optimal bounds for t singularities in stable surfaces abstract we explicitly bound t singularities on normal projective surfaces w with one singularity and k w ample this bound depends only on k w 2 and it is optimal when w is not rational we classify and realize surfaces attaining the bound for each nonnegative kodaira dimension of the minimal resolution of w this answers effectiveness of bounds see 1 2 17 for those surfaces

nevanlinna test of stability abstract in this paper a new test of stability for scalar autonomous systems known as nevanlinna test of stability is introduced this test can be derived using the bezoutian of the characteristic polynomial of a given system it is shown in this paper that an associated quadratic differential form called the bezoutian functional is positive if and only if the given system is asymptotically stable nevanlinna test of stability proceeds by checking if the bezoutian functional associated with a given system is positive

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

stable maps in higher dimensions we formulate a notion of stability for maps between polarised varieties which generalises kontsevich s definition when the domain is a curve and tian donaldson s definition of k stability when the target is a point we give some examples such as kodaira embeddings and fibrations we prove the existence of a projective moduli space of canonically polarised stable maps generalising the kontsevich alexeev moduli space of stable maps in dimensions one and two we also state an analogue of the yau tian donaldson conjecture in this setting relating stability of maps to the existence of certain canonical kahler metrics

a comparison of model reduction techniques from structural dynamics numerical mathematics and systems and control in this paper popular model reduction techniques from the fields of structural dynamics numerical mathematics and systems and control are reviewed and compared the motivation for such a comparison stems from the fact that the model reduction techniques in these fields have been developed fairly independently in addition the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique on the basis of the desired objectives and properties of the model reduction problem in particular a detailed review is given on mode displacement techniques moment matching methods and balanced truncation whereas important extensions are outlined briefly in addition a qualitative comparison of these methods is presented hereby focusing both on theoretical and computational aspects finally the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example

reduced order controller design using coprime factor model reduction two procedures for reduced order controller design that incorporate coprime factor model reduction techniques and a related robust stabilization problem are proposed it is shown that robust stability can be achieved with these controllers the results obtained show how to reduce the controller degree systematically they clearly indicate how the maximum stability margin influences allowable model reduction error

gramian matrices and balanced model of generalized systems in this work the generalization of reachability and observability gramian matrices of control generalized systems have been studied the properties of these matrices to be solutions of lyapunov equations have been analyzed in addition an algorithm to obtain balanced generalized systems is given

bounded real and positive real balanced truncation using σ normalised coprime factors in this article we will extend the method of balanced truncation using normalised right coprime factors of the system transfer matrix by meyer 1990 3 to balanced truncation with preservation of half line dissipativity special cases are preservation of positive realness and bounded realness we consider a half line dissipative input output system with quadratic supply rate given by a nonsingular symmetric matrix sigma with the property that its positive signature is equal to the number of input components of the system the transfer matrix of such system allows a sigma normalised right coprime factorisation we associate with such factorisation two lyapunov equations one of which is nonstandard involving the indefinite matrix sigma balancing will be based on making the unique solutions of these two lyapunov equations equal and diagonal the diagonal elements will be called the hankel sigma singular values because their squares are the nonzero eigenvalues of the composition of the graph hankel operator multiplication by sigma and the adjoint graph hankel operator this method of balanced truncation will be shown to preserve stability minimality and half line dissipativeness we will characterize the classical positive real and bounded real characteristic values in terms of the new hankel sigma singular values finally we will derive one step error bounds for the special case of balanced truncation of bounded real systems c 2009 elsevier b v all rights reserved

curve counting via stable pairs in the derived category for a nonsingular projective 3 fold x we define integer invariants virtually enumerating pairs c d where c x is an embedded curve and d c is a divisor a virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of x the resulting invariants are conjecturally equivalent after universal transformations to both the gromov witten and dt theories of x for calabi yau 3 folds the latter equivalence should be viewed as a wall crossing formula in the derived category

balanced realizations canonical form parametrization model reduction abstract balanced realizations are used to construct a canonical form for the set of minimal and asymptotically stable mimo systems of a given order a parametrization resutt is derived that allows us to show a truncation property of this canonical form

