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Springer Optimization and Its Applications 131 Nicholas J. Daras Themistocles M. Rassias Editors Modern Discrete Mathematics and Analysis With Applications in Cryptography, Information Systems and Modeling Springer Optimization and Its Applications Volume 131 ManagingEditor PanosM.Pardalos,UniversityofFlorida Editor–CombinatorialOptimization Ding-ZhuDu,UniversityofTexasatDallas AdvisoryBoards J.Birge,UniversityofChicago S.Butenko,TexasA&MUniversity F.Giannessi,UniversityofPisa S.Rebennack,KarlsruheInstituteofTechnology T.Terlaky,LehighUniversity Y.Ye,StanfordUniversity AimsandScope Optimizationhasbeenexpandinginalldirectionsatanastonishingrateduringthe lastfewdecades.Newalgorithmicandtheoreticaltechniqueshavebeendeveloped, thediffusionintootherdisciplineshasproceededatarapidpace,andourknowledge ofallaspectsofthefieldhasgrownevenmoreprofound.Atthesametime,oneof themoststrikingtrendsinoptimizationistheconstantlyincreasingemphasisonthe interdisciplinarynatureofthefield.Optimizationhasbeenabasictoolinallareasof appliedmathematics,engineering,medicine,economicsandothersciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focusonalgorithmsforsolvingoptimizationproblemsandalsostudyapplications involvingsuchproblems.Someofthetopicscoveredincludenonlinearoptimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multi-objective programming, description of soft- warepackages,approximationtechniquesandheuristicapproaches. Moreinformationaboutthisseriesathttp://www.springer.com/series/7393 Nicholas J. Daras • Themistocles M. Rassias Editors Modern Discrete Mathematics and Analysis With Applications in Cryptography, Information Systems and Modeling 123 Editors NicholasJ.Daras ThemistoclesM.Rassias DepartmentofMathematics DepartmentofMathematics HellenicMilitaryAcademy NationalTechnicalUniversityofAthens Vari,Greece Athens,Greece ISSN1931-6828 ISSN1931-6836 (electronic) SpringerOptimizationandItsApplications ISBN978-3-319-74324-0 ISBN978-3-319-74325-7 (eBook) https://doi.org/10.1007/978-3-319-74325-7 LibraryofCongressControlNumber:2018943447 MathematicsSubjectCodes(2010):06-XX,11T71,11YXX,14H52,14G50,34L25,34A34,41A05, 41-XX,49M30,60G25,65C20,68M10,68M12,68P25,68P30,68U20,74J20,78A46,81U40,81P94, 90B10,90B20,90C90,94A05,94A15,94A60,97R30,97R60,97U70 ©SpringerInternationalPublishingAG,partofSpringerNature2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Modern Discrete Mathematics and Analysis with Applications in Cryptography consists of contributions written by research scientists from the international mathematicalcommunity. The chapters are devoted to significant advances in a number of theories and problemsofmathematicalanalysisbothcontinuousanddiscretewithapplications. These chapters focus on both old and modern developments of mathematics. Thevolumealsopresentsafewsurveypaperswhichdiscusstheprogressmadein broader areas which could be particularly useful to graduate students and young researchers. We would like to express our deepest thanks to the contributors of chapters as well as to the staff of Springer for their excellent collaboration in the presentation ofthispublication. Vari,Greece NicholasJ.Daras Athens,Greece ThemistoclesM.Rassias October2017 v Contents FixedPointTheoremsinGeneralizedb-MetricSpaces...................... 1 HassenAydiandStefanCzerwik Orlicz Dual Brunn-Minkowski Theory: Addition, Dual QuermassintegralsandInequalities ........................................... 11 Chang-JianZhaoandWingSumCheung ModelingCyber-Security........................................................ 