): 43-47, 2011, India.

29. R. Sharma and A. Thakur, Inequalities related to variance of complex numbers, Journal of inequalities and special functions, 2(1):8-15, 2011, Kosovo.

30. R. Sharma, On Jensen’s inequality for positive linear functionals, International J. of Math. Sci. & Engg. Appls.,5(5): 263-271, 2011, India.

31. R. Sharma, R.G. Shandil and G. Kapoor, A note on Karl Pearson’s Co-efficient of Dispersion, Journal of H.P. University, 1(1): 147-149, 2011, India.

32. R. Sharma, R. Bhandari and A. Thakur, Some bounds for integrals with re…nements of the gruss inequality, Indian journal of pure and applied mathematics, 42(3): 187-202, 2011, India.

33. R. Sharma A. Thakur and R. Bhandari, On covariance bounds related to discrete gruss type inequalities, International J. of Math. Sci. & Engg. Appls., 5(2): 287–301,2011, India.

34. R. Sharma and R. Bhandari, On inequalities involving positive definite matrices and its extreme eigenvalues,Recent advances in continuum mechanics & algebra. Regal publication-New-Delhi, 2011, India.

35. R. Sharma and M. Gupta,On some inequalities involving harmonic mean and moments, Recent advances in continum mechanics & algebra. Regal publication-New-Delhi, 2011, India.

36. R. Sharma and P.L. Sharma, A note on inequalities between the moments, International Journal of theoretical and applied sciences, 2(2): 30-33, 2010, India.

37. R. Sharma and R. Bhandari, On Some Kantorovich Type Inequalities and their Applications, Journal of Combinatorics, Information & System Sci-ences, 35(3-4): 459-470, 2010, India.

38. R. Sharma and M. Gupta, Stress strain distribution and elastic moduli: multiphase composite bodies, International J. of Math. Sci. & Engg. Ap-pls., 4(4): 405-411, 2010, India.

39. R. Sharma, G. Kapoor and M. Gupta, Some better bounds on the vari-ance with applications, Journal of Mathematical inequalities, 4(3), 355-363, 2010, Croatia.

40. R. Sharma, S. Devi, G. Kapoor, S. Ram and N.S. Barnett, A brief note on some bounds connecting lower order moments for random variables defined on a finite interval, International Journal of theoretical and applied sciences, 1(2): 83-85, 2009, India.

41. R. Sharma, S. Ram and S. Devi, Some inequalities for the ratio and di¤ er-ence of moments, International journal of theoretical and applied sciences, 1(1): 103-110, 2009, India.

42. R. Sharma, A. Kaura, M. Gupta and S. Ram, Some bounds on sample parameters with re…nements of Samuelson and Brunk inequalities, Journal of mathematical inequalities, 3(1): 99-106, 2009, Croatia.

44. R. Sharma, Some More Inequalities for Arithmetic Mean, Harmonic Mean and Variance, Journal of Mathematical Inequalities, 2(1): 109-114, 2008, Croatia.

45. R. Sharma, S. Ranta and A. Ranjan, On Inverse Mixture Rule of Multi-phase Composite Bodies, Journal of Reinforced Plastics and Composites, 24(7): 2005, USA.

46. R. Sharma, R.G. Shandil, S. Devi, and M. Dutta, Some Inequalities be-tween Moments of Probability Distributions, Journal of Inequalities in Pure and Applied Mathematics, 5(4): 1-12, 2004, Australia.

47. R. Sharma and S. Ranta, On Simplified Composite Micromechanics Equa-tion and Mixture Rule, Journal of Reinforced Plastics and Composites, 23(14): 1465-1472, 2004, USA.

48. R. Sharma, S. Ranta and A. Ranjan, Bounds on Elastic Modulus of a Mul-tiphase Composite Bodies, Journal of Reinforced Plastics and Composites, 23(3): 317-325, 2004, USA.

49. R. Sharma and A. Ranjan, Bounds on Longitudinal and Transverse Mod-ulus of a Multiphase Composite: Journal of Reinforced Plastics and Com-posites, 22(11): 1017-1027, 2003, USA.

50. R. Sharma and A. Ranjan, Bounds on Transverse Modulus of a Multiphase Composite, Journal of Reinforced Plastics and Composites, 21(16): 1467-1476, 2002, USA.

51. R. Sharma and A. Ranjan, Elastic Properties of Reinforced Solid: Analo-gus of Mohr Circle Diagram-II, Journal of Reinforced Plastics and Com-posites, 21(14): 1319-1336, 2002, USA.

52. R. Sharma and A. Ranjan, Elastic Properties of Reinforced Solids: Ana-logus of Mohr Circle Diagram, Journal of Reinforced Plastics and Com-posites, 19(14): 1147-1158, 2000, USA.

53. R. Sharma, J.S. Dhiman and M.S. Pattanayak, On Reducing Banerjee-Shandil Semi-Circle, Ganita, Vol. 50(1): 5-8, 1999, India.

54. R. Sharma and K.S.Parihar, Young’s Modulus and Poisson’s Ratio of An n-Phase Composite Body Reinforced with Inclined Inclusions, Journal of Reinforced Plastics and Composites, , 16 (2): 167-181, 1997, USA.

55. R. Sharma, Distribution of Body Stresses in an n-Phase Composite Body:Prior to Outside Loading, Journal of Reinforced Plastics and Composites, 14( 12): 1307-1316, 1995, USA.

56. B.B.Sharma and R. Sharma, Elastic Constants for a two phase Isotropic Composite, Journal of Reinforced Plastics and Composites, Vol. 14(11): 1144-1149, 1995, USA.

57. R. Sharma and Anupam Sharma, Young’s modulus of A Composite: Rein-forced with (n-1) Di¤ erent Inclusions, Journal of Reinforced Plastics and Composites, 12(6): 670-676, 1993, USA.

58. B.B.Sharma and R. Sharma, Young’s modulus of Reinforced Compos-ite, Advanced Composite Materials, 2(4): 277-288, 1992, Japan.

59. B.B. Sharma, R. Sharma and Rajinder Gupta, Continuum Damage Me-chanics and Heterogeneity of Reinforced Composites, Journal of Reinforced Plastics and Composites, 11(10): 1103-1110, 1992, USA.

60. B.B. Sharma, R. Sharma and Rajinder Gupta, On the Rupture Properties of Reinforced Solids, Journal of Reinforced Plastics and Composites, 2(1): 1-6, 1992, Japan.

61. B.B. Sharma and R. Sharma, A Study on the Elastic Properties of Rein-forced Solids, Journal of Reinforced Plastics and Composites, 11(9): 860-967, 1992, USA.

62. B.B. Sharma, R. Sharma and Rajinder Gupta, A Statistical Study on the Rupture of Composite Materials, Acta Ciencia India, 17(3): 433-442, 1991, India.

63. B.B. Sharma, R. Sharma and Rajinder Gupta, Conditions on the time of Rupture of Reinforced Materials, Acta Ciencia India, 17(3): 440-456, 1991, India.

64. B.B. Sharma, R. Sharma and Rajinder Gupta, A Study on Rupture and Economy of Composite Material, Advanced Composite Materials, 1(3): 169-179, 1991, Japan.

65. B.B. Sharma, R. Sharma and Rajinder Gupta, A Study on the Damage of Reinforced Material, Journal of Reinforced Plastics and Composites, 10(6): 585-593, November, 1991, USA.

66. B.B. Sharma, R. Sharma and Rajinder Gupta, A Condition on the time of Rupture of Reinforced Materials, Journal of Reinforced Plastics and Composites, 9(4): 362-368, 1990, USA.