morse theory for periodic solutions of hamiltonian systems and the maslov index in this paper we prove morse type inequalities for the contractible 1 periodic solutions of time dependent hamiltonian differential equations on those compact symplectic manifolds m for which the symplectic form and the first chern class of the tangent bundle vanish over q m the proof is based on a version of infinite dimensional morse theory which is due to floer the key point is an index theorem for the fredholm operator which plays a central role in floer homology the index formula involves the maslov index of nondegenerate contractible periodic solutions this maslov index plays the same role as the morse index of a nondegenerate critical point does in finite dimensional morse theory we shall use this connection between floer homology and maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every i periodic solution has at least one floquet multiplier which is not equal to 1

a form of schwarz s lemma and a bound for the kobayashi metric on convex domains abstract we present a form of schwarz s lemma for holomorphic maps between convex domains d 1 and d 2 this result provides a lower bound on the distance between the images of relatively compact subsets of d 1 and the boundary of d 2 this is a natural improvement of an old estimate by bernal gonzalez that takes into account the geometry of d 1 using similar techniques we also provide a new estimate for the kobayashi metric on bounded convex domains

the denjoy wolff theorem in cn abstract if d is a bounded and strictly convex domain in c n and f d d is holomorphic and fixed point free then there exists d such that the sequence f n of the iterates of f converges in the compact open topology to the constant mapping taking the value

dilatation and order of contact for holomorphic self maps of strongly convex domains let d be a bounded strongly convex domain and let f be a holomorphic self map of d in this paper we introduce and study the dilatation alpha f of f defined if f has no fixed points in d as the usual boundary dilatation coefficient of f at its wolff point or if f has some fixed points in d as the ratio of shrinking of the kobayashi balls around a fixed point of f in particular we show that the map alpha defined as alpha f mapsto alpha f in 0 1 is lower semicontinuous among other things this allows us to study the limits of a family of holomorphic self maps of d in the case of an inner fixed point the dilatation is an intrinsic measure of the order of contact of f d to partial d finally using complex geodesics we define and study a directional dilatation which is a measure of the shrinking of the domain along a given direction again results of semicontinuity are given and applied to a family of holomorphic self maps

on the morse index of lagrangian systems we give a new proof of the identity between the morse index of a periodic solution of a lagrangian system positive definite in the velocities and its maslov index furthermore we give an interpretation of the maslov index when the lagrangian system is not positive definite in the velocities our approach consists in relating the morse index of the solution to a relative morse index obtained passing to the hamiltonian formulation the main concepts used are the notion of commensurable subspaces relative dimension fredholm pairs and relative index of strongly indefinite bilinear forms

the bar partial cauchy problem and nonexistence of lipschitz levi flat hypersurfaces in mathbb c p n with n ge 3 in this paper we study the cauchy riemann equation in complex projective spaces specifically we use the modified weight function method to study the bar partial neumann problem on pseudoconvex domains in these spaces the solutions are used to study function theory on pseudoconvex domains via the bar partial cauchy problem we apply our results to prove nonexistence of lipschitz levi flat hypersurfaces in complex projective spaces of dimension at least three which removes the smoothness requirement used in an earlier paper of siu

the denjoy wolff theorem for condensing holomorphic mappings if b is the open unit ball of a strictly convex banach space x and f b b is holomorphic condensing with respect to and fixed point free then there exists b such that the sequence lcub fn of the iterates of f converges in the compact open topology to the constant map taking the value

weighted boundary limits of the generalized kobayashi royden metrics on weakly pseudoconvex domains the purpose of this paper is to study the existence of weighted boundary limits of the generalized kobayashi royden metrics on weakly pseudoconvex domains in cn and to explore the connections between the limits and the levi invariants the main result extends graham s result on strongly pseudoconvex domains to a large class of weakly pseudoconvex domains

the denjoy wolff theorem in the open unit ball of a strictly convex banach space letxbe a complex strictly convex banach space with an open unit ballb for each compact holomorphic and fixed point free mappingf b bthere exists bsuch that the sequence fn of iterates offconverges locally uniformly onbto the constant map taking the value

