Volume-1 Issue-1

  • Version
  • Download 17
  • File Size 4.00 KB
  • File Count 1
  • Create Date August 27, 2017
  • Last Updated October 23, 2017

Volume-1 Issue-1

 Download Abstract Book

S. No

Volume-1 Issue-1, December 2012, ISSN: 2319–6386 (Online)
Published By: Blue Eyes Intelligence Engineering & Sciences Publication Pvt. Ltd. 

Page No.



Lemba D. Nyirenda

Paper Title:

P versus NP Millennium Prize Problem 2000-2013 Olympics: NP=P for NP-Class by Dedekind-Cut TSP P-Solvability

Abstract: The paper presents the P-Solvability characteristics of the TSP, an NP-Complete problem, in a 3D Dedekind-Cut-weight Periodic Table domain as defined in the Zambian PACRA Patent No. 2/2008. Hence by Cooks theorem, the status of all problems in the NP-Complete Class is NP=P, by virtue of the TSP being a member of the NP-Complete Class having the NP=P solvability status. This African Computer Science finding is opposite to Dr Vinay Deolalikar’s   2010 finding of P NP. This settles the ‘P versus NP’ open millennium prize problem in computer science. The research work was concluded on the 10th Day of August, 2012 before the deadline of 1st January 2013 at 5pm CET USA. The TSP NP=P status is due to the discovery of ND[dn]= {d1 to dn}, the third missing weighted network dimension. This has for the first time made the crossing of the combinatorial intractability barrier practically possible. ND[dn], the Dedekind-Cut weight   index set is analogous to:  the points of a real number line  in one-to-one correspondence with the source-node period weights in accordance with the Cantor-Dedekind axiom.

 Dedekind-cut periodic table, Cantor-Dedekind axiom, millennium prize problem, p vesus np problem, TSP.


1.        Barrow, John D., (1998). Impossibility: The Limits of Science and the Science of limits, pages 8-19, 100-107, 208, 221-228. Oxford University Press (UK). 
2.        Baumslag, Benjamin and Bruce Chandler (1968). Group Theory, pages 107-115, 158-166. McGraw Hill Schaum’s Outline Series. New York ,USA)

3.        Boyer, Carl B. (1949). The History of the Calculus and its Conceptual Development, pages 33, 291-293. Dover. New York,USA.

4.        Cohen, Daniel I. A. (1978) Basic Techniques of Combinatorial Theory.John Wiler & Sons, New York 1978. Pages 15-18.

5.        Cordeau, Jean-François.  2006. A Branch-and-Cut Algorithm for the Dial-a-Ride Problem. Operations Research 54(3), May-June, pp 573-586.

6.        Davis, Martin.  (1982). Computability and Unsolvability, pages 69 - 70, 199 - 200. Dover, New York (USA). 

7.        Deo, Narsingh. (1974). Graph Theory with Applications to Engineering and Computer Science, pages 1-11, 52 - 64 , 112 - 135 , 314 - 316. Prentice Hall, Englewood Cliffs (USA).

8.        Diestel, Reinhard (1990). Graph Decompositions: A study in Infinite Graph Theory, pages xii-xiii, 5-47. Oxford University Press. New York, USA.

9.        Deolalikar, Vinay. (2010). www.hp.com/people; (www.theregister.co.uk/2010/08/11/the_p_versus_np_problem/Duchene Eric, Gilbert Larporte, Frederic Semetet.  2007.

10.     The “Undirected m-Peripatetic Salesman Problem: Polyhedral results and New algorithms,” Oper. Res.  55(5), pp949-945. Copyright Informs.

11.     Ege, Seyhan N. (1984). Organic Chemistry, pages 12-13, 21, 558. D.C. Health and Co. Lexington, USA.

12.     Freifelder, David   (1985). Essentials of Molecular Biology, pages 17, 47-59. Jones and Bartlett Publishers. Boston, USA.

13.     Gass, Saul I. (1969). Linear Programming Methods and Applications, page 32-33, 49-53, 54-88. McGraw-Hill Kogakusha, Ltd (London). 

14.     Grattan-Guinnes, I.  Editor (1980). History and Phylosopy of Logic, pages 78, 219, 238-239.  Volume I. Abacus Press, UK.

15.     Hall, Randolph. (2006). On the Road to Integration: 2006 survey of vehicle routing software, OR/MS TODAY,  June 2006, Volume 33, Number 3. Lionheart Publishing(USA), pages 50-57

16.     Hocking, John G. and Gail S. Young. (1961). Topology, pages 1-3, 193-199, 203-213. Dover Publication 0-486-65676-4. New York.

17.     Jenkins, Richard A. (1986). Supercomputers of Today and Tomorrow: The Parallel Processing Revolution. Tab Books Inc, Blue Ridge Summit, PA 17214, USA. Pages 117-118.

18.     Kasner, Edward and James R. Newman.  (1989). Mathematics and the Imagination, pages 48 – 49, 265, 276. Microsoft Press, Redmond (USA). 

19.     Körner, Stephan. (1968). The Phylosophy of Mathematics:  An Introductory Essay, pages 187-191. Dover Publication 0-486-25048-2. New York. 

