a nonlinear elliptic equation arising from gauge field theory and cosmology we study radially symmetric solutions of a nonlinear elliptic partial differential equation in r 2 with critical sobolev growth i e the nonlinearity is of exponential type this problem arises from a wide variety of important areas in theoretical physics including superconductivity and cosmology our results lead to many interesting implications for the physical problems considered for example for the self dual chern simons theory we are able to conclude that the electric charge magnetic flux or energy of a non topological n vortex solution may assume any prescribed value above an explicit lower bound for the einstein matter gauge equations we find a necessary and sufficient condition for the existence of a self dual cosmic string solution such a condition imposes an obstruction for the winding number of a string in terms of the universal gravitational constant

the dixmier moeglin equivalence morita equivalence and homeomorphism of spectra abstract let k be a field and let r be a left noetherian k algebra the algebra r satisfies the dixmier moeglin equivalence if the annihilators of irreducible representations are precisely those prime ideals that are locally closed in the spec r and if moreover these prime ideals are precisely those whose extended centres are algebraic extensions of the base field we show that if r and s are two left noetherian k algebras with dim k r dim k s k then if r and s have homeomorphic spectra then r satisfies the dixmier moeglin equivalence if and only if s does in particular the topology of spec r can detect the dixmier moeglin equivalence in this case in addition we show that if k is uncountable and r is affine noetherian and its prime spectrum is a finite disjoint union of locally closed subspaces that are each homeomorphic to the spectrum of an affine commutative ring then r satisfies the dixmier moeglin equivalence we show that neither of these results need hold if k is countable and r is infinite dimensional finally we make the remark that satisfying the dixmier moeglin equivalence is a morita invariant and finally we show that r and s are left noetherian k algebras that satisfy the dixmier moeglin equivalence then r k s does too provided it is left noetherian and satisfies the nullstellensatz and we show that ere also satisfies the dixmier moeglin equivalence where e is a nonzero idempotent of r

self dual maxwell chern simons theory on a cylinder in this paper we study the relativistic maxwell chern simons vortices on an asymptotically flat cylinder a topological multivortex solution is constructed by variational methods and the maxwell and the chern simons limits are verified

existence of bubbling solutions for chern simons model on a torus we study the existence of bubbling solutions for the the following chern simons higgs equation delta u frac1 varepsilon 2 rm e u 1 rm e u 4 pi sum i 1 2k delta p i quad text in omega where is a torus if k 1 for any critical point q of the associated sum of the green functions we introduce a quantity d q see 1 11 below we show that for any non degenerate critical point q with d q 0 the above problem has a solution ue satisfying that e 0 ue blows up at q the calculations in this paper also show that if a sequence of solutions ue blows up at q as e 0 then q must be a critical point of the associated sum of the green functions and d q leqq 0 so the condition d q 0 is almost necessary to obtain our result we also construct solutions with k bubbles for k geqq 2

su 3 chern simons vortex theory and toda systems motivated by the study of the asymptotic properties of non topological condensates in the non abelian chern simons vortex theory see 26 we analyze the su 3 toda system p 1 2 zj j e 2i 1kijzi me i 12kijzi 1 on m mzj 0j 1 2 where m r2 z2 k kij 2 1 12 is the su 3 cartan matrix and j are positive parameters we study the variational problem associated with the system p 1 2 in a range of parameters where the trivial solution is a strict local minimum and the corresponding sobolev type inequality fails to apply in this situation a lack of compactness may occur due to concentration phenomena nonetheless we are able to establish the existence of a non trivial solution for p 1 2 which is not a minimizer

the relativistic non abelian chern simons equations we study ther xr system of nonlinear elliptic equations delta u a lambda sum limits b 1 r k ab e u b lambda sum limits b 1 r sum limits c 1 r e u b k ab e u c k bc 4 pi sum limits j 1 n a delta p aj a 1 2 r x r 2 where 0 is a constant parameter k kab is the cartan matrix of a semi simple lie algebra and p is the dirac measure concentrated atp r 2 this system of equations arises in the relativistic non abelian chern simons theory and may be viewed as a nonintegrable deformation of the integrable toda system we establish the existence of a class of solutions known as topological multivortices the crucial step in our method is the use of the decomposition theorem of cholesky for positive definite matrices so that a variational principle can be formulated

chern simons limit of the standing wave solutions for the schrodinger equations coupled with a neutral scalar field abstract we show the existence of standing wave solutions to the schrodinger equation coupled with a neutral scalar field we also verify the chern simons limit for these solutions more precisely we prove that solutions to eqs 1 3 1 4 converge to the unique positive radially symmetric solution of the nonlinear schrodinger equation 1 6 as the coupling constant q goes to infinity

