h control via output feedback for state delayed systems a sufficient condition is derived such that the closed loop state delayed system is stable and guarantees a prescribed h norm bound of the closed loop transfer matrix from the disturbance to the controlled output based on this derivation a full order observer based h controller for the stace delayed linear systems is constructed by solving two modified algebraic riccati equations the state feedback h controller for the state delayed linear systems is also obtained by solving a modified algebraic riccati equation an illustrative example is given to show the applicability of the proposed approach

twistor spaces of hypercomplex manifolds are balanced abstract a hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations if in addition there exists a metric on the manifold which is hermitian with respect to the three structures and such that the corresponding hermitian forms are closed the manifold is said to be hyperkahler in the paper non hermitian yang mills connections 13 kaledin and verbitsky proved that the twistor space of a hyperkahler manifold admits a balanced metric these were first studied in the article on the existence of special metrics in complex geometry 17 by michelsohn in the present article we review the proof of this result and then generalize it and show that twistor spaces of general compact hypercomplex manifolds are balanced

betti numbers of holomorphic symplectic quotients via arithmetic fourier transform a fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field this technique in turn gives information on betti numbers of holomorphic symplectic quotients as a consequence simple unified proofs are obtained for formulas of poincare polynomials of toric hyperkahler varieties recovering results of bielawski dancer and hausel sturmfels poincare polynomials of hilbert schemes of points and twisted atiyah drinfeld hitchin manin adhm spaces of instantons on 2 recovering results of nakajima yoshioka and poincare polynomials of all nakajima quiver varieties as an application a proof of a conjecture of kac on the number of absolutely indecomposable representations of a quiver is announced

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

moment maps scalar curvature and quantization of kahler manifolds building on donaldson s work on constant scalar curvature metrics we study the space of regular kahler metrics e i e those for which deformation quantization has been defined by cahen gutt and rawnsley after giving in sects 2 and 3 a review of donaldson s moment map approach we study the essential uniqueness of balanced basis i e of coherent states in a more general setting theorem 2 5 we then study the space e in sect 4 and we show in sect 5 how all the tools needed can be defined also in the case of non compact manifolds

modularity quaternion kahler spaces and mirror symmetry we provide an explicit twistorial construction of quaternion kahler manifolds ob tained by deformation of c map spaces and carrying an isometric action of the modular group sl 2 z the deformation is not assumed to preserve any continuous isometry and therefore this construction presents a general framework for describing ns5 brane instanton effects in string compactifications with n 2 supersymmetry in this context the modular invariant parametrization of twistor lines found in this work yields the complete non perturbative mirror map between type iia and type iib physical fields

partner symmetries and non invariant solutions of four dimensional heavenly equations we extend our method of partner symmetries to the hyperbolic complex monge ampere equation and the second heavenly equation of plebanski we show the existence of partner symmetries and derive the relations between them for certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate legendre transformation the solutions of these linear equations are generically non invariant as a consequence we obtain explicitly new classes of heavenly metrics without killing vectors

noncommutative instantons and twistor transform recently n nekrasov and a schwarz proposed a modification of the adhm construction of instantons which produces instantons on a noncommutative deformation of 4 in this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces we exhibit one to one correspondences between three classes of objects framed bundles on a noncommutative 2 certain complexes of sheaves on a noncommutative 3 and the modified adhm data the modified adhm construction itself is interpreted in terms of a noncommutative version of the twistor transform we also prove that the moduli space of framed bundles on the noncommutative 2 has a natural hyperkahler metric and is isomorphic as a hyperkahler manifold to the moduli space of framed torsion free sheaves on the commutative 2 the natural complex structures on the two moduli spaces do not coincide but are related by an so 3 rotation finally we propose a construction of instantons on a more general noncommutative 4 than the one considered by nekrasov and schwarz a q deformed 4

hodge cohomology of gravitational instantons we study the space of l2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type these metrics generalize the geometric structures at infinity of several different well known classes of metrics including asymptotically locally euclidean manifolds the known types of gravitational instantons and also poincare metrics on q rank 1 ends of locally symmetric spaces and on the complements of smooth divisors in kahler manifolds the answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold the l2 signature formula implied by our result is closely related to the one proved by dai 25 and more generally by vaillant 67 and identifies dai s invariant directly in terms of intersection cohomology of differing perversities this work is also closely related to a recent paper of carron 12 and the forthcoming paper of cheeger and dai 17 we apply our results to a number of examples gravitational instantons among them arising in predictions about l2 harmonic forms in duality theories in string theory

