self dual instantons and holomorphic curves a gradient flow of a morse function on a compact riemannian manifold is said to be of morse smale type if the stable and unstable manifolds of any two critical points intersect transversally for such a morse smale gradient flow there is a chain complex generated by the critical points and graded by the morse index the boundary operator has as its x y entry the number of gradient flow lines running from x to y counted with appropriate signs whenever the difference of the morse indices is 1 the homology of this chain complex agrees with the homology of the underlying manifold m and this can be used to prove the morse inequalities cf 33 26 around 1986 floer generalized this idea to infinite dimensional variational problems in which every critical point has infinite morse index but the moduli spaces of connecting orbits form finite dimensional manifolds for every pair of critical points the dimensions of these spaces give rise to a relative morse index and the boundary operator is defined by counting connecting

stability and isolation phenomena for yang mills fields in this article a series of results concerning yang mills fields over the euclidean sphere and other locally homogeneous spaces are proved using differential geometric methods one of our main results is to prove that any weakly stable yang mills field overs4 with groupg su2 su3 oru2 is either self dual or anti self dual the analogous statement for so4 bundles is also proved the other main series of results concerns gap phenomena for yang mills fields as a consequence of the non linearity of the yang mills equations we can give explicitc0 neighbourhoods of the minimal yang mills fields which contain no other yang mills fields in this part of the study the nature of the groupg does not matter neither is the dimension of the base manifold constrained to be four

direct digital control auto tuning and supervision using fuzzy logic abstract we describe algorithms for the design and implementation of fuzzy logic controllers and present results of their application to temperature control of a heated air stream auto tuning methods are studied for adjustment of conventional parameters to compensate for actual values of control variables or of external variables and for improvement of performance from observation of results conditions for verifying the consistency of the linguistic protocol with its implementation are presented in an appendix

energy gap for yang mills connections ii arbitrary closed riemannian manifolds abstract we prove an l d 2 energy gap result for yang mills connections on principal g bundles p over arbitrary closed riemannian smooth manifolds of dimension d 2 we apply our version of the ojasiewicz simon gradient inequality 16 19 to remove a positivity constraint on a combination of the ricci and riemannian curvatures in a previous l d 2 energy gap result due to gerhardt 23 theorem 1 2 and a previous l energy gap result due to bourguignon lawson and simons 10 theorem c 11 theorem 5 3 as well as an l 2 energy gap result due to nakajima 42 corollary 1 2 for a yang mills connection over the sphere s d but with an arbitrary riemannian metric

instanton approximation periodic asd connections and mean dimension abstract we study a moduli space of asd connections over s 3 r we consider not only finite energy asd connections but also infinite energy ones so the moduli space is infinite dimensional in general we study the local mean dimension of this infinite dimensional moduli space we show the upper bound on the mean dimension by using a runge approximation for asd connections and we prove its lower bound by constructing an infinite dimensional deformation theory of periodic asd connections

a direct method for minimizing the yang mills functional over 4 manifolds a direct method is employed to minimize the yang mills functional over a 4 dimensional manifold the limiting connection is shown to be yang mills but in a possibly new bundle we show that a topological invariant of the bundle is preserved by the minimizing process this implies the existence of an absolute minimum of the yang mills functional in a wide class of bundles

robust design of rule based fuzzy controllers this paper deals with the design of stable and robust rule based fuzzy control systems new expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented the relation between the modification of the rules and the stability is studied through the so called sensitivity indices the paper presents procedures that make use of these indices to improve the design of fuzzy control systems including the modification of the rules to obtain the global stability of an unstable system with multiple attractors and to improve the dynamic behavior or the robustness of a non linear plant an example with a fuzzy controller for a system with non linear damping and saturation in the actuation is presented to illustrate the design procedure

a pid type fuzzy controller with self tuning scaling factors by relating to the conventional pid control theory we propose a new fuzzy controller structure namely pid type fuzzy controller in order to improve further the performance of the transient state and the steady state of the pid type controller we develop a method to tune the scaling factors of the pid type fuzzy controller on line simulation of the pid type fuzzy controller with the self tuning scaling factors shows a better performance in the transient and steady state response

min max theory for the yang mills higgs equations in each monopole sector there exist an infinite number of finite energy solutions to the prasad sommerfield limit of the su 2 yang mills higgs equations on 3 whose energy is greater than any finite number

a bridge principle for minimal and constant mean curvature submanifolds of rn on demontre un principe de pont qui generalise l etablissement du theoreme de meeks yau la dimension ainsi que la codimension de n 1 et n 2 peuvent etre arbitraires et on ne suppose pas la stabilite on demontre un principe de pont pour des hypersurfaces de courbure moyenne constante

