New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences

365 Pages·2017·3.795 MB·English

by  Bourama Toni (eds.)

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
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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