twistor theory of hyper kahler metrics with hidden symmetries we review the hierarchy for the hyper kahler equations and define a notion of symmetry for solutions of this hierarchy a four dimensional hyper kahler metric admits a hidden symmetry if it embeds into a hierarchy with a symmetry it is shown that a hyper kahler metric admits a hidden symmetry if it admits a certain killing spinor we show that if the hidden symmetry is tri holomorphic then this is equivalent to requiring symmetry along a higher time and the hidden symmetry determines a twistor group action as introduced by bielawski twistor quotients of hyper kahler manifolds world scientific river edge nj 2001 this leads to a construction for the solution to the hierarchy in terms of linear equations and variants of the generalized legendre transform for the hyper kahler metric itself given by ivanov and rocek commun math phys 182 291 1996 we show that the ale spaces are examples of hyper kahler metrics admitting three tri holomorphic killing spinors these metrics are in this sense

hyper kahler metrics and harmonic superspace the most general unconstrained superfield action for self interactingn 2 matter hypermultiplets in analyticn 2 superspace is argued to produce a most generaln 2 hyper kahler model after eliminating an infinite set of auxiliary fields this suggests a new possibility of classifying hyper kahler metrics according to then 2 analytic superfield self interactions and provides an effective tool to compute these metrics explicitly as the simplest example the u 2 invariant quartic self coupling of a singleq hypermultiplet is analyzed and is shown to yield the familiar taub nut metric to see the geometric pattern directly in terms ofn 2 superfields we introduce a new on shell representation ofq hypermultiplets inn 2 harmonic superspace similar to the description ofn 2 gauge theories for the u 2 example this formulation is checked to coincide with that by sierra and townsend

abcd of instantons we solve open image in new window 2 supersymmetric yang mills theories for an arbitrary classical gauge group i e su n so n sp n in particular we derive the prepotential of the low energy effective theory and the corresponding seiberg witten curves we manage to do this without resolving singularities of the compactified instanton moduli spaces

manifolds of g2 holonomy from the n 4 sigma model using the two dimensional 2d n 4 sigma model with u 1 r gauge symmetry and introducing the ade cartan matrices as gauge matrix charges we build toric hyper kahler eight real dimensional manifolds x8 dividing by one toric geometry circle action of x8 manifolds we present examples describing quotients x7 x8 u 1 of g2 holonomy in particular for the ar cartan matrix the quotient space is a cone on an s2 bundle over r intersecting wcp2 1 2 1 weighted projective spaces according to the ar dynkin diagram

robust h control for uncertain discrete stochastic time delay systems this paper deals with the problems of robust stabilization and robust h control for discrete stochastic systems with time varying delays and time varying norm bounded parameter uncertainties for the robust stabilization problem attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed loop system for all admissible uncertainties while for the robust h control problem a state feedback controller is designed such that in addition to the requirement of the robust stochastic stability a prescribed h performance level is also required to be satisfied a linear matrix inequality lmi approach is developed to solve these problems and delay dependent conditions for the solvability are obtained it is shown that the desired state feedback controller can be constructed by solving certain lmis an example is provided to demonstrate the effectiveness of the proposed approach

hyperkahler manifolds and nonlinear supermultiplets we present a new construction of hyperkahler metrics that derives from the 3 dimensionaln 4 nonlinear supermultiplet further we give a detailed description of the nonlinear multiplet inn 2 and 4 superspace

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

subsolution theorem and the dirichlet problem for the quaternionic monge ampere equation in this paper we obtain the existence of solution to the dirichlet problem for quaternionic monge ampere equation after showing a stability theorem we prove the subsolution theorem for quaternionic monge ampere equation by combining our stability theorem and kolodziej s approach for the complex case

gravitational instantons with faster than quadratic curvature decay iii this is our third paper in a series on the gravitational instantons in this paper we classify alg and alh gravitational instantons in alg case we extend tian yau hein s construction slightly and show that it is the only alg gravitational instanton in alh case we prove a torelli type theorem

