invariants of 3 manifolds via link polynomials and quantum groups the aim of this paper is to construct new topological invariants of compact oriented 3 manifolds and of framed links in such manifolds our invariant of a link in a closed oriented 3 manifold is a sequence of complex numbers parametrized by complex roots of 1 for a framed link in s 3 the terms of the sequence are equale to the values of the suitably parametrized jones polynomial of the link in the corresponding roots of 1 in the case of manifolds with boundary our invariant is a sequence of finite dimensional complex linear operators this produces from each root of unity q a 3 dimensional topological quantum field theory

on classification of modular tensor categories we classify all unitary modular tensor categories umtcs of rank 4 there are a total of 35 umtcs of rank 4 up to ribbon tensor equivalence since the distinction between the modular s matrix s and s has both topological and physical significance so in our convention there are a total of 70 umtcs of rank 4 in particular there are two trivial umtcs with s 1 each such umtc can be obtained from 10 non trivial prime umtcs by direct product and some symmetry operations explicit data of the 10 non trivial prime umtcs are given in sect 5 relevance of umtcs to topological quantum computation and various conjectures are given in sect 6

a note on a certain boundary layer equation abstract this paper deals with a differential equation of mixing layer the existence of a solution is established by using weyl technique

radiation effects for the blasius and sakiadis flows with a convective surface boundary condition abstract this study aims to analyze the effects of thermal radiation on the laminar boundary layer about a flat plate in a uniform stream of fluid blasius flow and about a moving plate in a quiescent ambient fluid sakiadis flow both under a convective surface boundary condition the resulting similarity energy equation is solved numerically and the variations of dimensionless surface temperature and fluid solid interface characteristics for different values of prandtl number pr radiation parameter nr and parameter a which characterizes our convection processes are graphed and tabulated quite different and interesting behaviours were encountered for a blasius flow compared with a sakiadis flow a comparison with previously published results on special case of the problem shows excellent agreement

a new solution branch for the blasius equation a shrinking sheet problem in this work a similarity equation of the momentum boundary layer is studied for a moving flat plate with mass transfer in a stationary fluid the solution is applicable to the practical problem of a shrinking sheet with a constant sheet velocity theoretical estimation of the solution domain is obtained it is shown that the solution only exists with mass suction at the wall surface the equation with the associated boundary conditions is solved using numerical techniques greatly different from the continuously stretching surface problem and the blasius problem with a free stream quite complicated behavior is observed in the results it is seen that there are three different solution zones divided by two critical mass transfer parameters f 0 1 1 7028 and f 0 2 1 7324 when f 0f 0 2 there is a terminating point for the solution domain and the terminating point corresponds to a special algebraically decaying solution for the current problem the current results provide a new solution branch of the blasius equation which is greatly different from the previous study and provide more insight into the understanding of the blasius equation

a new algorithm for solving classical blasius equation in this paper a reliable algorithm is employed to investigate the classical blasius equation the algorithm is based mainly on applying the adomian decomposition method to the transformation of the blasius equation the results demonstrate reliability and efficiency of the proposed algorithm

fuzzy quantifiers defined over fuzzy domains abstract in this paper we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains the development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers we provide basic examples of these quantifiers and define and investigate also several semantic properties of them finally we prove a theorem saying among other things that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one argument fuzzy quantifiers of this kind

thermal boundary layer problems in a semi infinite flat plate by the differential transformation method this paper investigates the velocity and temperature field in the thermal boundary layer over a semi infinite flat plate the differential transformation method is used to determine some solutions of these velocity and thermal boundary layer problems numerical results for the dimensionless temperature profiles are presented graphically for different values of prandtl number it is found that the results obtained by the present method are in good agreement with those provided by other numerical methods

a finite difference method for the falkner skan equation we present a finite difference method for the solution of the falkner skan equation the method uses a coordinate transformation to map a semi infinite physical domain to the unit interval 0 1 after using a suitable change of variables the transformed third order boundary value problem for this domain is solved using a finite difference scheme the numerical solutions obtained by the present method are in agreement with those obtained by previous authors

