cooperative fuzzy model predictive control in this paper a cooperative fuzzy model predictive control cfmpc is presented the overall nonlinear plant is assumed to consist of several parallel input coupled takagi sugeno t s fuzzy models each such t s fuzzy subsystem is represented in the form of a local linear model network llmn the control of each local linear model in each llmn is realized by model predictive control mpc for each llmn the outputs of the associated mpcs are blended by the fuzzy membership functions which leads to a fuzzy model predictive controller fmpc the resulting structure is one fmpc for each llmn subsystem overall a parallel combination of fmpcs results which mutually affects all llmn subsystems by their respective manipulated variables to compensate detrimental cross couplings in this setup a cooperation between the fmpcs is introduced for this cooperation convergence is proven and for the closed loop system a stability proof is given it is demonstrated in a simulation example that the proposed input constraint cfmpc algorithm achieves convergence of the fuzzy llmns within few cooperative iteration steps simulations are given to demonstrate the effectiveness of the theoretical results

on the interpretation and identification of dynamic takagi sugeno fuzzy models dynamic takagi sugeno fuzzy models are not always easy to interpret in particular when they are identified from experimental data it is shown that there exists a close relationship between dynamic takagi sugeno fuzzy models and dynamic linearization when using affine local model structures which suggests that a solution to the multiobjective identification problem exists however it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes due to the multiobjective nature of the identification problem studied here special considerations must be made during model structure selection experiment design and identification in order to meet both objectives some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied these include constrained and regularized identification and locally weighted identification their usefulness in the present context is illustrated by examples

conformal blocks and generalized theta functions let yp be the moduli space of rank r vector bundles with trivial determinant on a riemann surface x this space carries a natural line bundle the determinant line bundle s we describe a canonical isomorphism of the space of global sections of sk with the space of conformal blocks defined in terms of representations of the lie algebra 5 c z it follows in particular that the dimension of h yk is given by the verlinde formula

gromov witten invariants in algebraic geometry gromov witten invariants for arbitrary non singular projective vari eties and arbitrary genus are constructed using the techniques from k behrend b fantechi the intrinsic normal cone

the cohomology rings of moduli spaces of bundles over riemann surfaces the cohomology of the moduli space ji n d of semistable bundles of coprime rank n and degree d over a fixed riemann surface m of genus g 2 has been much studied over the last two decades and a great deal is known about it it is known that the cohomology has no torsion 2 the betti numbers have been computed using various different methods 2 5 11 and a set of generators for the cohomology ring is known 2 the purpose of this article is to provide a method of deciding when an expression in these generators is a relation and in particular when the rank n is two to prove two conjectures about the relations between the generators due to mumford and to newstead and ramanan newstead and ramanan conjectured that certain relations hold among the generators whereas mumford conjectured that a certain set of relations is a complete set in fact the conjecture of newstead and ramanan has two parts the first of which was proved by gieseker in 1982 4 the second part of their conjecture which is the part examined in this article was given an independent proof recently by thaddeus 19 who has a very different method of obtaining information about the relations in the cohomology ring the computation of the betti numbers of the moduli spaces i n d in 2 stimulated a general method of computing betti numbers of quotients in the sense of mumford s geometric invariant theory 14 of nonsingular complex projective varieties by complex reductive group actions see 8 9 10 similarly the ideas applied in this article to finding generators and relations for the cohomology rings of the moduli spaces i n d also lead to an analogous method of obtaining generators and relations for the rational cohomology rings of geometric invariant theoretic quotients the first section provides background material on the cohomology of the moduli spaces i n d in the second section mumford s conjecture is proved when the rank n is two the method could in principle be used to decide whether the conjecture is true for rank n 2 but appears to become significantly more complicated in the general case the third section gives a method for deciding when an expression in the generators is a relation and the fourth