weighted sensitivity minimization for delay systems in this note we discuss the h infty sensitivity minimization problem for linear time invariant delay systems while the unweighted case reduces to simple nevanlinna pick interpolation the weighted case turns out to be much more complicated and demands certain functional analytic techniques for its solution

robust h sub spl infin performance for linear delay differential systems with time varying uncertainties the present paper concerns robust h spl infin performance for linear delay differential systems which involve an uncertain time delay and time varying norm bounded parameter uncertainties based on the lyapunov functional a simple criterion is proposed which assures the pseudo quadratic stability as a well as an h sub spl infin norm bound the criterion is given in the form of a linear matrix inequality which is affine or convex in additional scalar parameters a simple criterion is presented to evaluate the extent of the performance robustness

the stark ladder and other one dimensional external field problems for a certain class of analytic potentialsv x matrix elements of the resolvent ofh f d 2 dx 2 fx v x with entire vectors of the translation group have meromorphic continuations from imz 0 to the whole complex plane the poles of these continuations are restricted to a discrete set independent of the analytic vectors chosen certain random potentials corresponding to an infinite number of particles distributed on the points of a poisson set lie in this class with probability one as do a large class of periodic potentials

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

hyperkahler quotient construction of bps monopole moduli spaces we use the hyperkahler quotient of flat space to obtain some monopole moduli space metrics in explicit form using this new description we discuss their topology completeness and isometries we construct the moduli space metrics in the limit when some monopoles become massless which corresponds to non maximal symmetry breaking of the gauge group we also introduce a new family of hyperkahler metrics which depending on the mass parameter being positive or negative tend to either the asymptotic metric on the moduli space of many su 2 monopoles or to previously unknown metrics these new metrics are singular or complete depending on the particular choice of the level set of the moment map the singular metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups finally we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow

hyper hamiltonian dynamics we introduce an extension of hamiltonian dynamics defined on hyper kahler manifolds which we call hyper hamiltonian dynamics we show that this has many of the attractive features of standard hamiltonian dynamics we also discuss the prototypical integrable hyper hamiltonian systems i e quaternionic oscillators

absolute continuity of the integrated density of states of the quantum lorentz gas for a class of repulsive potentials for a class of repulsive potentials for instance of the type phi x mod x mod kappa 1 x2 lambda kappa lambda positive in a certain range in the random schrodinger operators h omega p2 v x omega p2 sigma j phi x xj acting in l2 rd with poisson distributed xjs the quantum lorentz gas we show that the integrated density of states n e is absolutely continuous for e zeta rho phi here is phi the integral of phi over rd rho the averaged density of points xj and zeta 0 depends on phi and d in the above example zeta d kappa 2 our method makes use of a fock space representation for the poisson random system recently developed by maassen and the author 1993 within this fock space formalism the mourre commutator method is then employed to obtain the announced result

supersymmetric sigma models twistors and the atiyah hitchin metric the legendre transform and its generalizations originally found in supersymmetric models are techniques that can be used to givelocal constructions of hyperkahler metrics we give a twistor space interpretation to the generalizations of the legendre transform construction the atiyah hitchin metric on the moduli space of two monopoles is used as a detailed example

n 2 super yang mills theory in projective superspace we constructn 2 yang mills theory in projective superspace by exploiting the analogy to ward s twistor construction of self dual yang mills fields

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

monopoles and clusters we define and study certain hyperkahler manifolds which capture the asymptotic behaviour of the su 2 monopole metric in regions where monopoles break down into monopoles of lower charges the rate at which these new metrics approximate the monopole metric is exponential as for the gibbons manton metric

integrating over higgs branches we develop some useful techniques for integrating over higgs branches in supersymmetric theories with 4 and 8 supercharges in particular we define a regularized volume for hyperkahler quotients we evaluate this volume for certain ale and alf spaces in terms of the hyperkahler periods we also reduce these volumes for a large class of hyperkahler quotients to simpler integrals these quotients include complex coadjoint orbits instanton moduli spaces on 4 and ale manifolds hitchin spaces and moduli spaces of parabolic higgs bundles on riemann surfaces in the case of hitchin spaces the evaluation of the volume reduces to a summation over solutions of bethe ansatz equations for the non linear schrodinger system we discuss some applications of our results