algebraic structure of multiparameter quantum groups let g be a connected semi simple complex lie group we define and study the multi parameter quantum group cq p g in the case where q is a complex parameter that is not a root of unity using a method of twisting bigraded hopf algebras by a cocycle 2 we develop a unified approach to the construction of cq p g and of the multi parameter drinfeld double dq p using a general method of deforming bigraded pairs of hopf algebras we construct a hopf pairing between these algebras from which we deduce a peterweyl type theorem for cq p g we then describe the prime and primitive spectra of cq p g generalizing a result of joseph in the one parameter case this description was conjectured and established in the sl n case by the first and second authors in 15 16 it was proved in the general case by joseph in 18 19 in particular the orbits in prim cq p g under the natural action of the maximal torus h are indexed as in the one parameter case by the elements of the double weyl group w w unlike the one parameter case there is not in general a bijection between symp g and prim cq p g however in the case when

a system of elliptic equations arising in chern simons field theory we prove the existence of topological vortices in a relativistic self dual abelian chem simons theory with two higgs particles and two gauge fields through a study of a coupled system of two nonlinear elliptic equations over r 2 we present two approaches to prove existence of solutions on bounded domains via minimization of an indefinite functional and via a fixed point argument we then show that we may pass to the full r 2 limit from the bounded domain solutions to obtain a topological solution in r 2

vortex condensations of a non relativistic maxwell chern simons theory abstract we study an elliptic system subject to periodic boundary conditions arising from the study of vortex condensates for a selfdual non relativistic model introduced by dunne et al phys rev d 43 1332 1345 1990 in the framework of chern simons gauge theory we prove the existence of a vortex condensate for all values of the relevant physical parameters involved in the model this completes a recent work of spruck and yang 16 who could deal only with a restricted set of those parameters uniqueness is also discussed

existence of topological vortices in an abelian chern simons model in this paper we prove the existence of topological vortices by variational method applied on an abelian chern simons model with a generic renormalizable potential we also establish some properties of the solutions

new type of nontopological bubbling solutions in the su 3 chern simons model in r2 abstract we are concerned with su 3 chern simons model in r 2 nontopological solutions were shown to exist in 10 in a radially symmetric situation also in 10 there constructed a sequence of partially bubbling solutions of which one component only bubbles we here construct a sequence of radial nontopological bubbling solutions of another type explicitly one component of these bubbling solutions locally converges to a nice function but both components blow up partially in different regions at infinity at the same time this type of bubbling solutions not only is a new phenomenon to this type of systems but also shows a more complicated pattern of the nontopological solution structure than the abelian chern simons higgs equation proposed by 13 15

asymptotic behavior of condensate solutions in the chern simons higgs theory we study the asymptotic behavior of condensate solutions in the chern simons higgs model as the chern simons coupling parameter tends to zero using the variational method we prove that there exist condensate solutions which show concentration phenomena

on the entire radial solutions of the chern simons su 3 system in this paper we study the entire radial solutions of the self dual equations arising from the relativistic su 3 chern simons model proposed by kao and lee phys rev d 50 6626 6632 1994 and dunne phys lett b 345 452 457 1995 nuclear phys b 433 333 348 1995 understanding the structure of entire radial solutions is one of the fundamental issues for the system of nonlinear equations in this paper we prove that any entire radial solutions must be one of topological non topological and mixed type solutions and completely classify the asymptotic behaviors at infinity of these solutions even for radial solutions this classification has remained an open problem for many years as an application of this classification we prove that the two components u and v have intersection at most finite times

on the chern simons higgs vortex equation without gauge fields abstract this paper is concerned with the nonself dual chern simons higgs model on r 2 with vanishing gauge fields we prove the existence of radial solutions with the topological boundary condition and the nonexistence of radial solutions with the nontopological boundary condition we also establish the asymptotic properties of solutions and derive the quantization of the potential energy

rule extraction for fuzzy modeling abstract in this paper a method based on genetic algorithms is proposed to automatically extract fuzzy rules to identify a system where only its input output data are available this method can determine a fuzzy system with fewer fuzzy rules as well as the antecedent and consequent parameters of the fuzzy rules at the same time a nonlinear system is utilized to illustrate the efficiency of the proposed method in the rule extraction for fuzzy modeling

