New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences PDF
Preview New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health Bourama Toni Editor New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health SeriesEditor BouramaToni DepartmentofMathematics&Economics VirginiaStateUniversity Petersburg,VA,USA Thegoalofthisinterdisciplinaryseriesistohighlightthewealthofrecentadvances in the pure and applied sciences made by researchers collaborating between fields ofstudywheremathematicsisacorefocus.Aswecontinuetomakefundamental advances in various scientific disciplines, the most powerful applications will increasingly be revealed by an interdisciplinary approach. This series will serve asacatalystfortheseresearchers,todevelopnovelapplicationsof,andapproaches to,themathematicalsciences.Assuch,weexpectthisseriestobecomeanational and international reference in STEAM-H education and research. Because the series will be interdisciplinary by design, a major focus will be on scientists and mathematiciansdevelopingnovelmethodologiesandresearchtechniquesthathave benefitsbeyondasingleresearchcommunity. Thisapproachseekstoconnectresearchersfromacrosstheglobe,unitedinthe common language of the mathematical sciences. Thus, volumes in this series will besuitableforbothstudentsandresearchersinavarietyofinterdisciplinaryfields, suchas:mathematics asitappliestoengineering; physical chemistryandmaterial sciences; environmental, health, behavioral and life sciences; nanotechnology and robotics;computerscience,signal/imageprocessing,andmachinelearning;aswell asfinance,economics,operationsresearch,andgametheory. Originating from the STEAM-H Lecture Series at Virginia State University, all talksaregivenbyinvitedresearchersonly,recognizedasexpertsintheirrespective fields. The weekly yearlong seminar is a dynamic forum for the best faculty to present contributions reflecting the most recent advances in scientific knowledge, deliveredinastandardized,self-containedandpedagogically-orientedmanner,toa multidisciplinary audience of faculty and students, with the objective of fostering student interest and participation in the STEAM-H disciplines as well as genuine interdisciplinary collaborative research. Plenary talks are followed by a one-hour discussion post-presentation on research collaboration and visits, mentorships, internships,andgrantproposals. Moreinformationaboutthisseriesathttp://www.springer.com/series/15560 Bourama Toni Editor New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences 123 Editor BouramaToni DepartmentofMathematics&Economics VirginiaStateUniversity Petersburg,VA,USA ISSN2520-193X ISSN2520-1948 (electronic) STEAM-H:Science,Technology,Engineering,Agriculture,Mathematics&Health ISBN978-3-319-55611-6 ISBN978-3-319-55612-3 (eBook) DOI10.1007/978-3-319-55612-3 LibraryofCongressControlNumber:2017943497 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The multidisciplinary STEAM-H series (Science, Technology, Engineering, Agri- culture, Mathematics, and Health) brings together leading researchers to present theirownworkintheperspectivetoadvancetheirspecificfieldsandinawaytogen- erate a genuine interdisciplinary interaction transcending disciplinary boundaries. All chapters therein were carefully edited and peer-reviewed; they are reasonably self-containedandpedagogicallyexposedforamultidisciplinaryreadership. Contributionsareinvitedonlyandreflectthemostrecentadvancesdeliveredin ahigh-standard,self-containedway.Thegoalsoftheseriesareasfollows: 1. Toenhancemultidisciplinaryunderstandingbetweenthedisciplinesbyshowing howsomenewadvancesinaparticulardisciplinecanbeofinteresttotheother discipline or how different disciplines contribute to a better understanding of a relevantissueattheinterfaceofmathematicsandthesciences 2. Topromotethespiritofinquirysocharacteristicofmathematicsfortheadvances ofthenatural,physical,andbehavioralsciencesbyfeaturingleadingexpertsand outstandingpresenters 3. To encourage diversity in the readers’ background and expertise while struc- turallyfosteringgenuineinterdisciplinaryinteractionsandnetworking Currentdisciplinaryboundariesdonotencourageeffectiveinteractionsbetween scientists; researchers from different fields usually occupy different buildings on universitycampuses,publishinjournalsspecifictotheirfield,andattenddifferent scientific meetings. Existing scientific meetings usually fall into either small gatheringsspecializingonspecificquestions,targetingspecificandsmallgroupof scientistsalreadyawareofeachother’sworkandpotentiallycollaborating,orlarge meetingscoveringawidefieldandtargetingadiversegroupofscientistsbutusually not allowing specific interactions to develop due to their large size and a crowded program. Traditional departmental seminars are becoming so technical as to be largely inaccessible to anyone who did not coauthor the research being presented. Here contributors focus on how to make their work intelligible and accessible to a diverse audience, which in the process enforces mastery of their own field of expertise. v vi Preface Thisvolume,asthepreviousones,stronglyadvocatesmultidisciplinaritywiththe goaltogeneratenewinterdisciplinaryapproaches,instruments,andmodelsinclud- ing new knowledge, transcending scientific boundaries to adopt a more holistic approach. For instance, it should be acknowledged, following Nobel laureate and presidentoftheUK’sRoyalSocietyofChemistry,ProfessorHarryKroto,“thatthe traditionalchemistry,physics,biologydepartmentaliseduniversityinfrastructures— which