20.     Krarup, J. 1975. The peripatetic salesman and some related unsolved problems.

21.     B. Roy, ed. Combinatorial Programming, Methods and Applications. Reidel, Dordrecht. The Netherlands, pp173-178.

22.     Kruskal, J.B., Jr. 1956. “On the Shortest Spanning Subtree of a Graph and the Travelling Salesman Problem,” Proc. Am. Math. Soc., Vol. 7, 48-50.

23.     Lawler, E. L. And J. K. Lenstra, A.H.G. Rinnooy Kan and B. Shmoys (Editors).  (1985).  The Travelling Salesman Problem,  page 2-3, 17 - 36,  290 - 320, 380 - 392, 443 - 448. John Wiley & Sons, New York. 

24.     Lipschutz, Seymour.  (1965). General Topology, Pages 87-90, 180-193 .Graw Hill Schaum’s Outline Series.

25.     Masterton, W. L., and E. J. Slowinski. (1969). Chemical Principles, second edition, pages 113-117, 152-153,178. W.B. Saunders Co. London.

26.     McMillan, C. (1970). Mathematical Programming: An Introduction to the Design and Application of Optimal Decision Machines, Wiley & Sons. Pages 271-333.

27.     Morrison, Robert T. and Robert N. Boyd. (1973). Organic Chemistry, page 1-11, 23, 36, 154-163, 177-185,219, 262-267, 440-448.Allyn and Bacon Inc. New York.

28.     Nemhauser, G. L. And L. A. Wosley.  (1988).  Integer and combinatorial Optimization, pages 83 - 43, 389-392, 469-495, 659 - 719. John Wiley & Sons. New York, USA. 

29.     Nyirenda, L.D. and R. Schinzinger, (1990). “Algebraic Network Solvability: Composition Series Constructive Proof and Topological Groupoids”. SIAM Discrete Mathematics Conference, Atlanta, Georgia, June 1990.

30.     Nyirenda, L.D.  (1991). Algebraic Network Protection and Restoration Logistics, pages 21-58, 109-127. Ph.D. dissertation, University of California Irvine, Irvine, California, USA. University Microfilm International Dissertation Information Service, order number 9129104. Ann Arbor, USA.

31.     Nyirenda, L. D., (1992) “Algebraic Solution of 1856 Travelling Salesman Problem”. Lifelines Networks Research, Department of Electrical & Computer Engineering, University of California at Irvine, USA. Pages 1-5. January 1992.

32.     Nyirenda, L.D. and R. Schinzinger, (1992).  “P- and NP-Completeness of the Travelling Salesman Problem”. ORSA/TIMS Bulletin Number 34, San Francisco, p.70-TB9.1, 1992.

33.     Nyirenda, L. D., (1993)   “Disaster Area Mutual Aid Circle Diagrams, Optimum-Value and Convex Hull Max-Cuts”. Disaster Protection Research Report, UC Irvine/ Fluor Daniel Inc., Irvine, California, December 1993.

34.     Nyirenda, L.D. (1997). “Dedekind-Cut Network Pathset Submodular Division TSP Simplex Algorithm”.  Paper presented at the Joint EURO XV - INFORMS XXXIV International Meeting, July 14-17, 1997 Barcelona, Spain.

35.     Nyirenda L.D.  (1997). “Historical Development: Dedekind-Cut Network Submodular Division STP & TSP SIMPLEX ALGORITHMS”.  Lifelines Research, University of Zambia, Lusaka, Zambia.

36.     Nyirenda L.D.  , (1998). “TSP-STP Dedekind-Cut Network Choice Functions”, Individual Research Report (1991-1995), November 1998. University of Zambia, Lusaka

37.     Nyirenda, Lemba D. and Roland Schinzinger. (2003). “Traveling Salesman Problem Linear Path Spanning Tree Simplex Algorithm”. Presented August 2003 at EURO XVI International Meeting, Istanmbul, Turkey. Book of Abstracts August 2003.

38.     Nyirenda, Lemba D.  (2004) , “Travelling Salesman Problem Solution as a D-Cut Simplex Protein Folding Problem”., VLIR Inter-Discilinary Research. University of Zambia, School of Engineering, Department of Electrical & Electronic Engineering, Lusaka, Zambia. February 2004. Pages 1-17.    

39.     Nyirenda, L. D. (2006). “Min nd2+ Linear SpanTree-Circle Math Programme TSP Intractability Barrier Crossing”. Research Discovery Series, Department of Electrical & Electronic Engineering, University of Zambia. January, 2006. Pages 1-15.

40.     Nyirenda, L. D. (2008) “Printed Circuit Board Computerized Hole-Drilling Robot-Travelling-Salesman-Problem-Tour Construction Methodology As A Min nd2+ Hyperconjugate D1-Path  Linear-Spantree-Circle Using Submodular Network Algebra in a Dedekind-Cut Distance-Metrics  / Weights & Measures Periodic Table  ” . Pacro-Zambia Patent Lodgement No. 41749, No 2/2008, 10th January 2008, Lusaka, Zambia.