pad analysis of fuzzy control stability abstract by means of an index represented rule mapping the response g of a fuzzy controller is decomposed into two parts f the classical component and g f the nonlinear component called pad we intend to analyse the pad in order to know what the relation is between fuzzy and classical pid controllers fuzzy controllers mentioned here are defuzzified by the typical center of gravity method in the 1 input case we get that f g 0 which means that the fuzzy controller is exactly the same as the classical p controller whenever the rule mapping is simple definition 1 2 and the linguistic values are a binary family definition 4 1 in the 2 input case of error and error change for simple rule mapping and for simple linguistic values family 4 7 and perfectly for the wxyz linguistic values family definition 6 1 the fuzzy controller can be viewed as a series connection of a classical pd controller and a 1 pad element the describing function of a 1 pad element is very simple and fine and ensures that such fuzzy controller will be stable if the pd controller is the similar consequences are also obtained for the case of three inputs

on the chern simons limit for a maxwell chern simons model on bounded domains abstract this paper concerns the chern simons limit for the abelian maxwell chern simons model on bounded domains with vanishing gauge fields we prove that every sequence of solutions of the maxwell chern simons equations has a subsequence converging to a solution of the chern simons equation in any c k norms we also show that the maxwell chern simons equations with the nontopological type boundary condition do not admit any nontrivial solutions on star shaped domains

existence of the semilocal chern simons vortices we consider the bogomol nyi equations of the abelian chern simons higgs model with su n global u 1 local symmetry this is a generalization of the well known abelian chern simons higgs model with u 1 local symmetry we prove existence of both topological and nontopological multivortex solutions of the system on the plane

designing fuzzy inference systems from data an interpretability oriented review fuzzy inference systems fis are widely used for process simulation or control they can be designed either from expert knowledge or from data for complex systems fis based on expert knowledge only may suffer from a loss of accuracy this is the main incentive for using fuzzy rules inferred from data designing a fis from data can be decomposed into two main phases automatic rule generation and system optimization rule generation leads to a basic system with a given space partitioning and the corresponding set of rules system optimization can be done at various levels variable selection can be an overall selection or it can be managed rule by rule rule base optimization aims to select the most useful rules and to optimize rule conclusions space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters structure optimization is of a major importance selecting variables reducing the rule base and optimizing the number of fuzzy sets over the years many methods have become available for designing fis from data their efficiency is usually characterized by a numerical performance index however for human computer cooperation another criterion is needed the rule interpretability an implicit assumption states that fuzzy rules are by nature easy to be interpreted this could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts the paper analyzes the main methods for automatic rule generation and structure optimization they are grouped into several families and compared according to the rule interpretability criterion for this purpose three conditions for a set of rules to be interpretable are defined

a hierarchical fuzzy clustering approach to fuzzy modeling abstract this paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy clustering scheme the method consists of a sequence of steps aiming towards developing a takagi sugeno ts fuzzy model of optimal structure where the fuzzy sets in the premise part are of gaussian type starting from an initial ordinary fuzzy partition of the input space the algorithm performs a nearest neighbor search and groups the original input training data into a number of clusters the centers of these clusters are further processed using an optimal fuzzy clustering technique which is based on the weighted fuzzy c means algorithm the resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters which in a next step are fine tuned using the well known gradient descend algorithm the proposed method is successfully applied to three test examples where the produced fuzzy models prove to be very accurate as well as compact in size

existence theorems for non abelian chern simons higgs vortices with flavor abstract in this paper we establish the existence of vortex solutions for a chern simons higgs model with gauge group su n u 1 and flavor su n these symmetries ensure the existence of genuine non abelian vortices through a color flavor locking under a suitable ansatz we reduce the problem to a 2 2 system of nonlinear elliptic equations with exponential terms we study this system over the full plane and over a doubly periodic domain respectively for the planar case we use a variational argument to establish the existence result and derive the decay estimates of the solutions over the doubly periodic domain we show that the system admits at least two gauge distinct solutions carrying the same physical energy by using a constrained minimization approach and the mountain pass theorem in both cases we get the quantized vortex magnetic fluxes and electric charges

the existence of chern simons vortices a new type of vortices called chern simons vortices is considered and the existence is established

topological multivortex solutions of the self dual maxwell chern simons higgs system abstract we study the existence and various behaviors of topological multivortex solutions of the relativistic self dual maxwell chern simons higgs system we first prove the existence of general topological solutions by applying variational methods to the newly discovered minimizing functional then by an iteration method we prove the existence of topological solutions satisfying some extra conditions which we call admissible solutions we establish asymptotic exponential decay estimates for these topological solutions we also investigate the limiting behavior of the admissible solutions as parameters in our system go to some limits for the abelian higgs limit we obtain strong convergence result while for the chern simons limit we only obtained that our admissible solutions weakly approximate one of the chern simons solutions

