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Np complete problems a minimalist mutatis

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Np complete problems a minimalist mutatis

  1. 1. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 NP Complete Problems-A Minimalist Mutatis Mutandis Model- Testament Of The Panoply *1 Dr K N Prasanna Kumar, 2Prof B S Kiranagi And 3Prof C S Bagewadi *1 Dr K N Prasanna Kumar, Post doctoral researcher, Dr KNP Kumar has three PhD’s, one each in Mathematics, Economics and Political science and a D.Litt. in Political Science, Department of studies in Mathematics, Kuvempu University, Shimoga, Karnataka, India Correspondence Mail id : drknpkumar@gmail.com 2 Prof B S Kiranagi, UGC Emeritus Professor (Department of studies in Mathematics), Manasagangotri, University of Mysore, Karnataka, India 3 Prof C S Bagewadi, Chairman , Department of studies in Mathematics and Computer science, Jnanasahyadri Kuvempu university, Shankarghatta, Shimoga district, Karnataka, IndiaAbstractA concatenation Model for the NP complete problems is given. Stability analysis, Solutional behaviorare conducted. Due to space constraints, we do not go in to specification expatiations and enucleation ofthe diverse subjects and fields that the constituents belong to in the sense of widest commonalty term.IntroductionNP Complete problems in physical reality comprise of(1) Soap Bubble(2) Protein Folding(3) Quantum Computing(4) Quantum Advice(5) Quantum Adiabatic algorithms(6) Quantum Mechanical Nonlinearities(7) Hidden Variables(8) Relativistic Time Dilation(9) Analog Computing(10) Malament-Hogarth Space Times(11) Quantum Gravity(12) Anthropic ComputingWe give a minimalist concatenation model. We refer the reader to rich repository, receptacle, andreliquirium of literature available on the subject: Please note that the classification is done based on thephysical parameters attributed and ascribed to the system or constituent in question with acomprehension of the concomitance of stratification in the other category. Any little intrusion intocomplex subjects would be egregiously presumptuous, an anathema and misnomer and will never dojustice to the thematic and discursive form. Any attempt to give introductory remarks, essentialpredications, suspensional neutralities, rational representations, interfacial interference and syncopatedjustifications would only make the paper not less than 500 pages. We shall say that the P-NP problemitself is not solved let alone all the NP complete problems. We have taken a small step in this direction.More erudite scholars, we hope would take the insinuation made in the paper for further developmentand proliferation of the thesis propounded.NotationSoap Bubble And Protein Folding System: Variables Glossary : Category One Of Soap Bubbles 176
  2. 2. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 : Category Two Of Soap Bubbles : Category Three Of Soap Bubbles : Category One Of Protein Folding : Category Two Of Protein Folding : Category Three Of Protein FoldingQuantum Computing And Quantum Advice : Category One Quantum Computing : Category Two Of Quantum Computing : Category Three Of Quantum Computing : Category One Of Quantum Advice : Category Two Of Quantum Advice : Category Three Of Quantum AdviceQuantum Adiabatic Algorithms And Quantum Mechanical Nonlinearities : Category One Of Quantum Adiabatic Algorithms : Category Two Of Quantum Adiabatic Algorithms : Category Three Of Quantum Adiabatic Algorithms : Category One Of Quantum Mechanical Nonlinearities : Category Two Of Quantum Mechanical Nonlinearities : Category Threeof Quantum Mechanical NonlinearitiesHidden Variables And Relativistic Time Dilation : Category One Of Hidden Variables : Category Two Of Hidden Varaibles : Category Three Of Hidden Variables : Category One Of Relativistic Time Dilation : Category Two Of Relativistic Time Dilation : Category Three Of Relativistic Time DilationAnalog Computing And Malament Hogarth Space Times :Category One Of Analog Computing : Category Two Of Analog Computing : Category Three Of Analog Computing : Category One Of Malament Hogarth Space Times : Category Two Of Malament Hogarth Space Times : Category Three Of Malament Hogarth Space TimesQuantum Gravity Anthropic Computing : Category One Of Quantum Gravity(Total Gravity Exists) : Category Two Of Quantum Gravity : Category Three Of Quantum Gravity : Category One Of Anthropic Computing : Category Two Of Anthropic Computing : Category Three Of Anthropic Computing 177