an index theorem for non periodic solutions of hamiltonian systems we consider a hamiltonian setup m h l p where m is a symplectic manifold l is a distribution of lagrangian subspaces in m p a lagrangian submanifold of m h is a smooth time dependent hamiltonian function on m and a b m is an integral curve of the hamiltonian flow h starting at p we do not require any convexity property of the hamiltonian function h under the assump tion that b is not p focal it is introduced the maslov index imaslov of given in terms of the first relative homology group of the lagrangian g rassmannian under generic circumstances imaslov is computed as a sort of algebraic count of the p focal points along we prove the following version of the index theorem under suitable hypothe ses the morse index of the lagrangian action functional restricted to suitable variations of is equal to the sum of imaslov and a convexity term of the hamiltonian h rela tive to the submanifold p when the result is applied to the case of the cotangent bundle m t mof a semi riemannian manifold m g and to the geodesic hamiltonian h q p 1 g 1 p p we obtain a semi riemannian version of the celebrated morse index theorem for geodesics with variable endpoints in riemannian geometry

goldilocks domains a weak notion of visibility and applications in this paper we introduce a new class of domains in complex euclidean space called goldilocks domains and study their complex geometry these domains are defined in terms of a lower bound on how fast the kobayashi metric grows and an upper bound on how fast the kobayashi distance grows as one approaches the boundary strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this goldilocks condition but we also present families of goldilocks domains that have low boundary regularity or have boundary points of infinite type we will show that the kobayashi metric on these domains behaves in some sense like a negatively curved riemannian metric in particular it satisfies a visibility condition in the sense of eberlein and o neill this behavior allows us to prove a variety of results concerning boundary extension of maps and to establish wolff denjoy theorems for a wide collection of domains c 2017 elsevier inc all rights reserved

predicting response bounds for friction damped gas turbine blades with uncertain friction coupling abstract friction dampers are often used to reduce high amplitude vibration within gas turbines they are a robust solution that are able to withstand extreme operating environments although the turbine blades are manufactured to tight tolerances there can be significant variability in the overall response of the assembly uncertainties associated with the frictional contact properties are a major factor contributing to this variability this paper applies a recently developed method for predicting response bounds to friction damped gas turbines when the characteristics of the friction dampers are unknown including uncertainty regarding the underlying functional form of the friction law the approach taken is to represent the frictional contact using a describing function and formulate an optimisation problem to seek upper and lower bounds on a chosen response metric such as displacement amplitude constraints are chosen that describe known properties of the frictional nonlinearity without needing to specify a particular constitutive law the method was validated by comparison with numerical and experimental results from an idealised test system the experimental test rig consisted of an array of eight beams coupled by pin contact friction dampers a modal description of this test rig formed the basis of a numerical model which uses the harmonic balance method hbm for nonlinear simulations a set of monte carlo tests was carried out numerically and experimentally for both a two beam sub assembly as well as for the full eight beam assembly comparisons with numerical results showed excellent agreement providing confident verification of the implementation and comparisons with experimental results revealed that the bounds became less conservative as the system complexity increased overall the results are promising upper and lower response bounds for an array of friction damped systems can be computed at similar cost to a single hbm simulation giving reliable bounds that are valid for both parametric and model uncertainties associated with the friction couplings

on the trend to global equilibrium in spatially inhomogeneous entropy dissipating systems the linear fokker planck equation we study the long time behavior of kinetic equations in which transport and spatial confinement in an exterior potential or in a box are associated with a degenerate collision operator acting only in the velocity variable we expose a general method based on logarithmic sobolev inequalities and the entropy to overcome the well known problem due to the degeneracy in the position variable of the existence of infinitely many local equilibria this method requires that the solution be somewhat smooth in this paper we apply it to the linear fokker planck equation and prove decay to equilibrium faster than o t 1 for all 0 2001 john wiley sons inc