existence and uniqueness of topological multivortex solutions of the self dual chern simons cp 1 model abstract in this paper we study the existence and uniqueness of the topological chern simons vortices in the cp 1 model in r 2 after reducing the self dual equations to semilinear elliptic partial differential equations we show that a topological solution exists and it is unique up to a real smooth function if the chern simons coupling constant is sufficiently small

studies on the output of fuzzy controller with multiple inputs abstract in this paper we discuss the output of a fuzzy controller in which an arbitrary number of fuzzy control inputs and an arbitrary number of fuzzy sets employed to fuzzify every linguistic variable are considered in the fuzzy control rules a rule base with a rule mapping concept is considered a defuzzifier with the general t norm and t conorm operators is formulated a triangular family is adopted so that the defuzzifier of the complete rule mapping is represented by a formula consisting of only some rules using a specific logic pair to evaluate values we derive that the output of the fuzzy controller can be simply represented by a linear parametric function of the inputs to the fuzzy controller

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

existence theorems for a general 2 2 non abelian chern simons higgs system over a torus in this paper we study a general 2 2 non abelian chern simons higgs system of the form ui 1e2 j 12kjieuj j 12 k 12kkjkjieujeuk 4 j 1ni pij x i 1 2 over a flat 2 torus t2 where e 0 p is the dirac measure at p ni n i 1 2 k is a non degenerate 2 2 matrix of the form k 1 a a b1 b which may cover the physically interesting case when k is a cartan matrix of a rank 2 semisimple lie algebra concerning the existence results of this type system over t2 usually in the literature there is a requirement that a b 0 however it is an open problem so far for the solvability about such system with a b 0 such that this system admits a solution over the torus if 0 e e0 provided a b are suitably small furthermore if ab 0 in addition with suitable condition on a b n1 n2 this system admits a mountain pass solution our argument is based on a perturbation approach and the mountain pass lemma

groups acting on affine algebras general actions of groups on commutative affine domains are studied we prove a finiteness theorem for orbits of ideals and an ergodic theorem inspired by results from the theories of group algebras and universal enveloping algebras this paper began as a reconsideration of ergodic theorems in the theory of group algebras 2 3 41 the philosophy of these results is the following if a is a lattice i e a group isomorphic to z7 and g is a group of automorphisms of a then g acts on the maximal spectrum of the group algebra k a thus g mixes up the points on a torus the ergodic theorems study the connections between the original action on a and the nature of orbits on the torus although one can obtain many analogues to classical theorems in ergodic theory in this way the program is ultimately insufficient one ought not confine the study to orbits of maximal ideals after all there are likely to be g invariant closed subsets of the torus which are not finite unions of closures of point orbits to account for these more complicated situations we introduce a simple minded but new notion to the theory of groups acting on rings it will turn out that this concept sheds light on old theorems concerning enveloping algebras of lie algebras and suggests new problems in commutative algebra for the remainder of the paper k denotes a commutative field and r is a commutative affine k algebra assume g is a group of k automorphisms of r we are particularly interested in the case that g is infinite the role played by maximal ideals above is taken over by g variant prime ideals a prime ideal p of r is g variant provided that p is maximal among all ideals q such that

asymptotics for maxwell chern simons multivortices chern simons gauge theories are of interest in several areas of physics including high tc superconductivity as they can describe particles which are both electrically and magnetically charged on the other hand the introduction of the chern simons term into the lagrangian results in serious di5culties for a rigorous treatment of the corresponding equations of motion therefore a considerable e7ort has been devoted in recent years to the study of models with a self dual structure such a structure allows us to obtain time independent energy minimizer solutions to the full second order equations of motion by solving appropriate rst order equations also known as the bogomol nyi equations 11 these particular solutions are called multivortices for an overview of self dual chern simons theories see the monograph of dunne 8 in 9 10 hong et al and jackiw and weinberg introduced a chern simons model where the maxwell term is neglected in order to achieve self duality we call this model the cs model the cs multivortices have proved to be particularly interesting from the mathematical viewpoint and have been extensively analyzed see references

nontopological n vortex condensates for the self dual chern simons theory we prove the existence of nontopological n vortex solutions for an arbitrary number n of vortex points for the self dual chern simons higgs theory with t hooft periodic boundary conditions we use a shadowing type lemma to glue together any number of single vortices obtained as a perturbation of a radially symmetric entire solution of the liouville equation 2003 wiley periodicals inc