39 NicholasJ.DarasandArgyriosAlexopoulos SolutionsofHardKnapsackProblemsUsingExtremePruning............ 81 E.Daravigkas,K.A.Draziotis,andA.Papadopoulou AComputationalIntelligenceSystemIdentifyingCyber-Attacks onSmartEnergyGrids.......................................................... 97 KonstantinosDemertzisandLazarosIliadis RecentDevelopmentsofDiscreteInequalitiesforConvexFunctions DefinedonLinearSpaceswithApplications.................................. 117 SilvestruSeverDragomir ExtrapolationMethodsforEstimatingtheTraceoftheMatrixInverse... 173 ParaskeviFika MomentGeneratingFunctionsandMomentsofLinearPositive Operators ......................................................................... 187 VijayGupta,NehaMalik,andThemistoclesM.Rassias ApproximationbyLupas.–KantorovichOperators........................... 217 VijayGupta,ThemistoclesM.Rassias,andDeepikaAgrawal Enumerationbye ................................................................ 227 MehdiHassani vii viii Contents Fixed Point and Nearly m-Dimensional Euler–Lagrange-Type AdditiveMappings............................................................... 235 HassanAzadiKenary DiscreteMathematicsforStatisticalandProbabilityProblems ............ 251 ChristosP.KitsosandThomasL.Toulias OntheUseoftheFractalBox-CountingDimension inUrbanPlanning ............................................................... 275 KonstantinaLantitsou,ApostolosSyropoulos,andBasilK.Papadopoulos Additive-Quadraticρ-FunctionalEquationsinBanachSpaces ............ 281 JungRyeLee,ChoonkilPark,andThemistoclesM.Rassias DeBruijnSequencesandSuffixArrays:AnalysisandConstructions..... 297 KonstantinosLimniotis,NicholasKolokotronis,andDimitriosKotanidis FuzzyEmpiristicImplication,ANewApproach............................. 317 KonstantinosMattasandBasilK.Papadopoulos AdaptiveTrafficModellingforNetworkAnomalyDetection............... 333 VassiliosC.Moussas BoundsInvolvingOperators-Godunova-Levin-DragomirFunctions ..... 353 Muhammad Aslam Noor, Muhammad Uzair Awan, andKhalidaInayatNoor Closed-Form Solutions for Some Classes of Loaded Difference EquationswithInitialandNonlocalMultipointConditions ................ 363 I.N.ParasidisandE.Providas Cauchy’sFunctionalEquation,Schur’sLemma,One-dimensional SpecialRelativity,andMöbius’sFunctionalEquation....................... 389 TeerapongSuksumran Plane-Geometric Investigation of a Proof of the Pohlke’s FundamentalTheoremofAxonometry........................................ 397 ThomasL.Toulias DiagonalFixedPointsofGeometricContractions ........................... 423 MihaiTurinici AMoreAccurateHardy–Hilbert-TypeInequality withInternalVariables.......................................................... 485 BichengYang AnOptimizedUnconditionallyStableApproachfortheSolutionof DiscretizedMaxwell’sEquations............................................... 505 TheodorosT.Zygiridis Contributors Deepika Agrawal Department of Mathematics, Netaji Subhas Institute of Tech- nology,NewDelhi,India ArgyriosAlexopoulos CroisySurSeine,France MuhammadUzairAwan GCUniversity,Faisalabad,Pakistan Hassen Aydi Department of Mathematics, College of Education in Jubail, Imam AbdulrahmanBinFaisalUniversity,Jubail,SaudiArabia Wing Sum Cheung Department of Mathematics, The University of Hong Kong, Pokfulam,HongKong Stefan Czerwik Institute of Mathematics, Silesian University of Technology, Gliwice,Poland Nicholas J. Daras Department of Mathematics, Hellenic Military Academy, Vari Attikis,Greece E. Daravigkas Department of Informatics, Aristotle University of