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

basepoint freeness for nef and big line bundles in positive characteristic a necessary and sufficient condition is given for semi ampleness of a numerically effective nef and big line bundle in positive characteristic one application is to the geometry of the universal stable curve over mg specifically the semi ampleness of the relative dualizing sheaf in positive characteristic an example is given which shows this and the semi ampleness criterion fail in characteristic zero a second application is to mori s program for minimal models of 3 folds in positive characteristic namely to the existence of birational extremal contractions

moduli of weierstrass fibrations with marked section abstract we study the moduli space of stable pairs x s s a i f i consisting of a weierstrass fibration x its section s and some fibers f i we find a compactification which is a dm stack and we describe the objects on the boundary we show that the fibration in the definition of weierstrass fibration extends to the boundary and it is equidimensional when s 1 we prove that there are wall crossing morphisms when the weights s and a i change when s 1 this recovers the work of la nave 36 and a special case of the work of ascher bejleri 11

stable limits of log surfaces and cohen macaulay singularities abstract given a family of surfaces of general type over a smooth curve one can apply semistable reduction and the minimal model program to obtain a stable reduction this is the basis for a geometric compactification for moduli spaces of surfaces of general type due to kollar shepherd barron and alexeev however this approach hinges on the fact that the resulting stable limit has relatively mild singularities in particular it should be cohen macaulay unfortunately the standard formalism does not guarantee that stable limits of families of log surfaces are cohen macaulay here we prove that this is the case

dissipativity preserving balancing for nonlinear systems a hankel operator approach abstract in this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system we discuss an approach that allows us to apply the theory of balancing based upon hankel singular value analysis in order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified asymptotically stable system then hankel singular value theory can be applied and the axis singular value functions of the modified system equal the nonlinear extensions of similarity invariants obtained from the required supply and available storage of the original system furthermore we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations the obtained relations are used to perform model order reduction based on balanced truncation yielding dissipative reduced order models for the original systems a second order electrical circuit example is included to illustrate the results

on quadratic differential forms this paper develops a theory around the notion of quadratic differential forms in the context of linear differential systems in many applications we need to not only understand the behavior of the system variables but also the behavior of certain functionals of these variables the obvious cases where such functionals are important are in lyapunov theory and in lq and h infty optimal control with some exceptions these theories have almost invariably concentrated on first order models and state representations in this paper we develop a theory for linear time invariant differential systems and quadratic functionals we argue that in the context of systems described by one variable polynomial matrices the appropriate tool to express quadratic functionals of the system variables are two variable polynomial matrices the main achievement of this paper is a description of the interaction of one and two variable polynomial matrices for the analysis of functionals and for the application of higher order lyapunov functionals

topology of the set of asymptotically stable minimal systems it is shown that the set of asymptotically stable and minimal single input single output systems of order n has n 1 connected components in the case of asymptotically stable and minimal multiple input multiple output systems however there is only one connected component

a functional approach to lqg balancing the paper has as its theme a circle of problems related to lqg balancing with a special emphasis on the related problems of model reduction and robust stabilization the aim is to present a unified point of view to both previously described problems the unification is achieved by focusing on the study of three functions and the relationships between them and the various operators that are associated with these functions with an arbitrary transfer function g one can associate canonically two objects the conjugate inner function which is based on the nrcf and the r which is associated with the lqg controller of the function g the approach that is taken is functional emphasizing operators a balanced realization of a stable g arises as a matrix representation of the shift realization with respect to a basis made out of suitably normalized hankel singular vectors a similar result holds for lqg balanced realizations here the underlying hankel operator we study is h r where r u m v n and u v s

on the projectivity of the moduli spaces of curves 1 there are basically three algebraic proofs of the projectivity of the moduli spaces of stable curves the original one by knudsen 8 9 the proof by mumford 12 and gieseker 5 which makes heavy use of the machinery of geometric invariant theory and the more recent one by viehweg 15 and kollar 10 which relies instead on the semipositivity of the direct images of powers of the relative dualizing sheaf and at least in kollar s version does not use geometric invariant theory at all in this note combining ideas from the above papers and from 4 we shall outline a proof of projectivity which we believe is simpler and more direct than any of the existing ones however while the proofs by mumford gieseker viehweg and kollar are applicable at least in principle to a wide variety of moduli problems ours uses in an essential way the peculiarities of the problem at hand and it is hard to see how it could be extended to other situations mumford s idea is to use the machinery of geometric invariant theory to directly construct the moduli space of stable curves as a projective quotient of the chow or hilbert scheme of pluricanonically embedded stable curves by the action of the projective linear group to be able to do so one needs to show that the k canonical images of stable curves are stable in the invariant theoretic sense for high k this is quite well understood although not really easy for smooth curves one notices that k canonically embedded stable curves are linearly stable and then proves that for smooth curves linear stability implies invariant theoretic stability in the singular case by contrast both mumford and gieseker have to rely on indirect arguments which are quite long and involved our main point is that one can avoid proving the invariant theoretic stability of singular stable curves provided one is willing to grant that moduli space exists as a complete algebraic space that this is the case incidentally is relatively easy to prove as in 10 we prove projectivity by applying to a suitable invertible sheaf one of the standard numerical ampleness criteria seshadri s criterion in our case the necessary numerical estimates are obtained using the techniques of 4 more precisely the invariant theoretic stability of linearly stable smooth curves is used to prove an inequality for families of stable curves which suitably interpreted says that the hypothesis of seshadri s criterion is satisfied for curves in moduli which are not contained in the boundary the case of curves lying in the boundary is then reduced to the previous one by standard elementary techniques in order to properly carry out this procedure which can be viewed as a sort of induction on the genus it is convenient to deal simultaneously with the moduli spaces of stable n pointed curves as well in a sense then our approach is to use invariant theoretic stability as a means of obtaining numerical inequalities rather than as a step in the construction of quotients by group actions