semistable bundles over an elliptic curve abstract we identify the moduli space m n d of semistable bundles of rank n and degree d on an elliptic curve c as a symmetric product of the curve its dimension being the greatest common divisor of n and d under this identification the determinant map det m n d corresponds to the abel jacobi map shc jh so that the fixed determinant moduli space is identified with a projective space we then describe the brill noether loci theta divisors and picard groups and compute the space of theta functions for both the full moduli space and the fixed determinant moduli space of any rank and any degree we extend to elliptic curves a theorem of drezet and narasimhan on the picard group of moduli spaces as well as two formuulas of beauville narasimhan and ramanan on theta functions of level one our results verify in particular for an elliptic curve a formula of e verlinde and an equality first noticed by bott and szenes relating theta functions over the full moduli space and over the fixed determinant moduli space

the tase nf model for function approximation problems optimization of the local sub models when using neuro fuzzy systems to model input output data can be spoiled during the global optimization process therefore special care has to be taken to avoid this loss some approaches involving grid input space partitioning that optimize local sub models whilst still obtaining a good global system performance have appeared however this is a more complex task for radial basis function networks scatter partitioning fuzzy systems and neuro fuzzy models in general this work presents a modified neuro fuzzy model known as the tase nf model which is a special case of a scatter partitioned takagi sugeno kang fuzzy system or normalized radial basis function neural network the tase nf model maintains the optimization properties of the local sub models fuzzy rules or rbf nodes when the model is globally optimized thanks to the modified calculation of the final normalized activation of the rules which provides an appropriate input space partitioning to achieve these objectives to show the characteristics of the proposed model a learning methodology for this model which consists of a clustering algorithm especially suited to function approximation problems a local search technique and a membership function merging approach with the objective of improving the transparency i e ease of interpretability of the extracted fuzzy rule set is also proposed

compactified picard stacks over the moduli stack of stable curves with marked points abstract in this paper we give a construction of algebraic artin stacks endowed with a modular map onto the moduli stack of stable curves of genus g with n marked points the stacks we construct are smooth irreducible and have dimension 4 g 3 n yielding a geometrically meaningful compactification of the universal picard stack parametrizing n pointed smooth curves together with a line bundle

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

a gieseker type degeneration of moduli stacks of vector bundles on curves we construct a new degeneration of the moduli stack of vector bundles over a smooth curve when the curve degenerates to a singular curve which is irreducible with one double point we prove that the total space of the degeneration is smooth and its special fibre is a divisor with normal crossings furthermore we give a precise description of how the normalization of the special fibre of the degeneration is related to the moduli space of vector bundles over the desingularized curve

poincare families of g bundles on a curve let g be a reductive group over an algebraically closed field k consider the moduli space of stable principal g bundles on a smooth projective curve c over k we give necessary and sufficient conditions for the existence of poincare bundles over open subsets of this moduli space and compute the orders of the corresponding obstruction classes this generalizes the previous results of newstead ramanan and balaji biswas nagaraj newstead to all reductive groups to all topological types of bundles and also to all characteristics

the quantization conjecture revisited a strong version of the quantization conjecture of guillemin and sternberg is proved for a reductive group action on a smooth compact polarized variety x l the cohomologies of l over the git quotient x g equal the invariant part of the cohomologies over x this generalizes the theorem of gs on global sections and strengthens its subsequent extensions jk li to riemannroch numbers remarkable by products are the invariance of cohomology of vector bundles over x g under a small change in the defining polarization or under shift desingularization as well as a new proof of boutot s theorem also studied are equivariant holomorphic forms and the equivariant hodgeto de rham spectral sequences for x and its strata whose collapse is shown one application is a new proof of the borel weil bott theorem of ti for the moduli stack of c bundles over a curve and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures collapse of the hodge to de rham sequences for these stacks is also shown