dirichlet and neumann boundary value problems for yang mills connections the yang mills equations have been extensively studied on compact riemannian manifolds without boundary a substantial amount of work has also been done on non compact examples with a boundary component at infinity see 5 10 11 14 15 here we define and describe a solution of dirichlet and neumann boundary value problems for yang mills connections on a compact four dimensional manifold with smooth boundary the equations in the interior are the full yang mills equations we do not restrict ourselves to self dual or anti self dual solutions in the case where the structure group in the gauge theory is abelian our results are contained in the hodge de rham theory for manifolds with boundary see 6 9 4 3 in the general case our results describe a non linear version of this theory the base manifold m of the theory is a compact orientable four dimensional manifold with smooth boundary m we assume that m is endowed with a riemannian metric we consider a principal fiber bundle p over m with structure group g a compact lie group which will have a metric invariant under the adjoint action in the usual example this comes from trace the unknown in the problem is the connection a i e a differential form in p ad g where g is the lie algebra of g there are two natural boundary value problems one of them requires fixing the tangential part of the connection a on the bundle restricted to m if m is locally described as x 0 this amounts to prescribing a1 x dx a2 x dx 2 a3 x dx 3 on m the connection is fixed in the sense that a particular choice is fixed in the gauge equivalence class of a on the boundary the yang mills equations are satisfied in the interior this corresponds to the dirichlet problem in the other boundary value problem we consider a is free at the boundary but the normal part of the curvature is set equal to zero we call this the neumann problem for the dirichlet problem we consider a sequence of l1 connections that minimizes the yang mills functional with prescribed admissible tangential boundary data we show that there exists a weak limiting connection a by finding local good gauges the limiting connection is only locally defined we show that a solves the yang mills equations and satisfies the boundary conditions up to

superconformal simple type and witten s conjecture abstract let x be a smooth closed connected orientable four manifold with b 1 x 0 and b x 3 and odd we show that if x has seiberg witten simple type then the so 3 monopole cobordism formula of 14 implies witten s conjecture relating the donaldson and seiberg witten invariants

a note on weak type l1 boundedness of czos with rough kernels abstract for f s r 2 and l 1 s 1 s 1 x d x 0 define t f x lim 0 x y y y y 2 f x y d y in this paper we shall prove that there is a class of functions in h 1 s 1 l ln l s 1 such that t is weak type l 1 bounded

a heuristic self tuning fuzzy controller abstract in this paper a self tuning fuzzy controller based on the tuning of scaling factors is presented the tuning schemes are tuning the scaling factors is individual tuning rules the tuning rules are transformed into numeric tuning tables by applying suitable membership functions so that the adjustings of the scaling factors are merely matrix mappings since the tuning rules are constructed with the control signal and the output error and change in output error of the plant as their antecedent parts the tuning processes have the advantage of real time property simulation results with a perturbed servo and the inverted pendulum system as the controlled plants show the performance and adaptivity of the proposed controller

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

path connected yang mills moduli spaces on utilise des techniques de min max dans le calcul des variations pour demontrer que les espaces modules des connexions auto duales sur des fibres principaux su 2 ou su 3 sur s 4 sont chemin connexe

energy gap for yang mills connections i four dimensional closed riemannian manifolds we extend an l2l2 energy gap result due to min oo 28 theorem 2 and parker 30 proposition 2 2 for yang mills connections on principal g bundles p over closed connected four dimensional oriented smooth manifolds x from the case of positive riemannian metrics to the more general case of good riemannian metrics including metrics that are generic and where the topologies of p and x obey certain mild conditions and the compact lie group g is su 2 su 2 or so 3 so 3

numerical study of yang mills classical solutions on the twisted torus the authors use the lattice cooling method to investigate the structure of some gauge fixed su 2 yang mills classical solutions of the euclidean equations of motion which are defined in the 3 torus with symmetric twisted boundary conditions

remarks on the yang mills equations in four dimensions cp2 this paper examines properties of solutions to the yang mills equations in four dimensions and in particular on the manifold cp2 two solutions are found one is neither self dual nor anti self dual but is a solution of the full yang mills equations the other is a self dual solution

a framework for morse theory for the yang mills functional on explique comment la theorie de morse pour la fonctionnelle de yang mills peut se retrouver en examinant la restriction de la fonctionnelle a un ensemble denombrable de varietes non compactes de dimension finie

