Table Of ContentTrends in Mathematics
V. Madhu
A. Manimaran
D. Easwaramoorthy
D. Kalpanapriya
M. Mubashir Unnissa
Editors
Advances in
Algebra and
Analysis
International Conference on
Advances in Mathematical Sciences,
Vellore, India, December 2017 -
Volume I
Trends in Mathematics
Trends in Mathematics is a series devoted to the publication of volumes arising
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V. Madhu • A. Manimaran • D. Easwaramoorthy
D. Kalpanapriya • M. Mubashir Unnissa
Editors
Advances in Algebra
and Analysis
International Conference on Advances
in Mathematical Sciences, Vellore, India,
December 2017 - Volume I
Editors
V.Madhu A.Manimaran
DepartmentofMathematics DepartmentofMathematics
SchoolofAdvancedSciences SchoolofAdvancedSciences
VelloreInstituteofTechnology VelloreInstituteofTechnology
Vellore,TamilNadu,India Vellore,TamilNadu,India
D.Easwaramoorthy D.Kalpanapriya
DepartmentofMathematics DepartmentofMathematics
SchoolofAdvancedSciences SchoolofAdvancedSciences
VelloreInstituteofTechnology VelloreInstituteofTechnology
Vellore,TamilNadu,India Vellore,TamilNadu,India
M.MubashirUnnissa
DepartmentofMathematics
SchoolofAdvancedSciences
VelloreInstituteofTechnology
Vellore,TamilNadu,India
ISSN2297-0215 ISSN2297-024X (electronic)
TrendsinMathematics
ISBN978-3-030-01119-2 ISBN978-3-030-01120-8 (eBook)
https://doi.org/10.1007/978-3-030-01120-8
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Preface
TheDepartmentofMathematics,SchoolofAdvancedSciences,VelloreInstituteof
Technology (Deemed to be University), Vellore, Tamil Nadu, India, organized the
International Conference on Advances in Mathematical Sciences—2017 (ICAMS
2017) in association with the Society for Industrial and Applied Mathematics
VIT Chapter from December 1, 2017 to December 3, 2017. The major objective
of ICAMS 2017 was to promote scientific and educational activities toward the
advancement of common man’s life by improving the theory and practice of
various disciplines of Mathematics. This prestigious conference was partially
financially supported by the Council of Scientific and Industrial Research (CSIR),
India. The Department of Mathematics has 90 qualified faculty members and 30
research scholars, and all were delicately involved in organizing ICAMS 2017
grandly. In addition, 30 leading researchers from around the world served as an
advisory committee for this conference. Overall, more than 450 participants (pro-
fessors/scholars/students)enrichedtheirknowledgeinthewingsofMathematics.
Therewere9eminentspeakersfromoverseasand33expertsfromvariousstates
of India who delivered the keynote address and invited talks in this conference.
Manyleadingscientistsandresearchersworldwidesubmittedtheirqualityresearch
articles to ICAMS. Moreover, 305 original research articles were shortlisted for
ICAMS 2017 oral presentations that were authored by dynamic researchers from
25 states in India and 20 countries around the world. We hope that ICAMS will
furtherstimulateresearchinMathematics,shareresearchinterestandinformation,
andcreateaforumofcollaborationandbuildatrustrelationship.Wefeelhonored
andprivilegedtoservethebestofrecentdevelopmentsinthefieldofMathematics
tothereader.
A basic premise of this book is that quality assurance is effectively achieved
throughtheselectionofqualityresearcharticlesbyascientificcommitteeconsisting
of more than 100 reviewers from all over the world. This book comprises the
contributionofseveraldynamicresearchersin52chapters.Eachchapteridentifies
the existing challenges in the areas of Algebra, Analysis, Operations Research,
and Statistics and emphasizes the importance of establishing new methods and
algorithmstoaddressthechallenges.Eachchapterpresentsaresearchproblem,the
v
vi Preface
techniquesuitableforsolvingtheproblemwithsufficientmathematicalbackground,
and discussions on the obtained results with physical interruptions to understand
the domain of applicability. This book also provides a comprehensive literature
survey which reveals the challenges, outcomes, and developments of higher level
mathematicsinthisdecade.Thetheoreticalcoverageofthisbookisrelativelyata
higher level to meet the global orientation of mathematics and its applications in
scienceandengineering.