output feedback predictive control with one free control move for nonlinear systems represented by a takagi sugeno model this paper addresses the output feedback predictive control for a takagi sugeno t s fuzzy system like many existing results the controller optimizes an infinite horizon objective function respecting input constraint the infinite horizon control moves are parameterized as a free control move followed by an output feedback based on the prespecified state estimator while the use of a free control move is well practiced in the existing research works of model predictive control mpc it was not previously applied in the output feedback mpc when 1 the future model parameters are uncertain and 2 the recursive feasibility and closed loop stability are guaranteed a key point for us to overcome this difficulty is to introduce a formula for refreshing the bound of the estimation error a numerical example is given to illustrate the effectiveness of the proposed output feedback controller

the local structure of compactified jacobians this paper studies the local geometry of compactified jacobians the main result is a presentation of the completed local ring of the compactified jacobian of a nodal curve as an explicit ring of invariants described in terms of the dual graph of the curve the authors have investigated the geometric and combinatorial properties of these rings in previous work and consequences for compactified jacobians are presented in this paper similar results are given for the local structure of the universal compactified jacobian over the moduli space of stable curves

dynamic output feedback predictive control for nonlinear systems represented by a takagi sugeno model this paper addresses the output feedback predictive control for a takagi sugeno t s fuzzy system with bounded noise the controller optimizes an infinite horizon objective function respecting the input and state constraints the control law is parameterized as a dynamic output feedback that is dependent on the membership functions and the closed loop stability is specified by the notion of quadratic boundedness online algorithms that guarantee the recursive feasibility of the convex optimization problem and the convergence of the augmented state to a neighborhood of the equilibrium point are proposed in this paper a numerical example is given to illustrate the effectiveness of the proposed output feedback controllers

ordered probability spaces abstract let c be an open cone in a banach space equipped with the thompson metric with closure a normal cone the main result gives sufficient conditions for borel probability measures on c with finite first moment for which in the stochastic order induced by the cone to be order approximated by sequences n n of uniform finitely supported measures in the sense that n n for each n and n n in the wasserstein metric this result is the crucial tool in developing a pathway for extending various inequalities on operator and matrix means which include the harmonic geometric and arithmetic operator means on the cone of positive elements of a c algebra to the space p 1 c of borel measures of finite first moment on c as an illustrative and important particular application we obtain the monotonicity of the karcher geometric mean on p 1 a for the positive cone a of a c algebra a

localization of the riemann roch character abstract we present a k theoretic approach to the guillemin sternberg conjecture v guillemin and s sternberg invent math 67 1982 515 538 about the commutativity of geometric quantization and symplectic reduction which was proved by e meinrenken j amer math soc 9 1996 373 389 adv math 134 1998 240 277 and tian zhang y tian and w zhang invent math 132 1998 229 259 besides providing a new proof of this conjecture for the full non abelian group action case our methods lead to a generalization for compact lie group actions on manifolds that are not symplectic these manifolds carry an invariant almost complex structure and an abstract moment map

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

existence and uniqueness of the karcher mean on unital c algebras abstract the karcher mean on the cone of invertible positive elements of the c algebra b e of bounded operators on a hilbert space e has recently been extended to a contractive barycentric map on the space of l 1 probability measures on in this paper we first show that the barycenter satisfies the karcher equation and then establish the uniqueness of the solution next we establish that the karcher mean is real analytic in each of its coordinates and use this fact to show that both the karcher mean and karcher barycenter map exist and are unique on any unital c algebra the proof depends crucially on a recent result of the author giving a converse of the inverse function theorem

intersection numbers on moduli spaces and symmetries of a verlinde formula we investigate the geometry and topology of a standard moduli space of stable bundles on a riemann surface and use a generalization of the verlinde formula to derive results on intersection pairings

effective optimization for fuzzy model predictive control this paper addresses the optimization in fuzzy model predictive control when the prediction model is a nonlinear fuzzy model nonconvex time consuming optimization is necessary with no guarantee of finding an optimal solution a possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control i e quadratic programming for long range predictive control however the influence of the linearization error may significantly deteriorate the performance in our approach this is remedied by linearizing the fuzzy model along the predicted input and output trajectories one can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories four different methods for the construction of the optimization problem are proposed making difference between the cases when a single linear model or a set of linear models are used by choosing an appropriate method the user can achieve a desired tradeoff between the control performance and the computational load the proposed techniques have been tested and evaluated using two simulated industrial benchmarks ph control in a continuous stirred tank reactor and a high purity distillation column