pid type fuzzy controller and parameters adaptive method abstract the authors of this paper try to analyze the dynamic behavior of the product sum crisp type fuzzy controller revealing that this type of fuzzy controller behaves approximately like a pd controller that may yield steady state error for the control system by relating to the conventional pid control theory we propose a new fuzzy controller structure namely pid type fuzzy controller which retains the characteristics similar to the conventional pid controller in order to improve further the performance of the fuzzy controller we work out a method to tune the parameters of the pid type fuzzy controller on line producing a parameter adaptive fuzzy controller simulation experiments are made to demonstrate the fine performance of these novel fuzzy controller structures

the eigenvalue equation on the eguchi hanson space we consider the eigenvalue equation for the laplace beltrami operator acting on scalar functions on the noncompact eguchi hanson space the corresponding differential equation is reducible to a confluent heun equation with ince symbol 0 2 12 we construct approximations for the eigenfunctions and their asymptotic scattering phases with the help of the liouville green approximation wkb furthermore for specific discrete eigenvalues obtained by a continued t fraction we construct the solution by the frobenius method and determine its scattering phase by a monodromy computation

a rule self regulating fuzzy controller abstract the most effective way to improve the performance of a fuzzy controller may be to optimize the fuzzy control rules usually fuzzy control rules are generated by 1 translating the operators experience into fuzzy linguistic form directly 2 monitoring and summarizing the control behaviour of the operators 3 modelling the process to be controlled using fuzzy set theory 4 self organizing in running of the control systems different from the above means the authors in 10 have proposed a method to regulate fuzzy control rules where the control rules are represented by an analytic expression with a regulating factor the authors in this paper employ such a method and use a simplified fuzzy control algorithm which allows fuzzy control rules to be regulated on line thus constructing a rule self regulating fuzzy controller rsfc simulation results demonstrate that the performance of rsfc is better than that of a non rule regulating fuzzy controller

a performance approach to fuzzy control design for nonlinear systems abstract this paper presents a systematic methodology to the design of a decentralized fuzzy logic controller for large scale nonlinear systems a new method which is based on a performance index of sliding mode control is used to derive fuzzy rules and an adaptive algorithm is used to reduce the chattering phenomenon the simulation results of a two inverted pendulum system and a two link manipulator demonstrate that the attractive features of the proposed approach include a smaller residual error and robustness against nonlinear interactions

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

the chern classes of sobolev connections assumef is the curvature field of a connection potential onr4 with finitel2 norm left int limits r 4 left f right 2 dx infty right we show the chern number c 2 1 mathord left vphantom 1 8 right kern nulldelimiterspace 8 pi 2 int limits r 4 f wedge f topological quantum number is an integer this generalizes previous results which showed that the integrality holds forf satisfying the yang mills equations we actually prove the natural general result in all even dimensions larger than 2

the palais smale conditions for the yang mills functional on considere la fonctionnelle de yang mills definie sur des connexions sur un fibre principal sur une variete de riemann compacte de dimension 2 ou 3 on montre que si on considere la fonctionnelle de yang mills comme etant definie sur une variete de hilbert appropriee d orbites des connexions sous l action du groupe des automorphismes du fibre principal alors la fonctionnelle satisfait la condition de palais smale

non self dual yang mills connections with quadrupole symmetry we prove the existence of non self dual yang mills connections onsu 2 bundles over the four sphere specifically on all bundles with second chern number not equal 1 we study connections equivariant under ansu 2 symmetry group to reduce the effective dimensionality from four to one and then use variational techniques the existence of non self dualsu 2 ym connections on the trivial bundle second chern number equals zero has already been established by sibner sibner and uhlenbeck via different methods

removable singularities in yang mills fields we show that a field satisfying the yang mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite we obtain the result that every yang mills field overr4 with bounded functional l2 norm may be obtained from a field ons4 r4 hodge or coulomb gauges are constructed for general small fields in arbitrary dimensions including 4

implementation of the fati hierarchical fuzzy inference system using the immutability decomposition method abstract most practical implementations of fuzzy inference systems chiefly encompass rule based systems fita due to their lower implementation cost classic fuzzy relational inference systems fati are rarely used in practice this paper presents a hierarchical architecture of the fati system which allows one to reduce the resources necessary for its software or hardware implementation the system consists of single input single output siso subsystems which have the same architecture but differ from each other in the contents of their knowledge in the form of fuzzy subrelations these subrelations are created using decomposition of a global fuzzy relation of the primary classic multiple input single output miso fuzzy inference system calculation of the global fuzzy relation based on the knowledge base of the fita system is time consuming and requires much memory to store it therefore decomposition has been moved to the linguistic level decomposition is a lossy operation thus the fuzzy inference result of the hierarchical system is fuzzier than the classic one to avoid inference error we present novel methods based on derivative linguistic values and partitioning of the primary knowledge base with immutability of its contents during the decomposition step which can be used for any fuzzy inference system an example of a fati system proves the suitability of the developed methods in a real practical application