are now clearly out-of-date and a serious hindrance to progress—must be replaced by new ones which actively foster the synergy inherent in multidisci- plinarity.” The National Institutes of Health and the Howard Hughes Medical Institutehave stronglyrecommended thatundergraduate biologyeducation should incorporate mathematics, physics, chemistry, computer science, and engineering until“interdisciplinarythinkingandworkbecomesecondnature.”Youngphysicists and chemists are encouraged to think about the opportunities waiting for them at theinterfacewiththelifesciences.Mathematicsisplayinganevermoreimportant role in the physical and life sciences, engineering, and technology, blurring the boundariesbetweenscientificdisciplines. Theseriesistobeareferenceofchoiceforestablishedinterdisciplinaryscientists andmathematiciansandasourceofinspirationforabroadspectrumofresearchers andresearchstudents,graduates,andpostdoctoralfellows;thesharedemphasisof thesecarefullyselectedandrefereedcontributedchaptersisonimportantmethods, research directions, and applications of analysis including within and beyond mathematics. As such the volume promotes mathematical sciences, physical and life sciences, engineering, and technology education, as well as interdisciplinary, industrial,andacademicgenuinecooperation. Towardsuchgoalsthefollowingchaptersarefeaturedinthecurrentvolume. Chapters 1, 2, 3, and 4 by Raymond Fletcher extensively study perfect polygons, geometric triple systems, and geometric ramifications in the ternary hypercom- mutativevariety. Chapter5byLarryKeeninvestigatesthepsychoneuroimmunologicalinfluencesof cannabinoids,offeringanopportunityformathematicalmodelingtechniquesin thisareaofneuropsychology. In Chapter 6 by Andrei Khrennikov et al., the authors propose a methodology for imagesegmentationwiththeaidofp-adicmetrics. Chapter7byKlaudiaOleschkoetal.showsthatprimesareeverywherebutnowhere. InChapter8byMarthaOrtiz-Posadas,theauthorpresentsalogicalcombinatorial approachforpatternrecognitioninmedicine. Chapter 9 by Rana Parshad and Brian Ewald is on the uniqueness of invariant measuresforthestochasticinfiniteDarcy-Prandtlnumbermodel. Chapter 10 by K.C. Patidar et al. is concerned with pricing barrier options using integraltransform. InChapter11MattiPitkänendiscussesatlengththephilosophyofadelicphysics. Chapter 12 by Bourama Toni proposes a game-theoretical analysis of cultural integrationandassimilationinAmericaasawayofunderstandingtheevolution ofAmericansocialdynamics. Preface vii The book as a whole certainly enhances the overall objective of the series, that is, to foster the readership interest and enthusiasm in the STEAM-H disciplines (science, technology, engineering, agriculture, mathematics, and health), stimulate graduateandundergraduateresearch,andgeneratecollaborationamongresearchers onagenuineinterdisciplinarybasis. TheSTEAM-HseriesishostedatVirginiaStateUniversity,Petersburg,Virginia, USA, an area that is socially, economically, intellectually very dynamic and home to some of the most important research centers in the USA, including NASA Langley Research Center, manufacturing companies (Rolls-Royce, Canon, Chromalloy, Sandvik, Siemens, Sulzer Metco, NN Shipbuilding, Aerojet), and theiracademicconsortium(CCAM),theUniversityofVirginia,VirginiaTech,the VirginiaLogisticsResearchCenter(CCAL),VirginiaNanotechnologyCenter,The AerospaceCorporation,C3IResearchandDevelopmentCenter,DefenseAdvanced Research Projects Agency, Naval Surface Warfare Center, National Accelerator Facility,andtheHomelandSecurityInstitute. The STEAM-H series, by now well established with a high impact through its intensive seminars and books published by Springer, a world-renowned publisher, is expected to become a national and international reference in interdisciplinary educationandresearch. Petersburg,VA,USA BouramaToni Acknowledgements We would like to express our sincere appreciation to all the contributors and to all the anonymous referees for their professionalism. They all made this volume a realityforthegreaterbenefitofthecommunityofscience,technology,engineering, agriculture,mathematics,andhealth. ix Contents PerfectPolygonsandGeometricTripleSystems ............................. 1 RaymondR.FletcherIII GeometricTripleSystemswithBaseZandZ ............................... 43 n RaymondR.FletcherIII GeometricRamificationsofInvariantExpressionsintheBinary HypercommutativeVariety ..................................................... 95 RaymondR.FletcherIII GeometricRamificationsofInvariantExpressionsintheTernary HypercommutativeVariety ..................................................... 107 RaymondR.FletcherIII ThePsychoneuroimmunologicalInfluencesofRecreationalMarijuana... 123 LarryKeenII,ArlenerD.Turner,DeidrePereira,CliveCallender, andAlfonsoCampbell ImageSegmentationwiththeAid ofthep-AdicMetrics ............................................................ 143 AndreiKhrennikovandNikolayKotovich ThePrimesareEverywhere,butNowhere::: ................................ 155 Klaudia Oleschko, Andrei Khrennikov, Beatriz F. Oleshko, andJean-FrancoisParrot The Logical Combinatorial Approach Applied to Pattern RecognitioninMedicine......................................................... 169 MarthaR.Ortiz-Posadas OntheUniquenessofInvariantMeasuresfortheStochasticInfinite Darcy–PrandtlNumberModel................................................. 189 RanaD.ParshadandBrianEwald xi
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