the index formula for the moduli of g bundles on a curve we prove the formulae conjectured by the first author for the index of k theory classes over the moduli stack of algebraic g bundles on a smooth projective curve the formulae generalize e verlinde s for line bundles and have witten s integrals over the moduli space of stable bundles as their large level limits as an application we prove the newstead ramanan conjecture on the vanishing of high chern classes of certain moduli spaces of semi stable g bundles

output tracking of constrained nonlinear processes with offset free input to state stable fuzzy predictive control this paper develops an efficient offset free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model the estimated disturbance signals account for all the plant model mismatch and unmodeled plant disturbances an augmented piecewise observer constructed by solving some linear matrix inequalities is used to estimate the system states and the lumped disturbances based on the reference from an online constrained target generator the fuzzy model predictive control law can be easily obtained by solving a convex semi definite programming optimization problem subject to several linear matrix inequalities the resulting closed loop system is guaranteed to be input to state stable even in the presence of observer estimation error the zero offset output tracking property of the proposed control approach is proved and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant

a wonderful embedding of the loop group i describe the wonderful compactification of loop groups these compactifications are obtained by adding normal crossing boundary divisors to the group lg of loops in a reductive group g or more accurately to the semi direct product c lg in a manner equivariant for the left and right c lg actions the analogue for a torus group t is the theory of toric varieties for an adjoint group g this is the wonderful compactification of de concini and procesi the loop group analogue is suggested by work of faltings in relation to the compactification of moduli of g bundles over nodal curves

borel weil bott theory on the moduli stack of g bundles over a curve let g be a semi simple group and m the moduli stack of g bundles over a smooth complex projective curve using representation theoretic methods i prove the pure dimensionality of sheaf cohomology for certain evaluation vector bundles over m twisted by powers of the fundamental line bundle this result is used to prove a borel weil bott theorem conjectured by g segal for certain generalized flag varieties of loop groups along the way the homotopy type of the group of algebraic maps from an affine curve to g and the homotopy type the hodge theory and the picard group of m are described one auxiliary result in appendix a is the alexander cohomology theorem conjectured in gro2 a self contained account of the uniformization theorem of ls for the stack m is given including a proof of a key result of drinfeld and simpson in characteristic 0 a basic survey of the simplicial theory of stacks is outlined in appendix b

partial desingularisations of quotients of nonsingular varieties and their betti numbers when a reductive group g acts linearly on a nonsingular complex projective variety x one can define a projective quotient variety x g using mumford s geometric invariant theory if the condition that every semistable point be properly stable is satisfied this quotient is the ordinary topological quotient of an open subset xss of the variety by the group in k a formula is obtained for the rational cohomology of x g under this condition the formula involves the rational cohomology of x and various linear sections of x together with the rational cohomology of the classifying spaces of g and certain reductive subgroups of g in many interesting examples the condition required in k is not satisfied thus the question arises as to what information we can obtain in general the quotient x g can now have serious singularities in contrast to the good case considered in k where the only singularities are those caused by finite isotropy groups it will be shown in this paper that there is a systematic way of blowing up x along a sequence of nonsingular subvarieties to obtain a variety x with a linear action of g such that every semistable point of x is stable the only assumption that we have to make is that there exists at least one stable point of x then x g is almost a resolution of singularities of x1 g in the sense that the most serious singularities have been resolved moreover there is a formula for the rational cohomology of x g again involving the rational cohomology of x and certain linear sections of x together with the rational cohomology of the classifying spaces of g and some reductive subgroups of g see theorem 8 14 for convenience we shall assume throughout that g is connected however the construction of x works in general and it is straightforward to modify the cohomological formulas to apply to the general case the construction of x g can also be modified to apply in some cases when x has no stable points the layout of the paper is as follows section 1 is a review of the basic facts of geometric invariant theory which will be needed and section 2 describes the relationship of geometric invariant theory with symplectic geometry and the moment map in section 3 semistability and stability in a blow up of x along a nonsingular c invariant subvariety are related to semistability and stability in x

