Department of Mathematicshttp://hdl.handle.net/123456789/122017-09-25T07:59:12Z2017-09-25T07:59:12ZA NEW APPROACH ON COMPLEMENT AND ISOMORPHISM OF BIPOLAR FUZZY GRAPHSNimra Jamil CIIT/FA14-MSMATH-023/LHRhttp://hdl.handle.net/123456789/4232016-12-29T10:57:36Z2016-01-01T00:00:00ZA NEW APPROACH ON COMPLEMENT AND ISOMORPHISM OF BIPOLAR FUZZY GRAPHS
Nimra Jamil CIIT/FA14-MSMATH-023/LHR
In this research, a new definition of bipolar fuzzy graphs is
introduced by using Lukasiewicz t-norm and used to
reconstructed definitions of operations of bipolar fuzzy graph.
Also, we investigated relations between operations union, join
and complement. We also verify different existing results in new
scenario.
2016-01-01T00:00:00ZAnalytical study of NLSE in optical solutionsIjaz Ali CIIT/FA14-MSMATH-015/LHRhttp://hdl.handle.net/123456789/4222016-12-29T10:27:46Z2016-01-01T00:00:00ZAnalytical study of NLSE in optical solutions
Ijaz Ali CIIT/FA14-MSMATH-015/LHR
A soliton is a wave pulse, which does not change its shape and speed and after collid-
ing with other solitons it maintains its shape and speed during the wave propagation.
Solitons have lots of applications in different fields of sciences like plasma physics,
optics. Optical solitons have great significance in field of telecommunication. There
are many types of solitons, for example temporal, vortex and spatial solitons. Solitons
were first observed as a solution of Non-Linear Schrodinger’s Equation (NLSE) by Za-
kharov. There are some other types of soliton solutions like bright soliton, dark soliton,
singular soliton. These soliton solutions can be found by using different laws of non-
linearities like Kerr law, Power law, Parabolic law, Dual-power law, Exponential law,
Logatithmic law etc. This dissertation finds out the bright, dark, singular 1-soliton
solutions for the Non-Linear Schrodinger’s Equation (NLSE)by using ansatz method
with the help of Dual-power law in two core fibers. We also compute the same soliton
solutions using Tripple power law of non-linearity
2016-01-01T00:00:00ZSome Inflationary Issues in Braneworld ScenarioAmara Ilyas CIIT/FA14-MSMATH-007/LHRhttp://hdl.handle.net/123456789/4212016-12-29T10:23:18Z2016-05-01T00:00:00ZSome Inflationary Issues in Braneworld Scenario
Amara Ilyas CIIT/FA14-MSMATH-007/LHR
In thisthesis,ourmaingoalistoexaminethepossiblerealizationofwarm
logamediate inflation,intermediateinflationandchaoticinflationwithinthe
frameworkofbrane-worldthroughmodifiedchaplygingasandbulkviscous
pressure. Inthiscontext,wedevelopinflaton(ϕ), effectivepotential(V (ϕ))
and entropydensity(S) forvariableaswellasconstantdissipationand
bulk viscouscoefficientsathighdissipativeregime.Wealsoinvestigate
the necessaryinflationaryparameters,i.e,theslow-rollparameters(ϵ, η),
numberofe-folds(N), scalar-tensorpowerspectra(PR), spectralindex
(ns), tensor-scalarratio(r) andrunningofscalarspectralindex(αs). These
parameters arebeinganalyzedforbothcasesofdissipationandbulkviscous
coefficients.Thetrajectoriesamongtheinflationaryparameterssuchas
ns−ϕ, ns−r, αs−ϕ and ns−αs are alsodevelopedtoexaminetheirbehavior
as wellasphysicalcosmology.Someresultsofinflationaryparametersare:
r < 0.11, ns = 0.96 ± 0.025 and αs = −0.019 ± 0.025. Itisinteresting
to mentionherethattheseresultsofinflationaryparametersareconsistent
with BICEP2,WMAP(7+9)andPlanckdata
2016-05-01T00:00:00ZExistence of Wormholes in f(R,T) Theory of GravityYasir Ahmad CIIT/FA14-MSMATH-016/LHRhttp://hdl.handle.net/123456789/4202016-12-29T09:58:42Z2016-05-01T00:00:00ZExistence of Wormholes in f(R,T) Theory of Gravity
Yasir Ahmad CIIT/FA14-MSMATH-016/LHR
In this thesis,weexplore wormholesolutionsin f(R, T) theoryofgravity,
where R is satisfyingthescalarcurvatureand T the traceofenergymomen-
tum tensorofthematter.ItiswidelyknownthattheEinsteinequations
in GRnecessarilyviolatedtheenergyconditionsduetoexoticmatterwhile
finding thesolutionsfortraversablewormholes.Intheframeworkofmod-
ified theories,staticwormholethroatsobeyingthenullenergycondition
(NEC) canexist.
In ourwork,weconsiderthenormalformofmatterwhichistreading
the wormholesandsatisfyingtheenergyconditions(afundamentalprop-
ertyofordinarymatter).Wehavealsoanalyzedthattheeffectiveenergy
momentumtensorarisingin f(R, T) theoryofgravityisresponsibleforthe
violation oftheNEC.Further,weinvestigatedthepossibilityofstaticand
spherically symmetricgeometriesrepresentingthetraversablewormholein
f(R, T) gravity.Thesearchofphysicalmodelsprovidingtherealisticworm-
hole existencerepresentsanimportantdirectioninwormholephysics.
Toinvestigatethis,weconsiderstaticsphericallysymmetricgeometry
with mattercontentsasanisotropic,isotropicandbarotropicfluidsinthree
separate cases.Bytakingaviable f(R) modelintoaccount,weanalyzethe
behaviorofenergyconditionsforthesedifferentkindoffluids.Itisshown
that thewormholesolutionscanbeconstructedwithoutexoticmatterin
few regionsofspacetime.Wealsogivethegraphicalillustrationofobtained
results anddiscusstheequilibriumpictureforanisotropiccaseonly.Itis
concluded thatthewormholesolutionswithanisotropicmatterarerealistic
and stableinthisgravity.
2016-05-01T00:00:00Z