some twisted self dual solutions for the yang mills equations on a hypertorus thesu n yang mills equations are considered in a four dimensional euclidean box with periodic boundary conditions hypertorus gauge invariant twists can be introduced in these boundary conditions to be labeled with integersn n defined modulon the pontryagin number in this space is often fractional whenever this number is zero there are solutions to the equationsg 0 hereg is the covariant curl when this number is not zero we find a set of solutions to the equations g mu nu tilde g mu nu provided that the periodsa of the box satisfy certain relations

gauge theories on four dimensional riemannian manifolds this paper develops the riemannian geometry of classical gauge theories yang mills fields coupled with scalar and spinor fields on compact four dimensional manifolds some important properties of these fields are derived from elliptic theory regularity an energy gap theorem the manifold structure of the configuration space and a bound for the supremum of the field in terms of the energy it is then shown that finite energy solutions of the coupled field equations cannot have isolated singularities this extends a theorem of k uhlenbeck

fuzzy multiple choice knapsack problem abstract this article is intended to present a multiple choice knapsack problem with fuzzy coefficients we propose an approximate algorithm for solving the problem and obtaining some non dominated approximate solutions in the interpretation of the constraints the degree satisfying the inequality between fuzzy numbers is defined on the basis of the agreement index finally a numerical example is shown

on the blow up set of the yang mills flow on kahler surfaces the yang mills flow on a kahler surface with holomorphic initial data converges smoothly away from a singular set determined by the harder narasimhan seshadri filtration of the initial holomorphic bundle

rule regulation of fuzzy sliding mode controller design direct adaptive approach on the basis of sliding mode control smc a fuzzy sliding mode controller fsmc synthesized through rule adaptation is proposed in this paper there are two sets of control rule bases the first set is utilized to approach the equivalent control of smc according to the adaptive scheme another set is used to attenuate the hitting control of smc in the sense of heuristic in particular instead of several tuning parameters needed in conventional fuzzy adaptive approaches only one tuning factor is characterized to adapt the control rules the results show that the rule adaptive fsmc system is stable in the sense of lyapunov under giving a common lyapunov function this direct rule adaptive fsmc is synthesized through the following stages first the control rules are constructed according to the concepts of smc and the fuzzy sets whose membership functions are symmetrically covered in the state space are defined then the derived adaptive law is applied to adjust the given parameter for changing the control rules to meet system dynamic this fsmc is employed to approximate the equivalent control of smc under the situations of the mathematical model of controlled system is unknown third the hitting control which guarantees the stability of control system is developed finally the hitting control signal is smoothed via the constructed heuristic control rules we apply this fsmc to control a nonlinear inverted pendulum system for demonstrating the availability of the proposed approach

a stable motion control system for manipulators via fuzzy self tuning in this paper we present a motion control scheme based on a gain scheduling fuzzy self tuning structure for robot manipulators we demonstrate by taking into account the full non linear and multivariable nature of the robot dynamics that the overall closed loop system is uniformly asymptotically stable besides the theoretical result the proposed control scheme shows two practical characteristics first the actuators torque capabilities can be taken into account to avoid torque saturation and second undesirable effects due to coulomb friction in the robot joints can be attenuated experimental results on a two degrees of freedom direct drive arm show the usefulness of the proposed control approach

quasiconformal 4 manifolds for any pseudo group of homeomorphism of euclidean space one can define the corresponding category of manifolds the most familiar examples in topology are the full pseudo group of homeomorphisms giving rise to the theory of topological manifolds and the subgroup of smooth differomorphisms giving rise to the theory of c manifolds in this paper we discuss an intermediate category quasiconformal homeomorphisms and manifolds recall that a homeomorphism 9 d r n from a domain d in r n to its image 9 d is k quasiconformal if for all x in d