The target audience of this book is postgraduate students, researchers, and
industrialists. This book promotes a vision of pure and applied mathematics as
integral to modern science and engineering. Each chapter contains important
information emphasizing core Mathematics, intended for the professional who
alreadypossessesabasicunderstanding.Inthisbook,theoreticallyorientedreaders
willfindanoverviewofMathematicsanditsapplications.Industrialistswillfinda
variety of techniques with sufficient discussion in terms of physical point of view
to adapt for solving the particular application based on mathematical models. The
reader can make use of the literature survey of this book to identify the current
trendsinMathematics.Itisourhopeandexpectationthatthisbookwillprovidean
effectivelearningexperienceandreferencedresourceforallyoungmathematicians.
AsEditors,wewouldliketoexpressoursincerethankstoalltheadministrative
authorities of Vellore Institute of Technology, Vellore, for their motivation and
support. We also extend our profound thanks to all faculty members and research
scholars of the Department of Mathematics and all staff members of our institute.
WeespeciallythankallthemembersoftheorganizingcommitteeofICAMS2017
who worked as a team by investing their time to make the conference a great
success.Wethankthenationalfundingagency,CouncilofScientificandIndustrial
Research (CSIR), Government of India, for the financial support they contributed
toward the successful completion of this international conference. We express our
sincere gratitude to all the referees for spending their valuable time to review the
manuscripts, which led to substantial improvements and selection of the research
papers for publication. The organizing committee is grateful to Mr. Christopher
Tominich, Editor at Birkhäuser/Springer, for his continuous encouragement and
supporttowardthepublicationofthisbook.
Vellore,India V.Madhu
Vellore,India A.Manimaran
Vellore,India D.Easwaramoorthy
Vellore,India D.Kalpanapriya
Vellore,India M.MubashirUnnissa
Contents
PartI Algebra
IT-2FuzzyAutomataandIT-2FuzzyLanguages ............................ 3
M.K.Dubey,P.Pal,andS.P.Tiwari
LevelSetsofi_v_Fuzzyβ-Subalgebras........................................ 13
P.HemavathiandK.Palanivel
Interval-ValuedFuzzySubalgebraandFuzzy
INK-IdealinINK-Algebra...................................................... 19
M.Kaviyarasu,K.Indhira,V.M.Chandrasekaran,andJacobKavikumar
OnDendritesGeneratedbySymmetricPolygonalSystems:The
CaseofRegularPolygons ....................................................... 27
MarySamuel,DmitryMekhontsev,andAndreyTetenov
EfficientAuthenticationSchemeBasedontheTwistedNear-Ring
RootExtractionProblem........................................................ 37
V.Muthukumaran,D.Ezhilmaran,andG.S.G.N.Anjaneyulu
DimensionalityReductionTechniquetoSolveE-CrimeMotives........... 43
R.AartheeandD.Ezhilmaran
PartiallyOrderedGammaNear-Rings........................................ 49
T.Nagaiah
NovelDigitalSignatureSchemewithMultiplePrivateKeyson
Non-commutativeDivisionSemirings ......................................... 57
G.S.G.N.AnjaneyuluandB.Davvaz
CozeroDivisorGraphofaCommutativeRoughSemiring ................. 67
B.Praba,A.Manimaran,V.M.Chandrasekaran,andB.Davvaz
vii
viii Contents
GorensteinFI-FlatComplexesand(Pre)envelopes.......................... 77
V.Biju
BoundsofExtremeEnergyofanIntuitionisticFuzzyDirectedGraph.... 85
B.Praba,G.Deepa,V.M.Chandrasekaran,KrishnamoorthyVenkatesan,
andK.Rajakumar
PartII Analysis
OnUltraSeparationAxiomsviaαω-OpenSets .............................. 97
M.Parimala,CenapOzel,andR.Udhayakumar