surjectivity for hamiltonian g spaces in k theory let be a compact connected lie group and a hamiltonian space with proper moment map we give a surjectivity result which expresses the theory of the symplectic quotient in terms of the equivariant theory of the original manifold under certain technical conditions on this result is a natural theoretic analogue of the kirwan surjectivity theorem in symplectic geometry the main technical tool is the theoretic atiyah bott lemma which plays a fundamental role in the symplectic geometry of hamiltonian spaces we discuss this lemma in detail and highlight the differences between the theory and rational cohomology versions of this lemma we also introduce a theoretic version of equivariant formality and prove that when the fundamental group of is torsion free every compact hamiltonian space is equivariantly formal under these conditions the forgetful map is surjective and thus every complex vector bundle admits a stable equivariant structure furthermore by considering complex line bundles we show that every integral cohomology class in admits an equivariant extension in

robust stability constraints for fuzzy model predictive control this paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the takagi sugeno t s type resulting in a stable closed loop control system conditions are given that guarantee closed loop robust asymptotic stability for open loop bounded input bounded output bibo stable processes with an additive l sub 1 norm bounded model uncertainty the idea is closely related to small gain based l sub 1 control theory but due to the time varying approach the resulting robust stability constraints are less conservative therefore the fuzzy model is viewed as a linear time varying system rather than a nonlinear one the goal is to obtain constraints on the control signal and its increment that guarantee robust stability robust global asymptotic stability and offset free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances

gromov witten theory of deligne mumford stacks given a smooth complex deligne mumford stack cal x with a projective coarse moduli space we introduce gromov witten invariants of cal x and prove some of their basic properties including the wdvv equation

intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a riemann surface let n and d be coprime positive integers and define m n d to be the moduli space of semi stable holomorphic vector bundles of rank n degree d and fixed determinant on a compact riemann surface e this moduli space is a compact kifhler manifold which has been studied from many different points of view for more than three decades see for instance narasimhan and seshadri 41 the subject of this article is the characterization of the intersection pairings in the cohomology ring1 h m n d a set of generators of this ring was described by atiyah and bott in their seminal 1982 paper 2 on the yangmills equations on riemann surfaces where in addition inductive formulas for the betti numbers of m n d obtained earlier using number theoretic methods 13 25 were rederived by poincare duality knowledge of the intersection pairings between products of these generators or equivalently knowledge of the evaluation on the fundamental class of products of the generators completely determines the structure of the cohomology ring in 1991 donaldson 15 and thaddeus 47 gave formulas for the intersection pairings between products of these generators in h m 2 1 in terms of bernoulli numbers then using physical methods witten 50 found formulas for generating functions from which could be extracted the intersection pairings between products of these generators in h m n d for general rank n these generalized his rigorously proved formulas 49 for the symplectic volume of m n d for instance the symplectic volume of m 2 1 is given by

fuzzy constrained min max model predictive control based on piecewise lyapunov functions this paper proposes two novel stable fuzzy model predictive controllers based on piecewise lyapunov functions and the min max optimization of a quasi worst case infinite horizon objective function the main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction and thus to obtain the optimal transient control performance which is of great importance in industrial process control moreover in both of these predictive controllers piecewise lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common lyapunov functions it is shown that the asymptotic stability of the resulting closed loop discrete time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities moreover the controller designs of the closed loop control systems with desired decay rate and input constraints are also considered simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers

neron models and compactified picard schemes over the moduli stack of stable curves we construct modular deligne mumford stacks representable over parametrizing neron models of jacobians as follows let b be a smooth curve and k its function field let be a smooth genus g curve over k admitting stable minimal model over b the neron model b is then the base change of via the moduli map b of f i e b moreover is compactified by a deligne mumford stack over giving a completion of neron models naturally stratified in terms of neron models

a compactification of the moduli space of twisted holomorphic maps abstract given compact symplectic manifold x with a compatible almost complex structure and a hamiltonian action of s 1 with moment map x i r and a real number k 0 we compactify the moduli space of twisted holomorphic maps to x with energy k this moduli space parameterizes equivalence classes of tuples c p a where c is a smooth compact complex curve of fixed genus g p is a principal s 1 bundle over c a is a connection on p and is a section of p s 1 x satisfying a 0 v f a c f a l 2 2 d a l 2 2 c l 2 2 k here f a is the curvature of a v is the restriction to c of a volume form on the universal curve over m g and c is a fixed constant two tuples c p a and c p a are equivalent if there is a morphism of bundles p p lifting a biholomorphism c c such that v v a a and the topology of the moduli space is the quotient topology of the topology of c convergence on the set of tuples c p a we also incorporate marked points in the picture there are two sources of noncompactness first bubbling off phenomena analogous to the one in gromov witten theory second degeneration of c to nodal curves in this case there appears a phenomenon which is not present in gromov witten near the nodes the section may degenerate to a chain of gradient flow lines of i

quantum riemann roch lefschetz and serre given a holomorphic vector bundle e over a compact kahler manifold x one defines twisted gromov witten invariants of x to be intersection numbers in moduli spaces of stable maps f x with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle h 0 f e h 1 f e using the formalism of quantized quadratic hamiltonians 25 we express the descendant potential for the twisted theory in terms of that for x this result theorem 1 is a consequence of mumford s grothendieck riemann roch theorem applied to the universal family over the moduli space of stable maps it determines all twisted gromov witten invariants of all genera in terms of untwisted invari ants when e is concave and the c equivariant inverse euler class is chosen as the characteristic class the twisted invariants of x give gromov witten invariants of the total space of e nonlinear serre duality 21 23 expresses gromov witten invariants of e in terms of those of the super manifold e it relates gromov witten invariants of x twisted by the inverse euler class and e to gromov witten invariants of x twisted by the euler class and e we derive from theorem 1 nonlinear serre duality in a very general form corollary 2 when the bundle e is convex and a submanifold y x is defined by a global section of e the genus zero gromov witten invariants of e coin cide with those of y we establish a quantum lefschetz hyperplane section principle theorem 2 expressing genus zero gromov witten invariants of a complete intersection y in terms of those of x this extends earlier results 4 9 18 29 33 and yields most of the known mirror formulas for toric complete intersections

gauged gromov witten theory for small spheres we relate the genus zero gauged gromov witten invariants of a smooth projective variety for sufficiently small area with equivariant gromov witten invariants as an application we deduce a gauged version of abelianization for gromov witten invariants in the small area chamber in the symplectic setting we prove that any sequence of genus zero symplectic vortices with vanishing area has a subsequence that converges after gauge transformation to a holomorphic map with zero average moment map

operator means of probability measures and generalized karcher equations abstract in this article we consider means of positive bounded linear operators on a hilbert space we present a complete theory that provides a framework which extends the theory of the karcher mean its approximating matrix power means and a large part of kubo ando theory to arbitrary many variables in fact to the case of probability measures with bounded support on the cone of positive definite operators this framework characterizes each operator mean extrinsically as unique solutions of generalized karcher equations which are obtained by exchanging the matrix logarithm function in the karcher equation to arbitrary operator monotone functions over the positive real half line if the underlying hilbert space is finite dimensional then these generalized karcher equations are riemannian gradients of convex combinations of strictly geodesically convex log determinant divergence functions hence these new means are their global minimizers in analogy to the case of the karcher mean as pointed out our framework is based on fundamental contraction results with respect to the thompson metric which provides us nonlinear contraction semigroups in the cone of positive definite operators that form a decreasing net approximating these operator means in the strong topology from above