  3. 3. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )( )( ) ( )( ) ( )( ) : ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ,( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )are Accentuation coefficients( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )( )( ) ( )( ) ( )( ) , ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )are Dissipation coefficientsGoverning Equations: System: Soap Bubble And Protein FoldingThe differential system of this model is now ( )( ) )( ) ( )( ) ( )] 1 [( ( )( ) )( ) ( )( ) ( )] 2 [( ( )( ) )( ) ( )( ) ( )] 3 [( ( )( ) )( ) ( )( ) ( )] 4 [( ( )( ) )( ) ( )( ) ( )] 5 [( ( )( ) )( ) ( )( ) ( )] 6 [( ( )( ) ( ) First augmentation factor ( )( ) ( ) First detritions factorGoverning Equations: System: Quantum Computing And Quantum AdviceThe differential system of this model is now ( )( ) )( ) ( )( ) ( )] 7 [( ( )( ) )( ) ( )( ) ( )] 8 [( ( )( ) )( ) ( )( ) ( )] 9 [( ( )( ) )( ) ( )( ) (( ) )] 10 [( ( )( ) )( ) ( )( ) (( ) )] 11 [( ( )( ) )( ) ( )( ) (( ) )] 12 [( ( )( ) ( ) First augmentation factor ( )( ) (( ) ) First detritions factorGoverning Equations: System: Quantum Adiabatic Algorithms And Quantum MechanicalNonlinearities:The differential system of this model is now ( )( ) )( ) ( )( ) ( )] 13 [( ( )( ) )( ) ( )( ) ( )] 14 [( 178
  4. 4. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 ( )( ) )( ) ( )( ) ( )] 15 [( ( )( ) )( ) ( )( ) ( )] 16 [( ( )( ) )( ) ( )( ) ( )] 17 [( ( )( ) )( ) ( )( ) ( )] 18 [( ( )( ) ( ) First augmentation factor ( )( ) ( ) First detritions factorGoverning Equations: System: Hidden Variables And Relativistic Time DilationThe differential system of this model is now ( )( ) )( ) ( )( ) ( )] 19 [( ( )( ) )( ) ( )( ) ( )] 20 [( ( )( ) )( ) ( )( ) ( )] 21 [( ( )( ) )( ) ( )( ) (( ) )] 22 [( ( )( ) )( ) ( )( ) (( ) )] 23 [( ( )( ) )( ) ( )( ) (( ) )] 24 [( ( )( ) ( ) First augmentation factor ( ) ( ) (( ) ) First detritions factorGoverning Equations: System: Analog Computing And Malament Hogarth Space TimesThe differential system of this model is now ( )( ) )( ) ( )( ) ( )] 25 [( ( )( ) )( ) ( )( ) ( )] 26 [( ( )( ) )( ) ( )( ) ( )] 27 [( ( )( ) )( ) ( )( ) (( ) )] 28 [( ( )( ) )( ) ( )( ) (( ) )] 29 [( ( )( ) )( ) ( )( ) (( ) )] 30 [( ( )( ) ( ) First augmentation factor ( )( ) (( ) ) First detritions factorGoverning Equations: System: Quantum Gravity And Anthropic ComputingThe differential system of this model is now ( )( ) )( ) ( )( ) ( )] 31 [( ( )( ) )( ) ( )( ) ( )] 32 [( ( )( ) )( ) ( )( ) ( )] 33 [( 179
  5. 5. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 ( )( ) )( ) ( )( ) (( ) )] 34 [( ( )( ) )( ) ( )( ) (( ) )] 35 [( ( )( ) )( ) ( )( ) (( ) )] 36 [( ( )( ) ( ) First augmentation factor ( )( ) (( ) ) First detritions factorSystem: Soap Bubble-Protein Folding –Quantum Computing-Quantum Advice-Quantum AdiabaticAlgorithms –Quantum Mechanical Nonlinearities-Hidden Variables-Relativistic Time Dilation-AnalogComputing-Malament Hogarth Space Times-Quantum Gravity-Anthropic Computing 37 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 38 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 39 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( )Where ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are first augmentation coefficients forcategory 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are second augmentation coefficientfor category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are third augmentation coefficientfor category 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are fourth augmentationcoefficient for category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fifth augmentationcoefficient for category 1, 2 and 3 ( )( ) ( ), ( )( ) ( ) , ( )( ) ( ) are sixth augmentationcoefficient for category 1, 2 and 3 40 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 41 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 42 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 180