uniqueness of topological multivortex solutions in the maxwell chern simons model abstract in this paper we prove the uniqueness of topological multivortex solutions for the self dual maxwell chern simons u 1 model if the chern simons coupling parameter is sufficiently large and the charge of electron is sufficiently small or large on the other hand we also establish the sharp region of the flux for non topological solutions and provide the classification of radial solutions of all types in the case of one vortex point

existence of the self graviting chern simons vortices we prove existence of multivortex solutions of the self dual einstein chern simons higgs system proposed by clement phys rev d 54 1844 1847 1996 we consider both the topological and the nontopological boundary conditions for open conformally flat manifolds for nontopological boundary conditions we use perturbation argument from a solution of the liouville equation combined with the implicit function theorem using this argument we have existence for arbitrary positive number for the gravitational constant for topological boundary condition we construct solutions for small gravitational constant by using the super subsolution method for sufficiently large gravitational constant we have a nonexistence result for the radially symmetric topological solutions we also obtain the decay estimates near infinity for both of the topological and the nontopological solutions

control of dynamical processes using an on line rule adaptive fuzzy control system abstract in this paper we present a detailed discussion on the design of a rule adaptive fuzzy control system along with simulation analysis demonstrating its usefulness in controlling plants of various dynamical natures conceived first by wang and further clarified in 8 the rule adaptive fuzzy controller considered here generates the fuzzy control signal as a convex combination of the standard fuzzy inputs to the controller the error and the error rate such a combination is automatically adjusted on line in response to the varying control situations with certain updating scheme this paper considers two different updating schemes the first one is based on a fuzzy relationship and is a revision of the rule presented in 11 the present paper also proposes the second updating rule that is essentially a nonlinear differential equation both of the rules are applied to the simulations of several selected dynamical plants the simulation results show that the controller is effective in controlling a wide range of dynamical plants especially it shows better performance in controlling the plants found difficult to be controlled by the conventional means the simulation also shows that the controller can be used to curb the effect of load disturbance in the control process

switching type fuzzy controller design by genetic algorithms in this paper we propose an effective method to select the parameters of the switching type fuzzy controller by using the genetic algorithm so that a high performance of the overall system s response can be achieved the proposed fitness function contains three performance measures the rise time overshoot and steady state error so that the selected parameters by the proposed method can simultaneously improve the transient response and the steady state response based on the direction of the fitness function an inverted pendulum control design problem is given to illustrate the validity of the proposed method

bubbling solutions for relativistic abelian chern simons model on a torus we prove the existence of bubbling solutions for the following chern simons higgs equation delta u frac 1 varepsilon 2 e u 1 e u 4 pi sum j 1 n delta p j quad rm in omega where is a torus we show that if n 4 and p 1 p j j 2 n then for small e 0 the above problem has a solution u e and as e 0 u e blows up at the vertex point p 1 and satisfies frac 1 varepsilon 2 e u 1 e u to 4 pi n delta p 1 this is the first result for the existence of a solution which blows up at a vertex point

actions of algebraic groups on the spectrum of rational ideals ii let k be an algebraically closed fleld and g a linear algebraic group over k acting rationally on a k algebra v generalizing work of moeglin and rentschler in characteristic zero we study the action of g on the spectrum of rational ideals of v the main result is the following suppose that v is semiprime left goldie let l be a g stable commutative semisimple subalgebra of the total ring of fractions q v of v such that l g k 1l this occurs for example if the zero ideal of v is g rational and l is the center of q v then there is for some closed subgroup h of g a g equivariant embedding of l into q g h the algebra of rational functions on g h such that q g h is purely inseparable over l this has applications to the closure of the orbit of a rational ideal

existence theorems for periodic non relativistic maxwell chern simons solitons abstract we study the system of elliptic equations formula defined over a doubly periodic domain in r 2 where the coefficients are specifically given by the physical model this system arises in a self dual non relativistic maxwell chern simons theory coupled with a neutral scalar field in 2 1 dimensional spacetime and the solutions represent multivortices known as condensates our existence results reveal that the number of vortices confined in a periodic cell domain can be arbitrary and that the chern simons coupling parameter imposes no restriction to the existence of solutions

periodic maxwell chern simons vortices with concentrating property in order to study electrically and magnetically charged vortices in fractional quantum hall effect and anyonic superconductivity the maxwell chern simons mcs model was introduced by lee et al phys lett b 252 79 83 1990 as a unified system of the classical abelian higgs model ah and the chern simons cs model in this article the first goal is to obtain the uniform cs limit result of mcs model with respect to the chern simons parameter without any restriction on either a particular class of solutions or the number of vortex points as the chern simons mass scale tends to infinity the most important step for this purpose is to derive the relation between the higgs field and the neutral scalar field our cs limit result also provides the critical clue to answer the open problems raised by ricciardi and tarantello comm pure appl math 53 811 851 2000 and tarantello milan j math 72 29 80 2004 and we succeed to establish the existence of periodic maxwell chern simons vortices satisfying the concentrating property of the density of superconductive electron pairs furthermore we expect that the cs limit analysis in this paper would help to study the stability multiplicity and bubbling phenomena for solutions of the mcs model