a fock space representation for the quantum lorentz gas a fock space representation is given for the quantum lorentz gas i e for random schrodinger operators of the form h p2 v p2 x xj acting in h l2 rd with poisson distributed xjs an operator h is defined in k h p h l2 p d l2 p d h by the action of h on its fibers in a direct integral decomposition the stationarity of the poisson process allows a unitarily equivalent description in terms of a new family h k k rd where each h k acts in p a tip j math phys 35 113 1994 the space p is then unitarily mapped upon the symmetric fock space over l2 rd dx with the intensity of the poisson process the average number of points xj per unit volume the scatterer density and the equivalent of h k is determined averages now become vacuum expectation values and a further unitary transformation removing in dx is made which leaves the former invariant the resulting operator hf k has an interesting structure on the nth fock layer we encounter a single particle mo

h sub spl infin compensator design with minimal order observers a method based on a bounded real lemma is presented in the form of sufficient conditions for designing observer based proper reduced order h sub spl infin compensators the proposed compensators are shown to include the strictly proper full order central h sub spl infin compensators as a special class a compensator design algorithm is included to illustrate the use of the proposed compensator design equations

robust control of state delayed systems with polytopic type uncertainties via parameter dependent lyapunov functionals abstract this paper considers the problem of robust stability and robust stabilization for linear systems with a constant time delay in the state and subject to real convex polytopic uncertainty first of all for robust stability problem we exploit new matrix inequalities characterization of delay dependent quadratic stability results demonstrate that it allows the use of parameter dependent lyapunov functionals and develop control design methods based on linear matrix inequalities lmis for solving the robust control problem next the problem of determining the maximum time delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by lmi techniques finally illustrative examples are given to demonstrate the advantage of these new representations

random time evolution and direct integrals constants of the motion and the mass operator the members h p2 v x of ergodic families of random operators defined in h l2 rd are considered as acting in fibers in a direct integral decomposition of k l2 p d h p being the underlying probability space such a formulation may turn out to be useful in providing a rigorous background for theoretical physical methods employed in treating random systems as an example a rigorous definition of the mass operator z is presented and the formulation of transport equations in a functional analytic setting is briefly indicated in case there is translational invariance in the probability law the operator h is shown to be unitarily equivalent to an operator h which can be decomposed h h k in a way that diagonalizes p thus problems about averaged time evolution can be formulated entirely in terms of h k in l2 p

reflection functors for quiver varieties and weyl group actions we introduce reflectionfunctors on quiver varieties they are hyper kahler isometries between quiver varieties with different parameters related by elements in the weyl group the definition is motivated by the origial reflection functor given by bernstein gelfand ponomarev 1 but they behave much nicely they are isomorphisms and satisfy the weyl group relations as an application we define weyl group representations of homology groups of quiver varieties they are analogues of slodowy s construction of springer representations of the weyl group

gravitational instantons of type d k and a generalization of the gibbons hawking ansatz we describe a quaternionic based ansatz generalizing the gibbons hawking ansatz to a class of hyperkahler metrics with hidden symmetries we then apply it to obtain explicit expressions for gravitational instanton metrics of type d k

cohomology of power sets with applications in quantum probability square integrable wiener functionals may be represented as sums of multiple ito integrals this leads to an identification of such functionals with square integrable functions on the symmetric measure space of the lebesgue spacer when the pointwise product of wiener functionals is thus carried over the product takes a pleasing form cf wick s theorem and various non commutative perturbations of this wiener product have been considered here we employ cohomological arguments to analyse deformations of an abstract wiener product this leads to the construction of levy fields which are neither bosonic nor fermionic and also gives rise to homotopies between quasi free boson and fermion fields finally we unify existence and uniqueness results for quantum stochastic differential equations by treating mixed noise differential equations