Common Fixed Point Theorems in 2-Metric Spaces Using
CompositionofmappingsviaA-Contractions................................ 103
J. Suresh Goud, P. Rama Bhadra Murthy, Ch. Achi Reddy,
andK.MadhusudhanReddy
CoefficientBoundsforaSubclassofm-FoldSymmetricλ-Pseudo
Bi-starlikeFunctions............................................................. 111
JayM.Jahangiri,G.Murugusundaramoorthy,K.Vijaya,andK.Uma
LaplacianandEffectiveResistanceMetricinSierpinski
GasketFractal.................................................................... 121
P.UthayakumarandG.Jayalalitha
SomePropertiesofCertainClassofUniformlyConvexFunctions
DefinedbyBesselFunctions .................................................... 131
V.Srinivas,P.ThirupathiReddy,andH.Niranjan
ANewSubclassofUniformlyConvexFunctionsDefinedbyLinear
Operator .......................................................................... 141
A.NarasimhaMurthy,P.ThirupathiReddy,andH.Niranjan
CoefficientBoundsofBi-univalentFunctionsUsingFaberPolynomial ... 151
T.JananiandS.Yalcin
ConvexityofPolynomialsUsingPositivityofTrigonometricSums......... 161
PriyankaSangalandA.Swaminathan
LocalCountableIteratedFunctionSystems.................................. 169
A.GowrisankarandD.Easwaramoorthy
OnIntuitionisticFuzzyC-Ends ................................................ 177
T.YogalakshmiandOscarCastillo
GeneralizedAbsoluteRieszSummabilityofOrthogonalSeries............ 185
K.KalaivaniandC.Monica
Holder’s Inequalities for Analytic Functions Defined by
Ruscheweyh-Typeq-DifferenceOperator..................................... 195
N.Mustafa,K.Vijaya,K.Thilagavathi,andK.Uma
Contents ix
FuzzyCutSet-BasedFilterforFixed-ValueImpulseNoiseReduction .... 205
P.S.EliahimJeevaraj,P.Shanmugavadivu,andD.Easwaramoorthy
On(p,q)-QuantumCalculusInvolvingQuasi-Subordination ............. 215
S.Kavitha,NakEunCho,andG.Murugusundaramoorthy
PartIII OperationsResearch
SensitivityAnalysisforSpanningTree ........................................ 227
K.KavithaandD.Anuradha
OnSolvingBi-objectiveFuzzyTransportationProblem .................... 233
V.E.SobanaandD.Anuradha
NonlinearProgrammingProblemforanM-DesignMulti-SkillCall
CenterwithImpatienceBasedonQueueingModelMethod................ 243
K.BanuPriyaandP.Rajendran
Optimizing a Production Inventory Model with Exponential
DemandRate,ExponentialDeteriorationandShortages ................... 253
M.DhivyaLakshmiandP.Pandian
Analysis of Batch Arrival Bulk Service Queueing System with
Breakdown,DifferentVacationPoliciesandMultiphaseRepair........... 261
M.ThangarajandP.Rajendran
AnImprovementtoOne’sBCMfortheBalancedandUnbalanced
TransshipmentProblemsbyUsingFuzzyNumbers ......................... 271
KirtiwantP.Ghadle,PriyankaA.Pathade,andAhmedA.Hamoud
An Articulation Point-Based Approximation Algorithm for
MinimumVertexCoverProblem............................................... 281
JayanthKumarThenepalleandPurusothamSingamsetty
OnBottleneck-RoughCostIntervalIntegerTransportationProblems.... 291
A.Akilbasha,G.Natarajan,andP.Pandian
Direct Solving Method of Fully Fuzzy Linear Programming
ProblemswithEqualityConstraintsHavingPositiveFuzzyNumbers..... 301
C.MuralidaranandB.Venkateswarlu
AnOptimalDeterministicTwo-WarehouseInventoryModelfor
DeterioratingItems .............................................................. 309
K.RangarajanandK.Karthikeyan
AnalysisonTimetoRecruitmentinaThree-GradeMarketing
OrganizationHavingClassifiedSourcesofDepletionofTwoTypes
withanExtendedThresholdandShortageinManpowerForms
GeometricProcess ............................................................... 315
S.PoornimaandB.EstherClara