integral ring homomorphisms abstract the purpose of this paper is to extend the classical notion of integral extensions of commutative rings to homomorphisms of affine pi rings it generalizes previous work r pare and w schelter j algebra 53 1978 477 479 w schelter j algebra 40 1976 245 254 errata 44 1979 576 which assumed the existence of centralizing elements without such elements the close relation between integrality and module finiteness breaks down cf examples 1 3 1 4 but the geometric implications of integrality remain our main result theorem 6 3 is an analogue of chevalley s theorem that a homomorphism r s is integral if and only if the induced map on spectra is proper it is proved in sections 6 8 by combining a geometric analysis with some explicit estimates of degrees a corollary is that the composition of integral homomorphisms is integral proposition 6 10 the main new tools we use are central homomorphisms of a ring r to orders over dedekind domains which we call curves we prove theorem 5 13 that the boundary of any constructible set in x spec r contains a dense set of points accessible along such a curve this fact contains a description corollary 5 14 of the zariski topology on x as well as the theorem of bergman and small on degrees of representations corollary 5 15 some of the results of this paper were announced in m artin in proceedings international symposium on algebraic geometry kyoto 1977 pp 237 247

non topological multivortex solutions to the self dual maxwell chern simons higgs systems in this paper we construct non topological multivortex solutions to the non relativistic self dual maxwell chern simons higgs system in r2 which make the energy functional finite moreover our proof of the existence of solutions reveals precise asymptotic behavior of solutions near spatial infinity using exactly the same method we also establish the existence of non topological multivortex solutions to the relativistic self dual maxwell chern simons higgs system

exact sequences of inner automorphisms of tensors abstract we produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor our sequence generalizes known sequences for associative and non associative algebras in a manner similar to those our sequence facilitates inductive reasoning about and calculation of the groups of symmetries of a tensor the new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics

bubbling solutions for the su 3 chern simons model on a torus we consider the following nonlinear system derived from the su 3 chern simons models on a torus where denotes the dirac measure at when if we look for a solution with then 0 1 is reduced to the chern simons higgs equation the existence of bubbling solutions to 0 1 has been a longstanding problem in this paper we prove the existence of such solutions such that even if 2012 wiley periodicals inc

existence of mixed type solutions in the chern simons gauge theory of rank two in r2 abstract we consider the self dual equations arising from the chern simons gauge theory of rank 2 such as the s u 3 s o 5 and g 2 chern simons model in r 2 there are three possible types of solutions in these theories namely topological nontopological and mixed type solutions the existence of a mixed type solution for an arbitrary configuration of vortex points has been a long standing open problem we construct here a family of mixed type solutions u 1 e u 2 e e 0 for an arbitrary configuration of vortex points under a mild non degeneracy condition the main new idea of our construction of an approximate solution is to use different scalings for different components in the process of the finite dimensional reduction all estimates for this particular construction become rather delicate

uniqueness of the topological multivortex solution in the self dual chern simons theory we establish a uniqueness result for the topological multivortex solution to the self dual equations of the abelian relativistic self dual chern simons higgs model we prove that the topological multivortex solution is unique if the chern simons coupling parameter 0 is sufficiently small we also establish a uniqueness result for 0 sufficiently large

nontopological solutions in the self dual maxwell chern simons gauged o 3 sigma model abstract in this paper we prove the existence of nontopological solutions in the self dual maxwell chern simons gauged o 3 sigma model in the plane if the scaling parameter is small enough the reduced equation can be regarded as a perturbation of the liouville equation then we use the generalized implicit function theorem to prove the existence of solutions with nontopological boundary conditions using this result we show the existence of symmetrically topological solutions and nontopological solutions for the original self dual equations whose magnetic fluxes are slightly bigger than the critical value moreover we also compute the topological charge and the degree of the spin vectors

global existence and nonrelativistic limit for the vlasov maxwell chern simons system the vlasov maxwell chern simons system is studied global existence of classical solutions is proved and then its nonrelativistic limit is investigated when the speed of light tends to infinity it is proved that solutions of the vlasov maxwell chern simons system converge to solutions of the vlasov yukawa system in a suitable sense