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

gromov witten gauge theory we introduce a modular completion of the stack of maps from stable marked curves to the quotient stack pt c x and use this stack to construct some gauge theoretic analogues of the gromov witten invariants we also indicate the generalization of these invariants to the quotient stacks x c x where x is a smooth proper complex algebraic variety

a degeneration formula of gw invariants this is the sequel to the paper 23 in this paper we construct the virtual moduli cycles of the degeneration of the moduli of stable morphisms constructed in 23 we also construct the virtual moduli cycles of the moduli of relative stable morphisms of a pair of a smooth divisor in a smooth variety based on these we prove a degeneration formula of the gromov witten invariants

compactified picard stacks over overline mathcal m _g we study algebraic artin stacks over overline mathcal m g giving a functorial way of compactifying the relative degree d picard variety for families of stable curves we also describe for every d the locus of genus g stable curves over which we get deligne mumford stacks strongly representable over overline mathcal m g

properness for scaled gauged maps we prove properness of moduli stacks of gauged maps satisfying a stability conditition introduced by mundet 42 schmitt 48 and ziltener 59 the proof combines a git construction of schmitt 48 properness for twisted stable maps by abramovich vistoli 1 a variation of a boundedness argument due to ciocan fontanine kim maulik 13 and a removal of singularities for bundles on surfaces in colliot thelene sansuc 14

the picard group of the universal moduli space of vector bundles on stable curves abstract we construct the moduli stack of properly balanced vector bundles on semistable curves and we determine explicitly its picard group as a consequence we obtain an explicit description of the picard groups of the universal moduli stack of vector bundles on smooth curves and of the schmitt s compactification over the stack of stable curves we prove some results about the gerbe structure of the universal moduli stack over its rigidification by the natural action of the multiplicative group in particular we give necessary and sufficient conditions for the existence of poincare bundles over the universal curve of an open substack of the rigidification generalizing a result of mestrano ramanan

suboptimal model predictive control feasibility implies stability practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex nonlinear optimization problems are possible in limited computational time in the paper we first establish conditions under which suboptimal model predictive control mpc controllers are stabilizing the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost second we present and analyze two suboptimal mpc schemes that are guaranteed to be stabilizing provided an initial feasible solution is available and for which the computational requirements are more reasonable

witten s formulas for intersection pairings on moduli spaces of flat g bundles abstract in a 1992 paper j geom phys 9 1992 303 witten gave a formula for the intersection pairings of the moduli space of flat g bundles over an oriented surface possibly with markings in this paper we give a general proof of witten s formula for arbitrary compact simple groups and any markings for which the moduli space has at most orbifold singularities

foncteur de picard d un champ algebrique resume in this article we study the picard functor and the picard stack of an algebraic stack we give a new and direct proof of the representability of the picard stack we prove that it is quasi separated and that the connected component of the identity is proper when the fibers of x are geometrically normal we study some examples of picard functors of classical stacks in an appendix we review the lisse etale cohomology of abelian sheaves on an algebraic stack

finiteness theorems for the picard objects of an algebraic stack abstract we prove some finiteness theorems for the picard functor of an algebraic stack in the spirit of sga 6 exp xii and xiii in particular we give a stacky version of raynaud s relative representability theorem we give sufficient conditions for the existence of the torsion component of the picard functor and for the finite generation of the neron severi groups or of the picard group itself we give some examples and applications in appendix a we prove the semicontinuity theorem for a non necessarily tame algebraic stack