a note on closed loop balanced truncation closed loop balanced truncation is a model reduction method that aims at preserving the closed loop properties of the original controller we show that this method is equivalent to frequency weighted balanced truncation with certain weighting and that for observer based controllers a significant amount of computation can be saved because of the observer state feedback structure of the controller

the resolution property for schemes and stacks we prove the equivalence of two fundamental properties of algebraic stacks being a quotient stack in a strong sense and the resolution property which says that every coherent sheaf is a quotient of some vector bundle moreover we prove these properties in the important special case of orbifolds whose associated algebraic space is a scheme mathematics subject classification primary 14a20 secondary 14l30

murphy s law in algebraic geometry badly behaved deformation spaces we consider the question how bad can the deformation space of an object be the answer seems to be unless there is some a priori reason otherwise the deformation space may be as bad as possible we show this for a number of important moduli spaces more precisely every singularity of finite type over up to smooth parameters appears on the hilbert scheme of curves in projective space and the moduli spaces of smooth projective general type surfaces or higher dimensional varieties plane curves with nodes and cusps stable sheaves isolated threefold singularities and more the objects themselves are not pathological and are in fact as nice as can be the curves are smooth the surfaces are automorphism free and have very ample canonical bundle the stable sheaves are torsion free of rank 1 the singularities are normal and cohen macaulay etc this justifies mumford s philosophy that even moduli spaces of well behaved objects should be arbitrarily bad unless there is an a priori reason otherwise thus one can construct a smooth curve in projective space whose deformation space has any given number of components each with any given singularity type with any given non reduced behavior similarly one can give a surface over mathbb f p that lifts to p 7 but not p 8 of course the results hold in the holomorphic category as well it is usually difficult to compute deformation spaces directly from obstruction theories we circumvent this by relating them to more tractable deformation spaces via smooth morphisms the essential starting point is mnev s universality theorem

balanced canonical forms for minimal systems a normalized coprime factor approach abstract canonical forms are derived for the set of minimal systems of given order from a canonical form for a class of coinner transfer functions one of these canonical forms is in terms of so called riccati balanced coordinates the application of this work to model reduction is discussed

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

interconnection of j lossless behaviours in this paper motivated by the phenomenon of the interconnection of lossless electrical networks a class of behaviours known as j lossless behaviours is introduced where j is a symmetric two variable polynomial matrix it is shown that for certain values of j interconnection of j lossless behaviours leads to an oscillatory behaviour physically this translates to the fact that interconnection of two multi port lossless electrical networks results in an autonomous lossless electrical network finally the problem of decomposition of an oscillatory behaviour with a given characteristic polynomial as an interconnection of two single input single output behaviours such that one has a lossless positive real transfer function and the other has a lossless negative real transfer function is also considered this problem can be viewed as an inverse problem to the one of interconnection of j lossless behaviours

the structure of characteristic values for classes of linear time invariant systems abstractin this paper a particular structure of the characteristic values found in some classes of systems is dealt with in particular for the linear time invariant systems in minimal form a b c d with transfer function matrix g s for which if i is a characteristic value then also 1 i is consequently when the system order is odd a singular value is equal to one the classes of systems for which this property holds are characterised by the existence of specific state space representations moreover the same structure of the characteristic values can be also retrieved for the class of even g s gt s and odd g s gt s systems several examples related to multi input multi output mimo systems are reported also referring to real physical systems