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

hyperkahler structures and infinite dimensional grassmannians abstract in this paper we describe an example of a hyperkahler quotient of a banach manifold by a banach lie group although the initial manifold is not diffeomorphic to a hilbert manifold not even to a manifold modelled on a reflexive banach space the quotient space obtained is a hilbert manifold which can be furthermore identified either with the cotangent space of a connected component gr res j j z of the restricted grassmannian or with a natural complexification of this connected component thus proving that these two manifolds are isomorphic hyperkahler manifolds moreover kahler potentials associated with the natural complex structure of the cotangent space of gr res j and with the natural complex structure of the complexification of gr res j are computed using kostant souriau s theory of prequantization

random hamiltonians ergodic in all but one direction letv 1 andv 2 be two ergodic random potentials on d we consider the schrodinger operatorh h0 v withh0 and forx x1 x2 v omega x left begin array 20 c v omega 1 x if x 1 over smash scriptstyle vphantom x 0 end array right we prove certain ergodic properties of the spectrum for this model and express the integrated density of states in terms of the density of states of the stationary potentialsv 1 andv 2 finally we prove the existence of the density of surface states forh

tangentially positive isometric actions and conjugate points let m g be a complete riemannian manifold with no conjugate points and f m g b g b a principal g bundle where g is a lie group acting by isometries and b the smooth quotient with g b the riemannian submersion metric we obtain a characterization of conjugate point free quotients b g b in terms of symplectic reduction and a canonical pseudo riemannian metric on the tangent bundle tm from which we then derive necessary conditions involving g and m for the quotient metric to be conjugate point free particularly for m a reducible riemannian manifold let g tm with the lie algebra of g be the moment map of the tangential g action on tm and let gp be the canonical pseudo riemannian metric on tm defined by the symplectic form d and the map f tm m x m f z exp z exp z first we prove a theorem stating that if gp is not positive definite on the action vector fields for the tangential action along g 1 0 then b g b acquires conjugate points we proved the converse result in 2005 then we characterize self parallel vector fields on m in terms of the positivity of the gp length of their tangential lifts along certain canonical subsets of tm we use this to derive some necessary conditions on g and m for actions to be tangentially positive on relevant subsets of tm which we then apply to isometric actions on complete conjugate point free reducible riemannian manifolds when one of the irreducible factors satisfies certain curvature conditions

a construction of non kahler calabi yau manifolds and new solutions to the strominger system abstract we propose a new construction of compact non kahler calabi yau manifolds with balanced metrics and study the strominger system on them in particular we obtain explicit solutions to the strominger system with degeneracies on g t 4 where g is an immersed minimal surface of genus g 3 in flat t 3

linear perturbations of quaternionic metrics we extend the twistor methods developed in our earlier work on linear deformations of hyperkahler manifolds 1 to the case of quaternionic kahler manifolds via swann s construction deformations of a 4d dimensional quaternionic kahler manifold mathcal m are in one to one correspondence with deformations of its 4d 4 dimensional hyperkahler cone mathcal s the latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space mathcal z mathcal s with a suitable homogeneity condition that ensures that the hyperkahler cone property is preserved equivalently we show that the deformations of mathcal m can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space mathcal z mathcal m of mathcal m by passing the swann bundle and its twistor space we specialize these general results to the case of quaternionic kahler metrics with d 1 commuting isometries obtainable by the legendre transform method and linear deformations thereof we illustrate our methods for the hypermultiplet moduli space in string theory compactifications at tree and one loop level

new hyperkahler metrics and new supermultiplets we present new constructions of hyperkahler metrics along with the three new classes ofn 4 supermultiplets that they derive from further we provide a general setting for understanding the constructions and give a detailed description of the multiplets inn 2 andn 4 superspace

lectures on nonlinear sigma models in projective superspace n 2 supersymmetry in four space time dimensions is intimately re lated to hyperkahler and quaternionic kahler geometries on one hand the target spaces for rigid supersymmetric sigma models are necessarily hy perkahler manifolds on the other hand when coupled to n 2 supergrav ity the sigma model target spaces must be quaternionic kahler it is known that such manifolds of restricted holonomy are dicult to generate explic itly projective superspace is a eld theoretic approach to construct general n 2 supersymmetric nonlinear sigma models and hence to generate new hyperkahler and quaternionic kahler metrics intended for a mixed audience consisting of both physicists and mathematicians these lectures provide a pedagogical introduction to the projective superspace approach

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

nahm s equations and hyperkahler geometry the geometry of certain moduli spaces of solutions to nahm s equations is studied and a family of gravitational instationsj is shown to arise as a deformation of theh atiyah hitchin maniford