  6. 6. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012Where ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are first detrition coefficients forcategory 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are second detrition coefficients forcategory 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are third detrition coefficients forcategory 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fourth detritioncoefficients for category 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are fifth detrition coefficientsfor category 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are sixth detrition coefficientsfor category 1, 2 and 3 43 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 44 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 45 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( )Where ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are first augmentation coefficientsfor category 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are second augmentation coefficientfor category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are third augmentation coefficientfor category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fourth augmentationcoefficient for category 1, 2 and 3 ( )( ) ( ), ( )( ) ( ) , ( )( ) ( ) are fifth augmentationcoefficient for category 1, 2 and 3 ( )( ) ( ), ( )( ) ( ) , ( )( ) ( ) are sixth augmentationcoefficient for category 1, 2 and 3 46 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 181
  7. 7. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 47 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 48 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are first detrition coefficients forcategory 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) , ( )( ) ( ) are second detrition coefficients forcategory 1,2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are third detrition coefficientsfor category 1,2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fourth detritioncoefficients for category 1,2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are fifth detritioncoefficients for category 1,2 and 3 ( )( ) ( ) ( )( ) ( ) , ( )( ) ( ) are sixth detritioncoefficients for category 1,2 and 3 ( )( ) ( )( ) ( ) ( )( )( ) ( )( )( ) 49 ( )( ) [ ] ( )( )( ) ( )( )( ) ( )( )( ) ( )( ) ( )( ) ( ) ( )( )( ) ( )( )( ) 50 ( )( ) [ ] ( )( )( ) ( )( )( ) ( )( )( ) ( )( ) ( )( ) ( ) ( )( )( ) ( )( )( ) 51 ( )( ) [ ] ( )( )( ) ( )( )( ) ( )( )( ) ( )( ) ( ), ( )( ) ( ), ( )( ) ( ) are first augmentation coefficients forcategory 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) , ( )( ) ( ) are second augmentationcoefficients for category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are third augmentationcoefficients for category 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) ( )( ) ( ) are fourthaugmentation coefficients for category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fifth augmentationcoefficients for category 1, 2 and 3 182
  8. 8. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are sixth augmentationcoefficients for category 1, 2 and 3 52 ( )( ) ( )( ) ( ) –( )( )( ) –( )( )( ) ( )( ) [ ] ( )( )( ) ( )( )( ) ( )( )( ) 53 ( )( ) ( )( ) ( ) –( )( )( ) –( )( )( ) ( )( ) [ ] ( )( )( ) ( )( )( ) ( )( )( ) ( )( ) ( )( ) ( ) –( )( )( ) –( )( )( ) 54 ( )( ) [ ] ( )( )( ) ( )( )( ) ( )( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are first detrition coefficients forcategory 1, 2 and 3 ( )( ) ( ) , ( )( ) ( ) , ( )( ) ( ) are second detrition coefficientsfor category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) , ( )( ) ( ) are third detrition coefficients forcategory 1,2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fourth detritioncoefficients for category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fifth detritioncoefficients for category 1, 2 and 3 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are sixth detritioncoefficients for category 1, 2 and 3 55 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 56 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 57 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 183
  9. 9. Mathematical Theory and Modeling www.iiste.orgISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)Vol.2, No.6, 2012 ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) are fourth augmentationcoefficients for category 1, 2,and 3 ( )( ) ( ), ( )( ) ( ) ( )( ) ( ) are fifth augmentationcoefficients for category 1, 2,and 3 ( )( ) ( ), ( )( ) ( ), ( )( ) ( ) are sixth augmentationcoefficients for category 1, 2,and 3 58 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) 59 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) 60 ( )( ) ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) –( )( ) ( ) –( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) , ( )( ) ( ) ( )( ) ( ), ( )( ) ( ), ( )( ) ( )–( )( ) ( ) –( )( ) ( ) –( )( ) ( ) 61 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 62 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 63 ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ( ) [ ] ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) 184

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