Department of Mathematics

Dr. P. L. Sharma

Name: Dr. P. L. Sharma
Designation: Professor  & Chairman, Department of Mathematics, Director, University Institute of Technology (UIT)
E-mail: plsharma1964@gmail.com 
Contact No.:   94180-03066 (M), 0177-2833769(O)
Address: Department of Mathematics and Statistics, Himachal Pradesh University, Shimla-5.
Qualifications:  M.Phil., Ph. D. (Mathematics), MCA
Specialization/ Area of Interest; Finite Fields, Rhotrices, Cryptography, Bent functions
Teaching and Research Experience: 37 Years and 6 months in June 2021
Research Information:
Research Publications (Total): 60
No. of Ph. D. guided: 7 completed ; 6- pursuing
No. of M.Phil. guided: 21
Books Publication: 4

List of Publications

Sr. No.

Research Paper

ISSN

1.

A Mathematical Theorem in Rotatory Thermohaline Convection?

Journal of Mathematical Analysis and Application in USA California. 189,351- 361 (1995). [ With Prof. M.B. Banerjee]

 

0022-247X

2.

On Howard’s Conjecture in Heterogeneous Shear flows instability of modified s-Waves? Indian J. pure app. Math 28 (6): 825-834 June 1997.

[ With Prof. M.B. Banerjee]

 

0019-5588

3.

Sharma, P.L. and Sharma, R., A note on inequalities between the moments,

International Journal of Theoretical & Applied Sciences, 2(2), P. 30-33, (2010).

 

0975-1718

4.

Sharma, P.L. and Sharma, R ., some optimization problems related with inequalities between the moments, Bulletin of Pure and Applied Sciences Volume 30 E (Math & Stat.) Issue (No.1) P. 135-144,(2011).

 

0970-6577

5.

Sharma, P.L. and Kanwar, R.K., A note on relationship between invertible rhotrices and associated invertible matrices, Bulletin of Pure and Applied Sciences Volume 30 E (Math & Stat.) Issue (No.2) P. 333-339, (2011).

 

0970-6577

6.

Sharma, P.L. and Sharma, R ., Some optimization problems involving moments of discrete random variables, International Journal of Theoretical & Applied Sciences, 3(2), P. 88-90,(2011).

 

0975-1718

7.

Sharma, P.L. and Sharma, R., On optimization problems and inequalities involving three moments , International Journal of Mathematical Sciences and Applications Vol. 2, No 1, P. 245-249, Jan.(2012).

 

2230-9888

8.

Sharma, P.L., Sharma, R. And Thakur, A., A note on inequalities involving moments of a discrete random variable, International J. Of Math. Sci. & Engg. Appls. (IJMSEA),Vol. 6 No. II, P. 133-143, (March, 2012).

 

0973-9424

9.

Sharma, P.L. and Kanwar, R.K., On inner product space and bilinear forms over rhotrices, Bulletin of Pure and Applied Sciences Volume 31 E (Math & Stat.) Issue (No.1) P. 109-118, (2012).

 

0970-6577

10.

Sharma, P.L. and Kanwar, R.K., Adjoint of a rhotrix and its basic properties, International Journal of Mathematical Sciences, Vol. .11, No.3-4, P.337-343, (2012).

 

0972-754X

11.

Sharma, P.L. and Kanwar, R.K., The Cayley-Hamilton theorem for rhotrices, International Journal Mathematics and Analysis, Vol.4,No.1, P.171-178, (2012).

0973-3604

12.

Sharma, P.L. and Kanwar, R.K., An overview of the Cayley-Hamilton Theorem,

American. J. Of Mathematics and Sciences, Vol. 1, No. 2,P. 249-256,(July 2012).

 

2250-3102

13.

Sharma, P.L. and Kanwar, R.K., A note on the arithmetic function (s f)(n) ,

International J. Of Math. Sci. & Engg. Appls. (IJMSEA),Vol. 6 No. V, P.145- 155 , (September, 2012).

 

0973-9424

14.