a self tuning fuzzy controller abstract the aim of a fuzzy controller is to compensate the dynamic characteristics of the controlled system it is the same purpose as for the fuzzy logic controller flc now the best design of the flc is required for achievement of this purpose but such a controller has not yet been completely designed because the fuzzy controller is constructed of control rules which are ambiguously described by conventional controller strategies and expert knowledge and because its structure theory is not well established yet that is in order to construct the best rules a highly skilled technique and a tuning technique using trial and error are required as a way to easily design a flc a method which improves a given standard flc is considered in this paper we propose a self tuning algorithm of the flc it has two functions in adjusting the scaling factors which are the parameters of the flc and in improving the control rules of flc by evaluating the control response at real time and the control results after operations we add these functions to the flc and design the self tuning fuzzy controller stfc this makes the flc a good controller

blow up at infinity in the su 3 chern simons model part i abstract we consider non topological solutions of a nonlinear elliptic system problem see 1 4 below derived from the s u 3 chern simons models in r 2 the existence of non topological solutions even for radial symmetric case has been a long standing open problem recently choe kim and lin in 7 8 showed the existence of radial symmetric non topological solution when the vortex points collapse however the arguments in 7 8 cannot work for an arbitrary configuration of vortex points in this paper we develop a new approach by using different scalings for different components of the system to construct a family of non topological solutions which blows up at infinity

the existence of non topological multivortex solutions in the relativistic self dual chern simons theory we construct a general type of multivortex solutions of the self duality equations the bogomol nyi equations of 2 1 dimensional relativistic chern simons model with the non topological boundary condition near infinity for such construction we use a perturbation argument around the explicit solutions of the liouville equation

existence and nonexistence in chern simons higgs theory with a constant electric charge density in this paper we are devoted to proving the existence and nonexistence of self dual equations arising in chern simons higgs theory with a constant electric charge density there are three kinds of boundary conditions that admit solitonic structures it is shown that there exist solutions in two cases of them in the other case we prove that there is a critical electric charge density with negative value such that above the value there exists a solution and below it we have no solution we also study asymptotic behaviors for solutions as the electric charge density goes to zero it is found that they converge to solutions of a topological chern simons system without constant electric charge density

bubbling solutions for a skew symmetric chern simons system in a torus abstract we establish the existence of bubbling solutions for the following skew symmetric chern simons system u 1 1 e 2 e u 2 1 e u 1 4 i 1 n 1 p i 1 u 2 1 e 2 e u 1 1 e u 2 4 i 1 n 2 p i 2 over a parallelogram with doubly periodic boundary condition where e 0 is a coupling parameter and p denotes the dirac measure concentrated at p we obtain that if n 1 1 n 2 1 1 there exists an e 0 0 such that for any e 0 e 0 the above system admits a solution u 1 e u 2 e satisfying u 1 e and u 2 e blow up simultaneously at the point p and 1 e 2 e u j e 1 e u i e 4 n i p 1 i j 2 i j as e 0 where the location of the point p defined by 1 12 satisfies the condition 1 13

zero order tsk type fuzzy system learning using a two phase swarm intelligence algorithm this paper proposes zero order takagi sugeno kang tsk type fuzzy system learning using a two phase swarm intelligence algorithm tpsia the first phase of tpsia learns fuzzy system structure and parameters by on line clustering aided ant colony optimization aco phase two aims to further optimize all of the free parameters in the fuzzy system using particle swarm optimization pso in clustering aided aco caco fuzzy system structure is learned through on line clustering once a new rule is generated by clustering the consequent is selected from a discrete set of candidate values by aco in aco the path of an ant is regarded as a combination of consequent values selected from every rule caco helps to locate good initial fuzzy systems for subsequent phase learning in phase two initial particles in pso are randomly generated according to the best solution found by caco all free parameters in the designed fuzzy system are optimally tuned by pso simulations on fuzzy control of three nonlinear plants are conducted to verify tpsia performance comparisons with other learning algorithms demonstrate tpsia performance