a simple perturbation approach to blasius equation in this paper we couple the iteration method with the perturbation method to solve the well known blasius equation the obtained approximate analytic solutions are valid for the whole solution domain comparison with howarth s numerical solution reveals that the proposed method is of high accuracy the first iteration step leads to 6 8 accuracy and the second iteration step yields the 0 73 accuracy of initial slop

infinite chiral symmetry in four dimensions we describe a new correspondence between four dimensional conformal field theories with extended supersymmetry and two dimensional chiral algebras the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four dimensional theory infinite chiral symmetry has far reaching consequences for the spectral data correlation functions and central charges of any four dimensional theory with mathcal n 2 superconformal symmetry

equivariant verlinde algebra from superconformal index and argyres seiberg duality in this paper we show the equivalence between two seemingly distinct 2d tqfts one comes from the coulomb branch index of the class ss theory t g on l k 1 s 1 the other is the lglg equivariant verlinde formula or equivalently partition function of lgclgc complex chern simons theory on s 1 we first derive this equivalence using the m theory geometry and show that the gauge groups appearing on the two sides are naturally g and its langlands dual lglg when g is not simply connected we provide a recipe of computing the index of t g as summation over the indices of t g with non trivial background t hooft fluxes where g is the universal cover of g then we check explicitly this relation between the coulomb index and the equivariant verlinde formula for g su 2 or so 3 in the end as an application of this newly found relation we consider the more general case where g is su n or psu n and show that equivariant verlinde algebra can be derived using field theory via generalized argyres seiberg duality we also attach a mathematica notebook that can be used to compute the su 3 equivariant verlinde coefficients

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

fuzzy quantification a state of the art abstract quantified sentences are a very powerful notion for modelling statements in natural language nl but in practice they have been used to solve several problems this paper is intended to offer a global view of the development on this branch until now focusing in the different approaches dealing with quantification specially those involving imprecision called fuzzy quantification we put attention to the different mechanisms for defining them the evaluation methods for measuring their fulfilment as well as the properties they should satisfy

disturbance observer based adaptive fuzzy control for nonlinear state constrained systems with input saturation and input delay abstract in this paper the problem of disturbance observer based adaptive fuzzy control is studied for nonlinear systems with full state constraints input constraints and unknown external disturbance compared with existing results the unknown compound disturbance is estimated by nonlinear disturbance observer ndo and the input delay is effectively processed by pade approximation different from the mean value theorem and nussbaum function method an auxiliary variable is introduced to obtain the actual control input which reduces the conservativeness of controller design in order to solve the difficulties caused by input saturation and state constraints the auxiliary design functions and barrier lyapunov functions blfs are employed respectively by utilizing adaptive backstepping technique and lyapunov stability theorem a ndo based novel controller is developed it is proved that all the signals of the closed loop systems are semi globally uniformly ultimately bounded sguub the disturbance estimation errors and the tracking errors converge on a small neighborhood of the origin and the full state constraints are not violated simulation results are provided to demonstrate the effectiveness of the proposed method

a framework for fuzzy quantification models analysis a framework for description of fuzzy quantification models is presented within this framework the fuzzy quantified statements evaluation problem is described as the compatibility between the fuzzy quantifier and a fuzzy cardinality or a fuzzy aggregation measure a list of desirable properties for quantification models is presented and those models that fit the framework are confronted with it

argyres douglas theories s 1 reductions and topological symmetries in a recent paper we proposed closed form expressions for the superconformal indices of the a1 a2n 3 and a1 d2n argyres douglas ad superconformal field theories scfts in the schur limit following up on our results we turn our attention to the small s 1 regime of these indices as expected on general grounds our study reproduces the s 3 partition functions of the resulting dimensionally reduced theories however we show that in all cases with the exception of the reduction of the a1 d4 scft certain imaginary partners of real mass terms are turned on in the corresponding mirror theories we interpret these deformations as r symmetry mixing with the topological symmetries of the direct s 1 reductions moreover we argue that these shifts occur in any of our theories whose fourdimensional n 2 superconformal u 1 r symmetry does not obey an su 2 quantization condition we then use our r symmetry map to find the four dimensional ancestors of certain three dimensional operators somewhat surprisingly this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four dimensional theory are encoded in accidental symmetries of the three dimensional theory we also comment on the implications of our work on the space of general n 2 scfts