Sharma, P.L. and Rehan, M., On Security of Hill Cipher using Finite Fields,

International Journal of Computer Applications, Vol. 71, No.4, P. 30-33, (May 2013)

0975- 8887

15.

Sharma, P.L. and Kanwar, R.K., On Involutory and Pascal rhotrices, International J. Of Math. Sci. & Engg. Appls. (IJMSEA),Vol. 7 No. IV, P.133- 146 , (July, 2013).

 

0973-9424

16.

Sharma, P. L. And Kumar, S., On Construction of MDS Rhotrices from Companion Rhotrices over Finite Field, International Journal of Mathematical Sciences, Vol.12, No. 3-4, P. 271-286, (July-Dec., 2013).

 

0972-754X

17.

Sharma, P. L., Kumar, S. And Rehan, M., On Vandermonde and MDS Rhotrices over GF(2q), International Journal of Mathematics and Analysis, Vol. 5, No. 2, P. 143-160, (July- Dec., 2013).

 

0973-3604

18.

Sharma, P. L. And Kumar S., Secure Communication & Digital Signature Verification Through RSA, International Journal of Computer Science and Information Technology Research Excellence, Vol. 3, No. 2, P. 11-16, (March- Apr., 2013).

 

2250-2734

19.

Sharma, P. L., Kumar, S. and Rehan, M., On Hadamard Rhotrix over Finite Field, Bulletin of Pure and Applied Sciences, Vol. 32 E (Math & Stat.), No.2, P. 181-190, (2013).

 

0970-6577

20.

Sharma, P. L. And Kumar, S., Balanced Incomplete Block Design (BIBD)Using Hadamard Rhotrices, International Journal of Technology, Vol. 4, No. 1, P. 62- 66, (Jan.-June, 2014).

 

2231-3907

21.

Sharma, P. L. And Sharma, S. An Application of Finite Field in Hill Cipher,

International Journal of Technology, Vol. 4, No. 1, P. 248- 251, (Jan.-June,

2014).

 

2231-3907

22.

Sharma, P.L. and Rehan, M., Modified Hill Cipher Using Vandermonde Matrix and Finite Field, International Journal of Technology, Vol. 4, No. 1, P. 252-  256, (Jan.-June, 2014).

 

2231-3907

23.

Sharma P. L. and Kumar S., Some applications of Hadamard rhotrices to design balanced incomplete block, International J. of Math. Sci. & Engg. Appls.

Vol. 8, No. II, P. 389-404, (March, 2014).

0973-9424

24.

Sharma P. L., Kumar S. And Rehan M. , On construction of Hadamard codes using Hadamard rhotrices, International Journal of Theoretical & Applied

Sciences , Vol. 6, No. 1, P. 102-111(2014).

0975-1718

25.

Sharma P. L. And Rehan Mansi, On approximate values of irreducible polynomials over GF(3) with first three given coefficients, International journal of Mathematics and analysis, Vol. 6, No. 1, P. 1-26, (January-June 2014),.

0973-3604

26.

Sharma P. L. and Rehan Mansi, Approximating number of irreducible polynomials over GF(p) with several given coefficients, Bulletin of Pure and Applied Sciences, Vol. 33 E (Math & Stat.), No.1, P. 51-74, (2014).

0970-6577

27.

Sharma P. L. And Rehan Mansi, On number of irreducible polynomials over finite field, Recent Trends in Algebra and Mechanics, P. 41-56, Indo-American Books Publisher, New Delhi, (2014).

93-82661- 23-9

28.

Sharma P. L. And Sharma Shabnam, Sequences of irreducible polynomials over GF  (2)with  three prescribed coefficients, Recent Trends in Algebra and Mechanics, P. 21-32, Indo-American Books Publisher, New Delhi, (2014).

93-82661- 23-9

29.

Sharma P. L. And Kumar Satish, On a special type of Vandermonde rhotrix and its decompositions, Recent Trends in Algebra and Mechanics, P. 33-40, Indo- American Books Publisher, New Delhi, (2014).

93-82661- 23-9

30.