conformal field theory and the cohomology of the moduli space of stable bundles let g be a compact riemann surface of genus g 2 and let be a line bundle over g of degree 1 then the moduli space of rank 2 stable bundles v over g such that v was shown by seshadri 19 to be a nonsingular projective variety ng its rational cohomology ring h ng is exceedingly rich and despite years of study has never quite been computed in full the object of this paper is to give an essentially complete characterization of this ring or at least to reduce the problem to a matter of linear algebra in particular we find a proof of newstead s conjecture that pg1 ng 0 we also obtain a formula for the volume of ng which can be regarded as a twisted version of the formula for the degree 0 moduli space recently announced by witten the approach we shall take is not from algebraic geometry but from mathematical physics it relies on the su 2 wess zumino witten model which is a functor zk associating a finite dimensional vector space to each riemann surface with marked points the relationship with the moduli space is that when the level k of the functor is even the vector space associated to g with no marked points can be identified with h ng l where l is a fixed line bundle over ng now the work of verlinde provides us with a means of calculating the dimension of any vector space arising from our functor and in particular dimh ng l which we shall denote d g k on the other hand newstead 14 found explicit generators for h ng and we can also express d g k in terms of them using a riemann roch theorem equating the two formulas enables us to evaluate any monomial in the generators on the fundamental class of ng and by poincare duality this is sufficient at least in principle to determine the ring structure of h ng in the discussion above one important point has been skated over the su 2 wzw model is of course associated to bundles of degree 0 not degree 1 so in order to make use of verlinde s work it is necessary to formulate a twisted version of the field theory this is carried out in 2 but the crucial properties of the twisted theory analogous to those which make the ordinary theory a modular functor are not proved in this paper rather we will confine ourselves to exploring the consequences of these claims and hope to return to justify them in a later paper an outline of the remaining sections goes as follows in 3 we review those parts of verlinde s work we shall need show how they must be modified in the twisted case and work out some explicit formulas for d g k in 4 we study the cohomology of ng which we regard throughout as a space of representations via the theorem of narasimhan and seshadri we define newstead s generators and i of h ng

fuzzy model based predictive control by instantaneous linearization a linearization technique for product sum crisp type fuzzy model and a multistep predictive control strategy for the construction of a model based predictive fuzzy controller is presented in this paper a model based predictive controller is based on a local linear model generated by using the proposed linearization technique that linearizes the product sum crisp type fuzzy process model around the current operating point the control of ph in a continuous stirred tank reactor is chosen as a realistic nonlinear case study for the demonstration of the proposed control algorithm the controller is shown to be capable of controlling the nonlinear processes that operate over a wide range and of providing better overall system performance than the optimal pi controller

picard group of moduli of hyperelliptic curves the main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves we compute their picard groups giving explicit description of the generators we get an application to the non existence of a tautological family over the coarse moduli space

affine ts model based fuzzy regulating servo control design an affine t s fuzzy system is derived naturally from linearizing a nonlinear system or from some data driven identification techniques for example cluster based algorithms or soft computation learning structures little research is proposed for the intrinsic analysis of an affine type fuzzy system further the controllers to regulate or to achieve servo control of affine ts based nonlinear systems are also few both affine type fuzzy regulation and servo control design scheme are theoretically derived a simple lyapunov based stability criterion and some extra conditions are proposed to guarantee the global stability of the generated closed loop fuzzy systems the exponential stability of the feedback fuzzy system is ensured under some conditions the performance of the proposed fuzzy controllers and fuzzy servo controllers is examined by three case studies simulation results show that the proposed controllers can stabilize these affine fuzzy systems and the proposed servomechanism can adapt itself to various incoming signals in very short time spans

the stochastic order of probability measures on ordered metric spaces abstract the general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first motivated by recent work on barycentric maps on spaces of probability measures on ordered banach spaces we introduce and study a stochastic order on the space of probability measures p x where x is a metric space equipped with a closed partial order and derive several useful equivalent versions of the definition we establish the antisymmetry and closedness of the stochastic order and hence that it is a closed partial order for the case of a partial order on a banach space induced by a closed normal cone with interior we also consider order completeness of the stochastic order for a cone of a finite dimensional banach space and derive a version of the arithmetic geometric harmonic mean inequalities in the setting of the associated probability space on positive invertible operators on a hilbert space