response bounds for complex systems with a localised and uncertain nonlinearity predicting the vibration response of complex nonlinear structures is a significant challenge the response may involve many modes of the structure nonlinearity precludes the use of efficient techniques developed for linear systems and there is often uncertainty associated with the nonlinear law even to the extent that its functional form is not always known this paper builds on a recently developed method for handling this class of problem in a novel way the method exploits the fact that nonlinearities are often spatially localised and seeks the best and worst case system response with respect to a chosen metric by regarding the internal nonlinear force as an independent excitation to the underlying linear system constraints are used to capture what is thought to be known about the nonlinearity without needing to specify a particular law this paper focuses on the case of systems with a single point nonlinearity but with arbitrarily complex underlying linear dynamics driven by a sinusoidal force excitation semi analytic upper and lower bounds are proposed for root mean square response metrics subject to constraints which specify that the nonlinearity should be a combination of a passive b displacement limited and or c force saturating the concept of equivalent linear bounds is also introduced for cases where the response metric is thought to be dominated by the same frequency as the input the bounds corresponding to a passive and displacement limited nonlinearity are compared with monte carlo experimental and numerical results from an impacting beam test rig the bounds corresponding to a passive and force saturating nonlinearity are compared with numerical results for a friction damped beam the global upper and lower bounds are satisfied for all input frequencies but are generally found to be rather conservative the equivalent linear bounds show remarkably good agreement for predicting the range of root mean square velocity responses finally the principle of maximum entropy is used to estimate the response distributions which was found to give surprisingly good agreement with experimental and numerical data

a denjoy wolff theorem for compact holomorphic mappings in reflexive banach spaces abstract using the kobayashi distance we establish a denjoy wolff theorem for compact holomorphic self mappings of a bounded and strictly convex domain in a complex reflexive banach space

the automorphism group and limit set of a bounded domain i the finite type case abstract for bounded pseudoconvex domains with finite type we give a precise description of the automorphism group if an orbit of the automorphism group accumulates on at least two different points of the boundary then the automorphism group has finitely many components and is the almost direct product of a compact group and connected lie group locally isomorphic to aut b k further the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2 k 1 as applications we prove a new finite jet determination theorem and a tits alternative theorem the geometry of the kobayashi metric plays an important role in the paper

holomorphic extension from the sphere to the ball abstract real analytic functions on the boundary of the sphere which have separate holomorphic extension along the complex lines through a boundary point have holomorphic extension to the ball this was proved in baracco 2009 4 by an argument of cr geometry we give here an elementary proof based on the expansion in holomorphic and antiholomorphic powers

the pluricomplex poisson kernel for strongly convex domains let d be a bounded strongly convex domain in the complex space of dimension n for a fixed point p epsilon partial derivative d we consider the solution of a homogeneous complex monge ampere equation with a simple pole at p we prove that such a solution enjoys many properties of the classical poisson kernel in the unit disc and thus deserves to be called the pluricomplex poisson kernel of d with pole at p in particular we discuss extremality properties such as a generalization of the classical phragmen lindelof theorem relations with the pluricomplex green function of d uniqueness in terms of the associated foliation and boundary behaviors finally using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

the bergman metric on complete kahler manifolds we use the existence of a bounded uniformly holder continuous plurisubharmonic exhaustion function to characterize the bergman completeness of a complete kahler manifold as an application we proved that any simply connected complete kahler manifold with sectional curvature bounded above by a negative constant is bergman complete

accurate extreme value based frequency response bounding for structures with a small number of highly random parameters abstract a modified extreme value based methodology is discussed for computing statistical bounds associated with the magnitude of the frequency response of a specified number of structures with high levels of random parameter uncertainty the methodology intended for small numbers of uncertain parameters is capable of constructing accurate statistical bounds in terms of quantiles associated with the extreme value distribution quantiles can be constructed for an ensemble of structural responses across the entire frequency range without using monte carlo simulation to test the methodology statistical bounds for the energy of an l shaped structure with low and high levels of uniformly distributed length and thickness variability are obtained i via direct integration using an ansys finite element model and ii via statistical energy analysis sea comparisons are shown with bounds obtained using monte carlo simulation the merit of direct integration for computing bounds associated with the responses of an ensemble of structures with high levels of random parameter uncertainty is demonstrated by its simplicity high accuracy and absence of statistical scatter