41.     Nyirenda , L.D. and R. Schinzinger, (2008). “Dedekind-Cut TSP Linear D1-Path Cumulated Corner Point Polarization Revised Simplex Method”.The Zambian Engineer, Journal of the Engineering Institution of Zambia. ISSN 1608-6678. Number 1, Volume 41, July/August 2008. Pages 22-35.

42.     Nyirenda , L.D. and R. Schinzinger, (2010). “Dedekind-Cut TSP D1-Path Cumulated Polarization Function Linear Span-Tree-Circle Simplex Method”.The Zambian Engineer, Journal of the Engineering Institution of Zambia. ISSN 1608-6678. Number 1, Volume 43, January/February 2010. Pages 25-39.

43.     Parker, R. Gary and Ronald L. Rardin.  (1988). Discrete Optimization, pages 1 - 10, 23 - 48, 93-100. Academic Press, Boston (USA). 

44.     Phillips, Don T. and Alberto Garcia-Diaz. 1981. Fundamentals of Network analysis, pages 97-111. Prentice Hall.  New York , USA. 

45.     Rosen, H. Kenneth (Editor In Chief).  (1999). Handbook of Discrete and Combinatorial Mathematics, pages 107-109, 676-687,  692-702, 959-962. CRC Press (London). 

46.     Royden, H.L. (1988). Real Analysis, pages 5-11, 72-74, 137-147, 171-189, 253-254. Mcmillan Publishing Company. New York, USA.

47.     Schrage, M. (1990). “Be Thankful Pythogoras Didn’t Have a PC,”Los Angeles Times, Orange County Edition, D15, July 26, 1990.

48.     Sommer Halder R. and S. C. van Westrhenen. (1988). The Theory of Computability: Programs, machines, effectiveness and Feasibility, pages 151, 337-353 , 394-417 . Addison-Wesley Publishers Ltd. (UK). 

49.     Suppess, Patrick. (1972). Axiomatic Set Theory, pages 68 - 69, 74 - 75, 239 - 240, 250 - 253. Dover, New York (USA)

50.     Tuma, Jan J. (1989).  Handbook of Numerical Calculations in Engineering, pages 16, 27, 36, 40, 98. McGraw Hill, New York (USA). 

51.     www.bhubdub.com; www.claymath.org

52.     www.theregister.co.uk/2010/08/11/the_p_versus_np_problem/

53.     www.Wikipedia: the free encyclopedia, page 2.

54.     www.claymath.org/millennium/ [Cook, Stephen (April 2000), P_vs_NP/ Official_Problem_Description.pdf. Retrieved 09 November 2012.] 

55.     www.iwr.uni- heidelberg.de/ iwr/ comopt/soft/ TSPLIB95/TSPLIB.html)





Archana M. Kadam, Satyen Dhamdhere, D. S. Bankar

Paper Title:

Application of DSTATCOM for Improvement of Power Quality using MATLAB Simulation

Abstract:  An increasing demand for high quality, reliable electrical power and increasing number of distorting loads may leads to an increased awareness of power quality both by customers and utilities. The most common power quality problems today are voltage sags, harmonic distortion and low power factor. This paper presents the reduction of voltage sags, using Distribution Static Compensator (D-STATCOM) with LCL Passive Filter in Distribution system. The model is based on the Voltage Source Converter (VSC) principle. D-STATCOM can use with different types of controllers. The D-STATCOM injects a current into the system to mitigate the voltage sags.LCL Passive Filter Was then added to D-STATCOM to improve harmonic distortion and low power factor. The simulations were performed using MATLAB SIMULINK.



1.        Bollen, M.H.J.,”Voltage sags in Three Phase Systems”, Power Engineering Review , IEEE, Volume 21, Issue :9, September 2001,PP: 11-15.
2.        1Noramin Ismail, 2 Wan Norainin Wan Abdullah “Enhancement of Power Quality in Distribution System Using D-STATCOM” 978-1-4244-7128-7/10/$26.00 ©2010 IEEE, The 4th International Power Engineering and Optimization Conference (PEOCO2010), Shah Alam, Selangor, MALAYSIA. 23-24 June 2010.

3.        “Operation of a DSTATCOM in Voltage Control Mode” by Mahesh K. Mishra, Student Member, IEEE, Arindam Ghosh, Senior Member, IEEE, and Avinash Joshi.

4.        Kolli Nageswar Rao1, C. Hari Krishna2, Kiran Kumar Kuthadi3 “Implementation of D-STACTOM for Improvement of Power Quality in Radial Distribution System” International Journal of Modern Engineering Research (IJMER) Vol. 2, Issue. 5, Sep.-Oct. 2012 pp-3548-3552.

5.        R.Meinski, R.Pawelek and I.Wasiak, “Shunt Compensation For Power Quality Improvement Using a STATCOM controller Modelling and Simulation”, IEEE Proce, Volume 151, No. 2,March 2004.

6.        M.Madrigal, E.Acha., “Modelling OF Custom Power Equipment Using Harmonics Domain Twchniques”,IEEE 2000.

7.        Improvement of Power Quality in Electric ship power system Using Controller of D-statcom, International Journal of Engineering Trends and Technology, 2(2) (2011)