projectivity of the moduli space of stable log varieties and subadditivity of log kodaira dimension reference epfl article 231100doi 10 1090 jams 871 url http dx doi org 10 1090 jams 871 record created on 2017 09 19 modified on 2017 10 02

methods for global concave minimization a bibliographic survey the global concave minimization problem is to find the constrained global minimum of a concave function since such a function may have many local minima finding the global minimum is a computationally difficult problem in this bibliographic survey which includes most of the recent papers on constrained global concave minimization we have attempted to briefly summarize the main ideas in each paper these recent papers include those concerned with large scale global concave minimization and bilinear programming

fibered stable varieties reference epfl article 231103doi 10 1090 tran 6386 url http dx doi org 10 1090 tran 6386 record created on 2017 09 19 modified on 2017 10 02

an implicit enumeration method for global optimization problems abstract this paper presents a new method for the global minimization of a function subject to linear constraints the feasible set is first covered by a union of simpler sets then some of them are eliminated using some global analytic information about the objective function e g lipschitz constants properties of the derivatives etc the remaining part of the cover is then refined and the process is repeated estimates for the computational complexity are given for some classes of problems numerical experience is also reported

lossless and dissipative distributed systems this paper deals with linear shift invariant distributed systems by this we mean systems described by constant coefficient linear partial differential equations we define dissipativity with respect to a quadratic differential form i e a quadratic functional in the system variables and their partial derivatives the main result states the equivalence of dissipativity and the existence of a storage function or a dissipation rate the proof of this result involves the construction of the dissipation rate we show that this problem can be reduced to hilbert s 17th problem on the representation of a nonnegative rational function as a sum of squares of rational functions

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

quasi projectivity of moduli spaces of polarized varieties by means of analytic methods the quasi projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of nonuniruled polarized varieties

normalised coprime factorizations for nonstrictly proper systems some earlier results of d g meyer and g f franklin see ibid vol ac 32 pp 227 8 march 1987 are extended and a procedure is derived for obtaining directly a normalized right coprime factorization of a system that may not be strictly proper

higher order linear lossless systems we define a lossless autonomous system as one having a quadratic differential form associated with it called the total energy which obeys the property of positivity and which is conserved in this paper we show that an autonomous system is lossless if and only if it is oscillatory next we discuss a suitable way of splitting the total energy function into its kinetic and potential energy components we also extend the investigation to the case of open systems

moduli spaces of weighted pointed stable curves abstract a weighted pointed curve consists of a nodal curve and a sequence of marked smooth points each assigned a number between zero and one a subset of the marked points may coincide if the sum of the corresponding weights is no greater than one we construct moduli spaces for these objects using methods of the log minimal model program and describe the induced birational morphisms between moduli spaces as the weights are varied in the genus zero case we explain the connection to geometric invariant theory quotients of points in the projective line and to compactifications of moduli spaces studied by kapranov keel and losev manin

tabu search methodology in global optimization abstract this paper investigates the application of tabu search methodology in global optimization a general multilevel tabu search algorithm is proposed the algorithm is applied to the problem of finding constrained global minima of a piecewise smooth function of the form x max 1 x m x subject to box constraints the tests are performed on a special class of problems of this type arising from the synthesis of radar polyphase codes it is shown that problems of this type are np hard

counting curves on surfaces in calabi yau 3 folds motivated by s duality modularity conjectures in string theory we define new invariants counting a restricted class of two dimensional torsion sheaves enumerating pairs z subset h in a calabi yau threefold x here h is a member of a sufficiently positive linear system and z is a one dimensional subscheme of it the associated sheaf is the ideal sheaf of z subset h pushed forward to x and considered as a certain joyce song pair in the derived category of x we express these invariants in terms of the mnop invariants of x

the uniformization of the moduli space of principally polarized abelian 6 folds author s alexeev valery donagi ron farkas gavril izadi elham ortega angela abstract abstractstarting from a beautiful idea of kanev we construct a uniformization of the moduli space mathcal a 6 of principally polarized abelian 6 folds in terms of curves and monodromy data we show that the general principally polarized abelian variety of dimension 6 is a prym tyurin variety corresponding to a degree 27 cover of the projective line having monodromy the weyl group of the e 6 lattice along the way we establish numerous facts concerning the geometry of the hurwitz space of such e 6 covers including 1 a proof that the canonical class of the hurwitz space is big 2 a concrete geometric description of the hodge hurwitz eigenbundles with respect to the kanev correspondence and 3 a description of the ramification divisor of the prym tyurin map from the hurwitz space to mathcal a 6 in the terms of syzygies of the abel prym tyurin curve