totally geodesic discs in strongly convex domains we prove that every isometry from the unit disk in mathbb c endowed with the poincare distance to a strongly convex bounded domain of class mathcal c 3 in mathbb c n endowed with the kobayashi distance is the composition of a complex geodesic of with either a conformal or an anti conformal automorphism of as a corollary we obtain that every isometry for the kobayashi distance from a strongly convex bounded domain of class mathcal c 3 in mathbb c n to a strongly convex bounded domain of class mathcal c 3 in mathbb c m is either holomorphic or anti holomorphic

a new obstruction to embedding lagrangian tori n let 2n be endowed with the canonical symplectic form a i 1 dxi dy i and consider a lagrangian embedding of a compact manifold j l r 2 a a well known result due to g r o m o v g states that the cohomology class of a in h z e 2 l is non zero we identify l with its image in r2 an equivalent assertion is that the liouville form 2 y 7 1 xldy i pulls back to a closed form j 2 on l whose cohomology class does not vanish g r o m o v s proof uses subtle properties of holomorphic maps into c he shows that there is always a holomorphic disk a in c with boundary in l on such a disk a is positive hence sa a soa 2 0 in this paper we shall only consider the case l t and give an elementary proof of gromov s result elementary should be understood in the sense of number theory that is without using holomorphic functions in fact our result is somewhat more precise and can be stated as follows

complex geodesics and iterates of holomorphic maps on convex domains in ⁿ we study complex geodesics f where is the unit disk in c and belongs to a class of bounded convex domains in c n with no boundary regularity assumption along with continuity up to the boundary existence of such complex geodesics with two prescribed values z w is established as a consequence we obtain some new results from iteration theory of holomorphic self maps of bounded convex domains in c n

extremal analytic discs with prescribed boundary data this paper concerns the existence and uniqueness of extremal analytic discs with prescribed boundary data in a bounded strictly linearly convex domain d in cn we prove that for any two distinct points p q in dd respectively p e dd and a vector v such that f lv e tp dd and v p p 2 vji j p 0 where v p is the outward normal to dd at p there exists an extremal analytic disc passing through p q if dd e ck k 3 respectively l p l v if dd e ck k 14 consequently we can foliate d with these extremal analytic discs introduction in this paper we always assume that d is a bounded strictly linearly convex domain in cn see 1 for definitions let u denote the open unit disc in c an extremal analytic disc of d is a holomorphic map from u into d such that the kobayashi distance of any two points in f u is realized by lempert in 6 7 has proved the existence uniqueness and boundary regularity of such maps with data given at interior points following 7 we shall use the term e mapping for the extremal analytic disc it is also known 6 proposition 5 that if dd is of class ck k 3 then any e mapping of d is in ck 2 u

a wolff theorem for finite rank bounded symmetric domains abstract we present a wolff theorem for all infinite dimensional bounded symmetric domains of finite rank namely if b is the open unit ball of any finite rank j b triple and f b b is a compact holomorphic map with no fixed point in b we prove convex f invariant subdomains of b of all sizes and at all points exist in the form of simple operator balls c t b for c b and t an invertible linear map these are exact infinite dimensional analogues of the invariant discs in the invariant ellipsoids in the hilbert ball and invariant domains in finite dimensional triples results are new for rank 2 even for classical spaces such as c algebras and j b algebras

estimation on invariant distances on pseudoconvex domains of finite type in dimension two we study the class of smooth bounded weakly pseudoconvex domains open image in new window that are of finite type in the sense of j kohn and prove effective estimates on the invariant distances of bergman and kobayashi and also for the inner distance that is associated to the caratheodory distance

comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains we prove that for a strongly pseudoconvex domain d subset mathbb c n the infinitesimal caratheodory metric g c z v and the infinitesimal kobayashi metric g k z v coincide if z is sufficiently close to bd and if v is sufficiently close to being tangential to bd also we show that every two close points of d sufficiently close to the boundary and whose difference is almost tangential to bd can be joined by a unique up to reparameterization complex geodesic of d which is also a holomorphic retract of d the same continues to hold if d is a worm domain as long as the points are sufficiently close to a strongly pseudoconvex boundary point we also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed this has consequences for the behavior of the squeezing function