Sharma P. L., Sharma Shabnam and Dhiman Neetu, Construction of infinite sequences of irreducible polynomials using Kloosterman sums, Bulletin of Pure and Applied Sciences, Vol. 33 E (Math. & Stat.), No. 2, P. 161-168, (2014).

0970-6577

31.

Sharma P. L., Rehan M. And Sharma S., Counting irreducible polynomials over GF(3) with first and third coefficients given, Asian-European Journal of Mathematics,Vol.8, No.1, 1550015( 27 Pages),(2015).

1793-5571

32.

Sharma P. L. and Rehan Mansi. And Sharma Shabnam, Irreducible polynomials over GF(3) with first and second prescribed coefficients, Asian Journal of Mathematics & Physics, Vol.2015, Article ID amp0209, 15 pages.

 

2308-3131

33.

Sharma P. L., Sharma S. And Rehan M., On construction of irreducible polynomials over F3 , Journal of Discrete Mathematical Sciences and Cryptography, Vol. 18, No. 4(2015), 335-347.

 

0972-0529

34.

Sharma P. L., Sharma Shabnam and Rehan Mansi , Construction of Infinite Sequences  of  Irreducible       Polynomials  over F2, International Journal of Mathematical Sciences & Engineering Applications, Vol. 9, No. 3, September

2015.

 

0973-9424

35.

Sharma P. L., Kumar Satish and Rehan Mansi, On Factorization of a Special Type of Vandermonde Rhotrix, Applications and Applied Mathematics: An International Journal (AAM), Vol.10, No.1, June 2015, 421-439.

 

1932-9466

36.

Sharma P. L. And Dhiman Neetu, Generalization of Cross-correlation in Boolean Functions and Some Generalized Constructions in gbent Functions, Asian-European Journal of Mathematics,Vol. 9, No.1(2016), 1650019 (7 pages).

 

1793-5571

37.

Sharma P. L. , Gupta Shalini and Rehan Mansi, Construction of MDS Rhotrices using Special Type of Circulant Rhotrices over Finite Fields, Himachal Pradesh University Journal (HPUJ), Vol. 3, No. 2(2015), pp. 25-43.

 

2277-1425

38.

Sharma P. L., Sharma Shabnam, Hill Cipher Cryptosystem using Irreducible Polynomials over Finite Fields, Himachal Pradesh University Journal (HPUJ), Vol. 3, No. 2(2015), pp. 44-52.

 

2277-1425

39.

Sharma P. L. And Devi Kiran, An Elliptic Curve Cryptosystem over Finite Fields,

Himachal Pradesh University Journal (HPUJ), Vol. 3, No. 2(2015), pp. 1-12.

2277-1425

40.

Sharma P. L. And Dhiman Neetu , A Characterization Theorem for gbent function over  Z16, Journal of Combinatorics, Information & System Sciences (JCISS), Vol. 41, No. 1-3 (2016), pp. 47-55.

 

0250-9628

41.

Sharma P. L. And Devi Kiran, A public key cryptosystem using normal bases over finite fields, International Journal of Technology, Vol. 6(2), pp. 143-149, July- December, 2016.

 

2231-3907

42.

Sharma P. L. And Dhiman Neetu, Some new constructions of gbent functions, Bulletin of Pure and Applied Sciences Volume 35 E (Math & Stat.) Issue No.2 pp. 89-107, 2016.

 

 

0970- 6577

43.

Sharma P. L. And Dhiman Neetu, Construction of a New Class of Bent and Semi-bent Functions, International Journal of Computer Applications Vol. 157, No 2, pp. 9-12, 2017.

 

0975- 8887

44.

Sharma P. L. And Dhiman Neetu, Construction of Some New Classes of Boolean Bent Functions and Their Duals, International Journal of Algebra, Vol. 11, No.2, pp. 53 – 64, 2017.

1312-8868 (print) 1314-7595 (online)

45.

Sharma P. L., Sharma Shabnam, On Identification of Irreducible Polynomials over Finite Fields with Characteristic P, International J. of Math. Sci. & Engg. Appls. (IJMSEA) Vol. 11 No. I (April), pp. 19-35, 2017.