on the relation between fuzzy and generalized quantifiers fuzzy quantified sentences have been widely applied for modeling statements in natural language since they allow to represent a broad type of intrinsically imprecise quantified statements that are usually linguistically expressed two different frameworks arise in order to model this imprecision in quantification zadeh s fuzzy quantifiers and the fuzzification of generalized quantification for both models several approaches have been developed for assessing the degree of satisfiability of fuzzy quantified sentences we present and compare both models concluding that although the concept of quantifier in each model has not the same semantics we can establish a connection between them and between the evaluation methods in both theories

numerical solutions of the classical blasius flat plate problem abstract this paper presents a numerical study of the non linear differential equation af ff 0 where a prime denotes differentiation with respect to the similarity variable and a is a parameter for a 1 and a 2 this equation is a form of the blasius relation for the flat plate flow in fluid mechanics several numerical solution are obtained using a runge kutta algorithm for high order initial value problems for 1 a 2

an overview of fuzzy quantifiers i interpretations quantification is an important topic in fuzzy theory and its applications an overview is presented for quantification in fuzzy theory after a brief review of quantifiers in first order logic two approaches of generalizing quantifiers are given the algebraic method and the substitution method by distinguishing the fuzziness of predicates and quantifiers various approaches to quantification in fuzzy logic can be organized quantifiers in first order logic can be generalized in crisp sense and these generalized quantifiers can also be applied to fuzzy sets moreover quantifiers themselves can be fuzzy i e they can only be represented by a fuzzy set these different kinds of quantifications are identified quantifiers relate close to the concept of the cardinality of a fuzzy set which is summarized before investigating fuzzy quantifications different to classical logic various semantics of propositions in fuzzy logic fall into different frameworks which are known as the possibility distribution based reasoning system and the many valued fuzzy logics accordingly numerical and possibilistic interpretation explored in literature are reviewed conforming to these two frameworks

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

monopoles and geodesics using the holomorphic geometry of the space of straight lines in euclidean 3 space it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve by means of the atiyah ward ansatz a k

viscous flow and heat transfer over a nonlinearly stretching sheet this paper presents a numerical analysis for flow and heat transfer in a viscous fluid over a nonlinear stretching sheet by employing a novel numerical procedure and two cases are studied namely i the sheet with constant surface temperature cst case and ii the sheet with prescribed surface temperature pst case the governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation the variations of dimensionless surface temperature dimensionless surface temperature gradient as well as flow and heat transfer characteristics with the governing parameters are graphed and tabulated

on fuzzification mechanisms for unary quantification abstract we address a salient issue arising in glockner s two step methodology for modeling vague quantifiers the design of quantifier fuzzification mechanisms qfms these are mechanisms to turn formal models of vague quantifiers operating only on crisp arguments semi fuzzy quantifiers into vague quantifiers accepting vague arguments as well fully fuzzy quantifiers we critically examine desiderata formulated by glockner for qfms and also point out that previous approaches to quantifier fuzzification largely ignored the question whether the resulting quantifiers can be expressed in suitable extensions of t norm based fuzzy logics in particular in ukasiewicz logic we also introduce a new family of qfms and assess it fares with respect to the mentioned desiderata we exclusively focus on unary quantifiers in order to circumvent interference with vagueness related problems arising for all truth functional accounts of quantifiers that refer to more than one argument formula

level based fuzzy generalized quantification abstract we propose a new type of generalized quantification using a recently developed representation of fuzziness by levels this proposal integrates the existent models allowing the extension of crisp quantification to the fuzzy case keeping all the algebraic boolean properties besides the model covers new types of quantification not covered by the existent approaches the advantages of our proposal are clear from the computational and practical perspective since it allows a parallelization of the algorithm by taking into account a fixed number of levels some authors have proposed several properties that a good evaluation method should satisfy we also prove that our proposal fulfills all the desired properties to be considered a good evaluation method

twisted harmonic maps and the self duality equations si m est une surface de riemann compacte on utilise des resultats de la theorie des applications harmoniques pour trouver une solution aux equations d auto dualite associees a une representation irreductible p 1 m psl 2 c