response variance prediction in the statistical energy analysis of built up systems in the statistical energy analysis sea of high frequency noise and vibration a complex engineering structure is represented as an assembly of subsystems the response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem and these energies are found by employing the principle of power balance strictly the computed energy is an average taken over an ensemble of random structures and for many years there has been interest in extending the sea prediction to the variance of the energy a variance prediction method for a general built up structure is presented here closed form expressions for the variance are obtained in terms of the standard sea parameters and an additional set of parameters alpha k that describe the nature of the power input to each subsystem k and alpha ks that describe the nature of the coupling between subsystems k and s the theory is validated by comparison with monte carlo simulations of plate networks and structural acoustic systems

characterizing domains by the limit set of their automorphism group abstract in this paper we study the automorphism group of smoothly bounded convex domains we show that such a domain is biholomorphic to a polynomial ellipsoid that is a domain defined by a weighted homogeneous balanced polynomial if and only if the limit set of the automorphism group intersects at least two closed complex faces of the set the proof relies on a detailed study of the geometry of the kobayashi metric and ideas from the theory of non positively curved metric spaces we also obtain a number of other results including the greene krantz conjecture in the case of uniform non tangential convergence new results about continuous extensions of biholomorphisms and complex geodesics and a new wolff denjoy theorem

the poincare hopf theorem for relative braid classes this paper studies the existence and multiplicity of closed integral curves of smooth vector fields on the closed 2 disc mathbb d 2 in the complement of a suitable geometric braid y called a skeleton the strands in a skeleton y must be trajectories of the vector field and the 1 periodic orbits to be counted must also be representatives of a suitable relative braid class x in the complement of y from leray schauder degree theory a signed count of the closed trajectories representing x in the complement of y is independent of the vector field it therefore suffices to compute or estimate the signed count of periodic orbits for a particularly convenient vector field we show that the signed count equals the euler floer characteristic of braid floer homology cf van den berg et al in j differ equ 259 5 1663 1721 2015 the latter can be computed via a finite cube complex which serves as a model for the given braid class

a quantitative analysis of oka s lemma in this paper we will examine a strong form of oka s lemma which provides sufficient conditions for compact and subelliptic estimates for the overline partial neumann operator on lipschitz domains on smooth domains the condition for subellipticity is equivalent to d angelo finite type and the condition for compactness is equivalent to catlin s condition p as an application we will prove regularity for the overline partial neumann operator in the sobolev space ws 0 leq s frac 1 2 on c2 domains

the level crossing rates and associated statistical properties of a random frequency response function abstract this work is concerned with the statistical properties of the frequency response function of the energy of a random system earlier studies have considered the statistical distribution of the function at a single frequency or alternatively the statistics of a band average of the function in contrast the present analysis considers the statistical fluctuations over a frequency band and results are obtained for the mean rate at which the function crosses a specified level or equivalently the average number of times the level is crossed within the band results are also obtained for the probability of crossing a specified level at least once the mean rate of occurrence of peaks and the mean trough to peak height the analysis is based on the assumption that the natural frequencies and mode shapes of the system have statistical properties that are governed by the gaussian orthogonal ensemble goe and the validity of this assumption is demonstrated by comparison with numerical simulations for a random plate the work has application to the assessment of the performance of dynamic systems that are sensitive to random imperfections