the resolution of the yang mills plateau problem in super critical dimensions abstract we study the minimization problem for the yang mills energy under fixed boundary connection in supercritical dimension n 5 we define the natural function space a g in which to formulate this problem in analogy to the space of integral currents used for the classical plateau problem the space a g can be also interpreted as a space of weak connections on a real measure theoretic version of reflexive sheaves from complex geometry we prove the existence of weak solutions to the yang mills plateau problem in the space a g we then prove the optimal regularity result for solutions of this plateau problem on the way to prove this result we establish a coulomb gauge extraction theorem for weak curvatures with small yang mills density this generalizes to the general framework of weak l 2 curvatures previous works of meyer riviere and tao tian in which respectively a strong approximability property and an admissibility property were assumed in addition

the riemannian geometry of the yang mills moduli space the moduli space of self dual connections over a riemannian 4 manifold has a natural riemannian metric inherited from thel 2 metric on the space of connections we give a formula for the curvature of this metric in terms of the relevant green operators we then examine in great detail the moduli space 1 ofk 1 instantons on the 4 sphere and obtain an explicit formula for the metric in this case in particular we prove that 1 is rotationally symmetric and has finite geometry it is an incomplete 5 manifold with finite diameter and finite volume

magnetic monopoles on three manifolds on etudie des monopoles magnetiques sur une 3 variete de riemann complete orientee m on associe a m une collection d espaces de modules de solutions des equations des monopoles pourvu que m soit non compacte et que la metrique de riemann sur m soit bonne pres de l infini

the so 3 monopole cobordism and superconformal simple type abstract we show that the so 3 monopole cobordism formula from 15 implies that all closed oriented smooth four manifolds with b 1 0 and b 3 and odd with seiberg witten simple type satisfy the superconformal simple type condition defined by marino moore and peradze 28 27 this implies the lower bound conjectured by fintushel and stern 18 on the number of seiberg witten basic classes in terms of topological data

a variational problem with lack of compactness for h1 2 s1 s1 maps of prescribed degree abstract we consider for maps in h 1 2 s 1 s 1 a family of semi norms equivalent to the standard one we ask whether for such a norm there is some map in h 1 2 s 1 s 1 of prescribed topological degree equal to 1 and minimal norm in general the answer is no due to concentration phenomena the existence of a minimal map is sensitive to small perturbations of the norm we derive a sufficient condition for the existence of minimal maps in particular we prove that for every given norm there are arbitrarily small perturbations of it for which the minimum is attained in case there is no minimizer we determine the asymptotic behavior of minimizing sequences we prove that for such minimizing sequences the energy concentrates near a point of s 1 we describe this concentration in terms of bubbling off of circles

weak type l1 boundedness of czos with odd rough kernels abstract for f s r d and l 1 s d 1 s d 1 x d x 0 the singular integral operator t is defined by t f x lim e 0 x y e y y y d f x y d y in this paper we prove some sufficient conditions for odd h 1 such that t is weak type l 1 bounded

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

index energy estimates for yang mills connections and einstein metrics we prove a conformally invariant estimate for the index of schrodinger operators acting on vector bundles over four manifolds related to the classical cwikel lieb rozenblum estimate applied to yang mills connections we obtain a bound for the index in terms of its energy which is conformally invariant and captures the sharp growth rate furthermore we derive an index estimate for einstein metrics in terms of the topology and the einstein hilbert energy lastly we derive conformally invariant estimates for the betti numbers of an oriented four manifold with positive scalar curvature

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

weak type 1 1 bounds for rough operators ii in this paper we consider four operators arising in harmonic analysis in r n 1 they share one feature each is known to be bounded on lp for all 1 p o but for each it has been an open question whether a weak type 1 1 bound also holds in two cases we show that the weak 1 1 bound does hold and for the others we establish weaker estimates which are still sharper than the lp boundedness although the four operators are quite distinct they all involve convolution kernels which are related to the singular integrals of calderon and zygmund but which lack the smoothness required for the usual analysis in each case this defect is mitigated by the presence of some form of curvature consider the bochner riesz means

pu 2 monopoles ii top level seiberg witten moduli spaces and witten s conjecture in low degrees in this article a continuation of 10 we complete the proof for a broad class of four manifolds of witten s conjecture that the donaldson and seiberg witten series coincide at least through terms of degree less than or equal to c 2 where c 1 4 7 11 andandare the euler characteristic and signature of the four manifold we use our computations of chern classes for the virtual normal bundles for the seiberg witten strata from the companion article 10 a comparison of all the orientations and the pu 2 monopole cobordism to compute pairings with the links of level zero seiberg witten moduli subspaces of the moduli space of pu 2 monopoles these calculations then allow us to compute low degree donaldson invariants in terms of seiberg witten invariants and provide a partial verification of witten s conjecture