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

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

twistor theory at fifty from contour integrals to twistor strings we review aspects of twistor theory its aims and achievements spanning the last five decades in the twistor approach space time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold the twistor space after giving an elementary construction of this space we demonstrate how solutions to linear and nonlinear equations of mathematical physics anti self duality equations on yang mills or conformal curvature can be encoded into twistor cohomology these twistor correspondences yield explicit examples of yang mills and gravitational instantons which we review they also underlie the twistor approach to integrability the solitonic systems arise as symmetry reductions of anti self dual asd yang mills equations and einstein weyl dispersionless systems are reductions of asd conformal equations we then review the holomorphic string theories in twistor and ambitwistor spaces and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes finally we discuss the newtonian limit of twistor theory and its possible role in penrose s proposal for a role of gravity in quantum collapse of a wave function

memoryless h controller design for linear systems with delayed state and control we present a memoryless h control design method for linear time invariant systems that have no parametric uncertainty but delay in the state and control based on the riccati equation approach we design a memoryless linear time invariant state feedback control law which guarantees the asymptotic stability of the closed loop control system and reduces the effect of the disturbance input on the controlled output to a prescribed level

energy of sections of the deligne hitchin twistor space we study a natural functional on the space of holomorphic sections of the deligne hitchin moduli space of a compact riemann surface generalizing the energy of equivariant harmonic maps corresponding to twistor lines we show that the energy is the residue of the pull back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by hitchin as a byproduct we show the existence of a hyper kahler potentials for new components of real holomorphic sections of twistor spaces of hyper kahler manifolds with rotating s 1 action additionally we prove that for a certain class of real holomorphic sections of the deligne hitchin moduli space the energy functional is basically given by the willmore energy of corresponding equivariant conformal map to the 3 sphere as an application we use the functional to distinguish new components of real holomorphic sections of the deligne hitchin moduli space from the space of twistor lines

a uniform estimate for general quaternionic calabi problem with appendix by daniel barlet abstract we prove a c 0 a priori estimate on a solution of the quaternionic calabi problem on an arbitrary compact connected hkt manifold this generalizes earlier results 9 and 7 where this result was proven under certain extra assumptions on the manifold

conification of kahler and hyper kahler manifolds given a kahler manifold m endowed with a hamiltonian killing vector field z we construct a conical kahler manifold hat m such that m is recovered as a kahler quotient of hat m similarly given a hyper kahler manifold m g j1 j2 j3 endowed with a killing vector field z hamiltonian with respect to the kahler form of j1 and satisfying mathcal l zj 2 2j 3 we construct a hyper kahler cone hat m such that m is a certain hyper kahler quotient of hat m in this way we recover a theorem by haydys our work is motivated by the problem of relating the supergravity c map to the rigid c map we show that any hyper kahler manifold in the image of the c map admits a killing vector field with the above properties therefore it gives rise to a hyper kahler cone which in turn defines a quaternionic kahler manifold our results for the signature of the metric and the sign of the scalar curvature are consistent with what we know about the supergravity c map

robust h sub spl infin compensator design for time delay systems with norm bounded time varying uncertainties considers robust h sub spl infin compensator design for linear systems that involve unknown time delays both in states and controls and time varying norm bounded parameter uncertainties sufficient conditions for designing robust compensators are obtained in terms of two riccati inequalities which are not mutually coupled through which a full order robust h sub spl infin compensator can be obtained finally a small example is given to show the applicability of the proposed approach

luenberger observer based h sub spl infin compensator design for nonstandard problems this paper presents luenberger observer based h sub spl infin compensator design methods for different nonstandard cases these design methods are developed based on the bounded real lemma and the resultant design algorithms are two riccati inequalities which are not mutually coupled

d instantons and twistors some exact results we present some results on instanton corrections to the hypermultiplet moduli space in calabi yau compactifications of type ii string theories previously using twistor methods only a class of d instantons d2 instantons wrapping a cycles was incorporated exactly and the rest was treated only linearly we go beyond the linear approximation and give a set of holomorphic functions which through a known procedure capture the effect of d instantons at all orders moreover we show that for a sector where all instanton charges have vanishing symplectic invariant scalar product the hypermultiplet metric can be computed explicitly

comments on n 2 supersymmetric σ models in projective superspace for the most general off shell supersymmetric model in projective superspace we elaborate on its formulation in terms of chiral superfields a universal model independent expression is obtained for the holomorphic symplectic two form which determines the second supersymmetry transformation this two form is associated with the two complex structures of the hyperk hler target space which are complimentary to the one used to realize the target space as a k hler manifold