Thessaloniki, Thessaloniki,Greece Konstantinos Demertzis School of Engineering, Department of Civil Engineer- ing, Faculty of Mathematics Programming and General Courses, Democritus UniversityofThrace,Xanthi,Greece Silvestru Sever Dragomir Mathematics, College of Engineering & Science, VictoriaUniversity,MelbourneCity,MC,Australia DST-NRFCentreofExcellenceintheMathematicalandStatisticalSciences,School of Computer Science & Applied Mathematics, University of the Witwatersrand, Johannesburg,SouthAfrica K. A. Draziotis Department of Informatics, Aristotle University of Thessaloniki, Thessaloniki,Greece ix x Contributors Paraskevi Fika National and Kapodistrian University of Athens, Department of Mathematics,Athens,Greece VijayGupta DepartmentofMathematics,NetajiSubhasInstituteofTechnology, NewDelhi,India MehdiHassani DepartmentofMathematics,UniversityofZanjan,Zanjan,Iran LazarosIliadis SchoolofEngineering,DepartmentofCivilEngineering,Faculty of Mathematics Programming and General Courses, Democritus University of Thrace,Xanthi,Greece Hassan Azadi Kenary Department of Mathematics, College of Sciences, Yasouj University,Yasouj,Iran ChristosP.Kitsos TechnologicalEducationalInstituteofAthens,Athens,Greece NicholasKolokotronis DepartmentofInformaticsandTelecommunications,Uni- versityofPeloponnese,Tripoli,Greece Dimitrios Kotanidis School of Pure and Applied Sciences, Open University of Cyprus,Latsia,Cyprus KonstantinaLantitsou DemocritusUniversityofThrace,Xanthi,Greece JungRyeLee DepartmentofMathematics,DaejinUniversity,Pocheon,Republic ofKorea Konstantinos Limniotis School of Pure and Applied Sciences, Open University ofCyprus,Latsia,Cyprus HellenicDataProtectionAuthority,Athens,Greece Neha Malik Department of Mathematics, Netaji Subhas Institute of Technology, NewDelhi,India Konstantinos Mattas Democritus University of Thrace, Department of Civil Engineering,Xanthi,Greece Vassilios C. Moussas Laboratory of Applied Informatics, Department of Civil Engineering,UniversityofWestAttica,Egaleo-Athens,Greece KhalidaInayatNoor COMSATSInstituteofInformationTechnology,Islamabad, Pakistan Muhammad Aslam Noor Mathematics Department, King Saud University, Riyadh,SaudiArabia COMSATSInstituteofInformationTechnology,Islamabad,Pakistan Basil K. Papadopoulos Democritus University of Thrace, Department of Civil Engineering,Xanthi,Greece Contributors xi A. Papadopoulou Department of Mathematics, Aristotle University of Thessa- loniki,Thessaloniki,Greece I. N. Parasidis Department of Electrical Engineering, TEI of Thessaly, Larissa, Greece Choonkil Park Research Institute for Natural Sciences, Hanyang University, Seoul,RepublicofKorea E. Providas Department of Mechanical Engineering, TEI of Thessaly, Larissa, Greece ThemistoclesM.Rassias DepartmentofMathematics,NationalTechnicalUniver- sityofAthens,Athens,Greece Teerapong Suksumran Center of Excellence in Mathematics and Applied, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai,Thailand ApostolosSyropoulos GreekMolecularComputingGroup,Xanthi,Greece ThomasL.Toulias TechnologicalEducationalInstituteofAthens,Egaleo,Athens, Greece Mihai Turinici A. Myller Mathematical Seminar, A. I. Cuza University, Ias¸i, Romania Bicheng Yang DepartmentofMathematics,Guangdong UniversityofEducation, Guangzhou,Guangdong,People’sRepublicofChina Chang-Jian Zhao Department of Mathematics, China Jiliang University, Hangzhou,People’sRepublicofChina Theodoros T. Zygiridis Department of Informatics and Telecommunications Engineering,UniversityofWesternMacedonia,Kozani,Greece
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