positive and negative solution of dual riccati equations by matrix sign function iteration abstract for a matrix algebraic riccati equation it is shown that the positive definite stabilizing solution the negative definite anti stabilizing solution and the positive and negative solutions of the corresponding dual equation may all be computed from a single matrix sign function iteration this is potentially far more efficient than four separate schur vector solutions moreover necessary and sufficient conditions are given for the existence of unique stabilizing or antistabilizing solutions of an algebraic riccati equation in terms of the matrix sign of an associated hamiltonian matrix

a gramian based approach to model reduction for uncertain systems the technical note considers a problem of model reduction for a class of uncertain systems with structured norm bounded uncertainty the technical note introduces controllability and observability gramians in terms of certain parameterized algebraic riccati inequalities based on these gramians three model reduction approaches are investigated for the underlying uncertain systems

on balanced realizations of bounded real and positive real functions based on normalized coprime factorizations with respect to indefinite metrics and the construction of suitable characteristic functions the ober balanced canonical forms for the classes of bounded real and positive real functions are derived this uses a matrix representation of the shift realization with respect to a basis related to sets of orthogonal polynomials

properties of optimally robust controllers abstract the robustness properties of controllers which are optimally robust with respect to normalized coprime factor uncertainty are analysed it is shown that such optimally robust controllers admit perturbations which are in size larger than the robustness measure it is shown how such perturbations can be constructed by solving hankel norm approximation problems

hypersurfaces in projective schemes and a moving lemma let x s be a quasi projective morphism over an affine base we develop in this article a technique for proving the existence of closed subschemes h s of x s with various favorable properties we offer several applications of this technique including the existence of finite quasi sections in certain projective morphisms and the existence of hypersurfaces in x s containing a given closed subscheme c and intersecting properly a closed set f assume now that the base s is the spectrum of a ring r such that for any finite morphism z s pic z is a torsion group this condition is satisfied if r is the ring of integers of a number field or the ring of functions of a smooth affine curve over a finite field we prove in this context a moving lemma pertaining to horizontal 1 cycles on a regular scheme x quasi projective and flat over s we also show the existence of a finite surjective s morphism to psd for any scheme x projective over s when x s has all its fibers of a fixed dimension d

linear quadratic gaussian balancing for discrete time infinite dimensional linear systems in this paper we study the existence of linear quadratic gaussian lqg balanced realizations for discrete time infinite dimensional systems lqg balanced realizations are those for which the smallest nonnegative self adjoint solutions of the control and filter riccati equations are equal we show that the control filter riccati equation has a nonnegative self adjoint solution if and only if the system is output input stabilizable our main result is that the transfer function of a discrete time linear system has an approximately controllable and observable lqg balanced realization iff it has an input and output stabilizable realization the corresponding control and filter riccati equations have unique nonnegative self adjoint solutions moreover approximately controllable and observable lqg balanced realizations are unique up to a unitary state space transformation finally we show that the spectrum of the product of the smallest nonnegative self adjoint solutions of the control and filter riccati equations is independent of the particular realization

nested hilbert schemes on surfaces virtual fundamental class abstract we construct virtual fundamental classes on nested hilbert schemes of points and curves in complex nonsingular projective surfaces these classes recover the virtual classes of seiberg witten theory as well as the reduced stable theory and play a crucial role in the reduced donaldson thomas theory of local surface threefolds that we study in 15 we show that certain integrals against the virtual fundamental classes of punctual nested hilbert schemes are expressed as integrals over the products of the hilbert scheme of points we are able to find explicit formulas for some of these integrals by relating them to carlsson okounkov s vertex operator formulas

a new set of invariants for linear systems application to reduced order compensator design a new set of invariants for linear systems weighting the contribution of each state component to the inherent closed loop lqg behavior of the system is presented together with applications to model order reduction and reduced order compensator design

positivity of relative canonical bundles and applications given a family f mathcal x to s of canonically polarized manifolds the unique kahler einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle mathcal k mathcal x s we use a global elliptic equation to show that this metric is strictly positive on mathcal x unless the family is infinitesimally trivial for degenerating families we show that the curvature form on the total space can be extended as a semi positive closed current by fiber integration it follows that the generalized weil petersson form on the base possesses an extension as a positive current we prove an extension theorem for hermitian line bundles whose curvature forms have this property this theorem can be applied to a determinant line bundle associated to the relative canonical bundle on the total space as an application the quasi projectivity of the moduli space mathcal m text can of canonically polarized varieties follows the direct images r n p f omega p mathcal x s mathcal k mathcal x s otimes m m 0 carry natural hermitian metrics we prove an explicit formula for the curvature tensor of these direct images we apply it to the morphisms s p mathcal t s to r p f lambda p mathcal t mathcal x s that are induced by the kodaira spencer map and obtain a differential geometric proof for hyperbolicity properties of mathcal m text can