 

0973-9424

46.

Sharma P. L. And Devi Kiran, A Secure Cryptosystem Based on Normal Bases over Finite Fields, CPUH-Research Journal 2(2), pp. 41-44, 2017.

2455-6076

(online)

47.

Sharma P. L., Sharma Shabnam and Kumar Arun, A Symmetric Cryptosystem Based on Irreducible Polynomials over Finite Fields, CPUH-Research Journal 2(2), pp. 45-50, 2017.

2455-6076

(online)

48.

Sharma P. L. , Gupta Shalini and Rehan Mansi, On Circulant-Like Rhotrices over Finite Fields, Applications and Applied Mathematics: An International Journal (AAM), Vol. 12, No. 1(June), pp. 506-520, 2017.

 

1932-9466

49.

Sharma P. L, Gupta Shalini and Dhiman Neetu, Construction of Maximum Distance Separable Rhotrices using Cauchy Rhotrices over Finite Fields, International Journal of Computer Applications, Vol.168, No. 9, pp. 8-17, 2017.

0975-8887

50.

Sharma P. L., Gupta Shalini and Dhiman Neetu, Sylvester Rhotrices and their Properties over Finite Fields, Bulletin of Pure and Applied Sciences, Vol. 36 E (Math. & Stat.), No. 1, pp. 70-80, 2017.

0970-6577   2320-3226 (online)

51.

Sharma P. L.  And Gupta Shalini , Constructions of Maximum Distance Separable Toeplitz Rhotrices over Finite Fields, J. of Combinatorics, Information & System Sciences Vol. 42, No. 1-4, pp. 89-110, 2017.

 

0250-9628

52.

Sharma P. L. And Devi Kiran, A class of Gaussian normal bases and their dual bases, Journal of Discrete Mathematical Sciences and Cryptography, Vol. 20, No. 8, pp.1741-1755, 2017.

 

0972-0529

53.

Sharma P. L. And Devi Kiran, Normal Elements using Trace Mapping over Finite Fields, International Journal of Computer Applications, Vol. 179, No.20, pp. 18-21, 2018.

 

0975–8887

54.

Sharma P. L. And Devi Kiran, Finding Normal Bases Over Finite Fields Using Prescribed Trace Vectors, International J. Of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 12, No. I, pp. 1-13, 2018.

 

0973-9424

55.

Sharma P. L., Devi Kiran and Kumar Arun, Construction of normal bases over Finite Fields, J. of Combinatorics, Information & System Sciences, Vol. 43, No. 1-4, pp. 1-11, 2018.

 

0250-9628

56.

Sharma P. L., Kumar Arun and Gupta Shalini, Maximum Distance Separable Hankel Rhotrices over Finite Fields, J. of Combinatorics, Information & System Sciences, Vol. 43, No. 1-4, pp. 13-45, 2018.

 

0250-9628

57.

Sharma P. L., Kumar Arun and Gupta Shalini, Hankel rhotrices and constructions of maximum distance separable rhotrices over finite fields, Applications and Applied Mathematics: An International Journal (AAM), Vol. 14, Issue 2 (December 2019), pp. 1197 – 1214

 

1932-9466

58.

Sharma P. L., Kumar Arun and Gupta Shalini, Trace of the positive integral powers of three and five dimensional rhotrices, Bulletin of Pure and Applied Sciences, Volume 39 E (Math & Stat.) Issue (No.1) pp. 165-175, (2020).

 

0970-6577

59.

Sharma P. L., Kumar Arun and Sharma Arun Kumar, On the characteristic roots and Heart of a class of Rhotrices over a finite field, Bulletin of Pure and Applied Sciences, Volume 39 E (Math & Stat.) Issue (No.2) pp. 277-288, (2020).

 

0970-6577

60.

Sharma P. L., Ashima and Sharma Arun Kumar, Recursive Construction of Normal Polynomial over Finite Fields, Journal of Discrete Mathematical Sciences and Cryptography (Accepted for Publication)

 

0972-0529

 


 

 

Last Updated:26-06-2021