endomorphisms of right ideals of the weyl algebra let a a k be the first weyl algebra over an infinite field k let p be any noncyclic projective right ideal of a and set s end p we prove that as k algebras s f a in contrast there exists a noncyclic projective right ideal q of s such that s end q thus despite the fact that they are morita equivalent s and a have surprisingly different properties for example under the canonical maps autk a pick a pick s in contrast autk s has infinite index in pick s introduction given a comnmutative domain r the first weyl algebra a r is defined to be the associative r algebra thus r is central subring generated by elements x and y subject to the relation xy yx 1 when no ambiguity is possible we write a for a r let f be a field of characteristic zero then a a f is a simple ring and indeed may be thought of as one of the nicest and most important examples of simple noetherian rings the initial motivation for this paper was the following result of smith if p is the noncyclic right ideal p x2a xy 1 a of a then end p t a as f algebras 11 note that as char f 0 a is a simple hereditary ring and so end p is automatically morita equivalent to a even worse as pedp ada 17 the full matrix rings m2 a and m2 end p are isomorphic thus any proof of smith s result must be fairly subtle and may therefore provide useful invariants for a the first main aim of this paper is to generalize smith s result to an arbitrary projective right ideal of a while the proof of this is harder than that of smith s result it does provide a more informative proof in the sense that unlike smith we do not and cannot require an explicit description of end p for the rest of this introduction k will denote a field of arbitrary characteristic and all isomorphisms of rings will be k algebra isomorphisms theorem a let p be a projective right ideal of a a k then end p a if and only if p is a cyclic right ideal of a see theorem 3 1 this has some easy corollaries corollary b let p and q be projective right ideals of a a k then end p end q if and only if p to q for some t e d k the division ring of fractions of a and a e autk a the group of k automorphisms of a received by the editors february 13 1986 1980 mathematics subject classification 1985 revision primary 16a65 16a72 16a19 supported in part by an nsf grant 1987 american mathematical society 0002 9947 87 1 00 25 per page

existence and asymptotics of topological solutions in the self dual maxwell chern simons o 3 sigma model we are concerned with the topological vortex equations arising in the self dual maxwell chern simons o 3 sigma model we prove the existence of solutions for any parameters and q by a variational method we also verify both the maxwell limit and the chern simons limit for the variational solutions

picard groups and infinite matrix rings we describe a connection between the picard group of a ring with local units t and the picard group of the unital overring end tt using this connection we show that the three groups pic r pic fm r and pic rfm r are isomorphic for any unital ring r furthermore eaclh ele ment of pic rfm r arises from an automorphism of rfm r which yields an isomorphsm between pic rfm r and out rfm r as one applica tion we extend a classical result of rosenberg and zelinsky by showing that the group outr rfm r is abelian for any commutative unital ring r

on invertible bimodules and automorphisms of noncommutative rings in this article we attempt to generalize the result that for a commu tative ring r the outer automorphism group of i automorphisms of m r is abelian of exponent n it is shown that a slightly weaker stable version of the result is still valid for affine semiprime noetherian pi rings we also show that the automorphism group of an affine commutative domain of positive di mension acts faithfully on the spectrum of the domain we investigate other questions involving bimodules and automorphisms and extend a result of smith on the first weyl algebra as a fixed ring let r be a ring with 1 in this article we are interested in comparing the automorphism group of mn r the ring of x matrices over r and the automorphism group of r in particular if r is commutative it is a classical result that the outer automorphism group of r automorphisms of mn r is an abelian group of exponent dividing this can be restated in terms of invertible bimodules the result is equivalent to the easy fact that any projective rank one module x with nx free over a commutative ring has order dividing in the picent group of r see rz and ko in the noncommutative case there is still a well known relationship between automorphisms and the picard

a self generating method for fuzzy system design abstract in this paper a self generating method based on genetic algorithms is proposed to automatically construct a fuzzy system a parameter structure of fuzzy system is presented along with a fuzzy set elimination method which enables the self generating method not only to determine an appropriate fuzzy system with a high performance but also to favor the selected system with fewer fuzzy rules an inverted pendulum control and a system modeling problem are utilized respective to illustrate the efficiency of the proposed method in the fuzzy system design

local and global solutions of the chern simons higgs system abstract we study low regularity solutions of the chern simons higgs equations the lorentz gauge condition makes them hyperbolic equations with the null form under the coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation the div curl decomposition is used in the temporal gauge

the solution structure of the o 3 sigma model in a maxwell chern simons theory in this paper a system of semilinear elliptic equations arising from a relativistic self dual maxwell chern simons o 3 sigma model is considered we reveal the uniqueness aspect of the topological solutions for the model the uniqueness result is associated with a clear solution structure of the equations of the radially symmetric case we locate each solution set denoted by a planar diagram

nonself dual chern simons and maxwell chern simons vortices on bounded domains abstract we first show the existence of the multivortex solutions of maxwell chern simons higgs mcsh model on bounded domains and prove that the solutions of the euler lagrange equations of the mcsh energy functional converge to those of the abelian higgs ah model and the chern simons higgs csh model in suitable limits respectively we also show the existence of the multivortex solutions of the nonself dual csh model on bounded domains besides we study asymptotics for the minimizers of mcsh energy functional when the gauge field vanishes