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

normalized coprime factorizations and balancing for unstable nonlinear systems in this paper we first study the normalized right and left coprime factorizations of a nonlinear system from a state space point of view in order to do so we introduce the notion of inner and co inner nonlinear systems secondly we deal with balancing for unstable nonlinear systems for linear systems there are several ways to approach this problem and we generalize the ideas of balancing the normalized coprime factorization and of lqg balancing to the nonlinear case lqg balancing can be seen as measuring the influence of a state component on a certain future and past energy function we extend this interpretation to the nonlinear case furthermore we use the normalized coprime factorization to give another way of balancing the unstable nonlinear system we give the relation between these two methods of balancing which is similar to the relation in the linear case

erratum for boundedness of families of canonically polarized manifolds a higher dimensional analogue of shafarevich s conjecture we show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is nite and that this number is uniformly bounded in any nite type family of base varieties as a corollary we show that a direct generalization of the geometric version of shafarevich s original conjecture holds for innitesimally rigid families of canonically polarized varieties

modular compactifications of the space of marked trigonal curves abstract we construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent beginning with the standard admissible cover compactification the sequence first proceeds through contractions of the boundary divisors and then through flips of the so called maroni strata culminating in a fano model for even genera and a fano fibration for odd genera while the sequence of divisorial contractions arises from a more general construction the sequence of flips uses the particular geometry of triple covers we explicitly describe the mori chamber decomposition given by this sequence of flips

continuous time lti systems under lossless positive real transformations open loop balanced representation and truncated reduced order models abstractin this paper new results on the open loop balanced representation of continuous time linear time invariant systems are reported more particularly the effect of lossless positive real transformations on open loop balanced representations is investigated with specific attention to the problem of model order reduction the properties of systems where a lossless positive real transformation has been applied are discussed showing that if the original system is open loop balanced the resulting transformed system is still open loop balanced furthermore the singular values of the transformed system are related to those of the original one these results allow to derive a model order reduction strategy for this class of systems that leads to a consistent decrease of the numerical complexity the proposed approach reveals to be of particular interest for the design of reduced order systems with specific amplitude responses including analog multiband filters

reduced order control based on approximate inertial manifolds a reduced order method based on approximate inertial manifolds is applied to optimal control problems in infinite dimensional state spaces a detailed analysis of the method is given for the linear quadratic regulator problem the method can also be applied to higher order control systems with an appropriate decomposition of the state space in terms of slow and fast exponential decay

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given

balanced model reduction for linear time varying symmetric systems the goal of this paper is to develop balancing theory for the linear time varying ltv symmetric systems to this end first we extend the concept of symmetry in terms of the dual system then we define the cross gramian for the ltv systems for ltv symmetric systems we establish a connection among the controllability observability and cross gramians in particular if one of these three gramians is obtained the other two gramians can be constructed based on this fact we show that the symmetry structure is preserved under balanced truncation if the hankel singular values are pointwise distinct

compactifications of smooth families and of moduli spaces of polarized manifolds let m h be the moduli scheme of canonically polarized manifolds with hilbert polynomial h we construct for v 2 with h v 0 a projective compactification m h of the reduced moduli scheme m h red such that the ample invertible sheaf corresponding to det f v x0 y0 on the moduli stack has a natural extension pic m h a similar result is shown for moduli of polarized minimal models of kodaira dimension zero in both cases natural means that the pullback of to a curve c mh induced by a family f 0 x 0 c o 1 m h is isomorphic to det f v x c whenever fo extends to a semistable model f x c besides of the weak semistable reduction of abramovich karu and the extension theorem of gabber there are new tools hopefully of interest by themselves in particular we will need a theorem on the flattening of multiplier sheaves in families on their compatibility with pullbacks and on base change for their direct images twisted by certain semiample sheaves