localization of the kobayashi metric and the boundary continuity of proper holomorphic mappings a classical theorem of carath6odory 8 states that every biholomorphic map f d d2 between domains in the complex plane c bounded by simple closed jordan curves extends to a homeomorphism of 31 onto 2 there are some well known generalizations of this result to domains in ie a if d t and d2 are bounded pseudoconvex domains in 112 with if2 boundary and if the infinitezimal kobayashi metric on d2 grows sufficiently fast near the boundary of d2 ko2 g x xl d z bdz for some e e 0 1 then every proper holomorphic map f dt d2 extends to a h61der continuous map of 51 onto 32 2 3 10 25 29 32 this holds in particular if 92 is strictly pseudoconvex or if it is pseudoconvex with real analytic boundary the same result holds if d2 is only piecewise smooth strongly pseudoconvex 31 further results treat exceptional cases such as the balls 1 reinhardt domains 5 24 domains with many symmetries 4 and analytically bounded hartogs domains in c 2 i1 biholomorphic maps between certain types of nonpseudoconvex domains with real analytic boundaries were treated in 13 and 27 besides the papers mentioned above there is a vast literature concerning smooth extension of proper holomorphic maps of smoothly bounded pseudoconvex domains 6 7 12 14 to mention just a few in the present paper we obtain some results on the continuous extension of proper holomorphic maps f d1 2 under local assumptions on the boundaries bd1 and bd2 one of the main results is

random iterations fixed points and invariant crf horospheres in complex banach spaces abstract for holomorphic noncontractive maps on not necessarily bounded domains in complex banach spaces we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations in particular we show that the problem concerning the existence of the horospheres determined by caratheodory reiffen finsler pseudometrics defined on unbounded domains has the solution and we prove new results of type of julia s lemma and wolff s theorem

horoballs and iteration of holomorphic maps on bounded symmetric domains abstract given a fixed point free compact holomorphic self map f on a bounded symmetric domain d which may be infinite dimensional we establish the existence of a family h 0 of convex f invariant domains at a point in the boundary d of d which generalises completely wolff s theorem for the open unit disc in c further we construct horoballs at and show that they are exactly the f invariant domains when d is of finite rank consequently we show in the latter case that the limit functions of the iterates f n with weakly closed range all accumulate in one single boundary component of d

embedding strictly pseudoconvex domains into balls every relatively compact strictly pseudocc nvex domain d with c2 boundary in a stein manifold can be embedded as a closed complex submanifold of a finite dimensional ball however for each n 2 there exist bounded strictly pseudoconvex domains d in cn with real analytic boundary such that no proper holomorphic map from d into any finite dimensional ball extends smoothly to d 0 introduction in this paper we study the representations of bounded strictly pseudoconvex domains d c cn if the boundary of d is of class ck k e 2 3 oo then by a theorem of fornaess 8 and khenkin 13 d can be mapped biholomorphically onto the intersection xn q of a bounded strictly convex domain q c cn with ck boundary and a closed complex submanifold x defirxed in a neighborhood of q in cn x intersecting the boundary of q transversally moreover the map f d x n q extends to a holomorphic map on a neighborhood of d the convex domain q depends on d hence a natural question is whether a similar result holds with q replaced by the unit ball b z z1l zn e cn z 2 e zjl2 n that intersects bbn transversally such that d is biholomorphically equivalent to xn e3ff this question has been mentioned by lempert 14 pinduk 20 bedford 2 and others our main result is that the answer to this question is negative in general if d is as above then every biholomorphism of d onto xne3n extends smoothly to d according to 3 however we will show that not all such domains d admit a proper holomorphic map into a finite dimensional ball that is smooth on d theorem 1 1 a similar local result was obtained independently by faran 7 we shall show that the answer to the question q is positive if we allow the intersections of complex submanifolds with strictly convex domains q c cn with real analytic boundaries theorem 1 2 thetheoremsoffornaess 8 andkhenkin 13 onlygiveanqwith smooth boundary received by the editors april 4t 1985 1980 mathematics subject classification primary 32h05 1research supported by a fellowship from the alfred p sloan foundation t 1986 american mathematical society 0002 9947 86 1 00 25 per page

numerical and experimental validation of variance prediction in the statistical energy analysis of built up systems in the statistical energy analysis sea approach to vibration modeling a complex system is represented as an assembly of coupled subsystems and the method leads to the prediction of the vibrational energy level of each subsystem the averaging procedures implicit in the technique imply that the predicted energy is the mean value taken over an ensemble of random structures such as a set of vehicles leaving a production line recently a new method has been developed to allow the ensemble variance in addition to the mean to be predicted within the context of sea and the present paper concerns further extension and validation of this work the theoretical extension concerns the variance of the energy density at a single point in any of the subsystems and the validation includes both simulation and experimental studies the simulation results concern plate assemblies while experimental results are presented both for a single plate and for a cylinder plate structure in each case an ensemble of random structures has been generated by adding small point masses at random locations on the structure in general good agreement between the predictions and the validation results is observed

backward iteration in strongly convex domains we prove that a backward orbit with bounded kobayashi step for a hyperbolic parabolic or strongly elliptic holomorphic self map of a bounded strongly convex c 2 domain in c d necessarily converges to a repelling or parabolic boundary fixed point generalizing previous results obtained by poggi corradini in the unit disk and by ostapyuk in the unit ball of c d

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

plurisubharmonic approximation and boundary values of plurisubharmonic functions we study the problem of approximating plurisubharmonic functions on a bounded domain omega by continuous plurisubharmonic functions defined on neighborhoods of omega over bar it turns out that t

response variance prediction for uncertain vibro acoustic systems using a hybrid deterministic statistical method imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance recently a hybrid method has been developed to predict the ensemble average response of a built up system by combining a deterministic model of parts of the system with a statistical model of other components shorter p j and langley r s 2005 j sound vib 288 669 700 in this paper the method is extended to predict the ensemble variance of the response expressions are derived for the variance of the vibrational energies in the statistical components and for the variance of the cross spectrum of the response of the deterministic components which augment the mean values of these quantities predicted by the original theory the method employs a nonparametric model of uncertainty in the sense that the statistical components are taken to carry diffuse wave fields and this obviates the requirement for a detailed description of the system uncertainties the method is validated by application to a range of coupled plate structures and good agreement with detailed monte carlo simulations is found

on the diffuse field reciprocity relationship and vibrational energy variance in a random subsystem at high frequencies a recent paper has shown that under certain conditions the cross spectral matrix of the forces exerted by a vibrational or acoustic wave field on its surrounding boundaries can be expressed in terms of i the energy of the wave field and ii the direct field dynamic stiffness matrix of the boundary this diffuse field reciprocity relation was derived using wave mechanics and it is not immediately clear how the required wave field properties translate to conditions on the vibrational modes of the system or the applied forcing this issue is addressed here by deriving an extended version of the reciprocity relation using modal methods and the conditions required for the extended version to reduce to the existing relation are delineated it is shown that the existing diffuse field reciprocity relation leads to an anomalous result when used to predict the energy variance of a subsystem and that this anomaly is resolved by using the present extended version of the relation a supplementary result arising from the analysis is that for systems with a sufficient degree of randomness the ensemble average of the dynamic stiffness matrix of a random subsystem is equal to the inverse of the ensemble average of the receptance matrix

the weak lower semicontinuity of the kobayashi distance and its applications in this paper we prove the lower semicontinuity with respect to the weak topology of the kobayashi distance in a bounded convex and open subset of a reflexive banach space we apply this result to the denjoy wolff theorem for condensing mappings in the unit open ball in a strictly convex reflexive banach space with the kadec klee property

random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces conditions which guarantee the uniform convergence of random iterations of holomorphic contractions on unbounded domains in complex hausdorff locally convex and sequentially complete topological vector spaces are established also conditions concerning the convergence of random iterations of weaker contractions in hausdorff uniform spaces are given

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

monge ampere foliations with singularities at the boundary of strongly convex domains let d c n be a bounded strongly convex domain with smooth boundary we consider a monge ampere type equation in d with a simple pole at the boundary using the lempert foliation of d in extremal discs we construct a solution u whose level sets are bound aries of horospheres among other things we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution

gromov hyperbolicity and the kobayashi metric on convex domains of finite type in this paper we prove necessary and sufficient conditions for the kobayashi metric on a convex domain to be gromov hyperbolic in particular we show that for convex domains with c infty boundary being of finite type in the sense of d angelo is equivalent to the gromov hyperbolicity of the kobayashi metric we also show that bounded domains which are locally convexifiable and have finite type in the sense of d angelo have gromov hyperbolic kobayashi metric the proofs use ideas from the theory of the hilbert metric