a non archimedean ohsawa takegoshi extension theorem we prove an ohsawa takegoshi type extension theorem on the berkovich closed unit disc over certain non archimedean fields as an application we establish a non archimedean analogue of demailly s regularization theorem for quasisubharmonic functions on the berkovich unit disc

compactness of the neumann operator on singular complex spaces let x be a hermitian complex space of pure dimension n we show that the neumann operator on p q forms is compact at isolated singularities of x if p q n 1 n and q 1 the main step is the construction of compact solution operators for the equation on such spaces which is based on a general characterization of compactness in function spaces on singular spaces and that leads also to a criterion for compactness of more general green operators on singular spaces

zariski decomposition of b divisors based on a recent work of thomas bauer s j algebr geom to appear reproving the existence of zariski decompositions for surfaces we construct a b divisorial analogue of zariski decomposition in all dimensions

fourierp element for the analysis of beams and plates the use of products of polynomials and fourier series instead of mpolynomials alone in the p element shape functions is recommended

new outlook on the minimal model program ii we prove that the finite generation of adjoint rings implies all the foundational results of the minimal model program the rationality cone and contraction theorems the existence of flips and termination of flips with scaling in the presence of a big boundary

the mean field scaling function of the universality class of absorbing phase transitions with a conserved field we consider two mean field like models which belong to the universality class of absorbing phase transitions with a conserved field in both cases we analytically derive the order parameter as a function of the control parameter and of an external field conjugated to the order parameter this allows us to calculate the universal scaling function of the mean field behaviour the obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models showing that four is the upper critical dimension of this particular universality class

siu s invariance of plurigenera a one tower proof in this article our main goal is to establish an l 2 version of the wisted invariance of plurigenera we equally simplify the original two towers approach of yum tong siu

on multiplicities of graded sequences of ideals abstract we generalize a result from l ein et al math ag 0202303 proving that for an arbitrary graded sequence of zero dimensional ideals the multiplicity of the sequence is equal to its volume this is done using a deformation to monomial ideals as a consequence of our result we obtain a formula which computes the multiplicity of an ideal i in terms of the multiplicities of the initial monomial ideals of the powers i m we use this to give a new proof of the inequality between multiplicity and the log canonical threshold from de fernex et al j alg geom to appear

on the birational automorphisms of varieties of general type we show that the number of birational automorphisms of a variety of general type x is bounded by c vol x kx where c is a constant that only depends on the dimension of x

scaling behavior of the conserved transfer threshold process we analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process we determined the steady state scaling behavior of the order parameter as a function of both the control parameter and an external field conjugated to the order parameter the external field is realized as a spontaneous creation of active particles which drives the system away from criticality the obtained results yield that the conserved transfers threshold process belongs to the universality class of absorbing phase transitions in a conserved field

division theorems for exact sequences under certain integrability and geometric conditions we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of koszul complex by introducing a singular hermitian structure on the trivial bundle our results recover skoda s division theorem for holomorphic functions on pseudoconvex domains in complex euclidean spaces

threefolds with vanishing hodge cohomology we consider algebraic manifolds y of dimension 3 over c with h i y j y 0 for all j 0 and i 0 let x be a smooth completion of y with d x y an effective divisor on x with normal crossings if the d dimension of x is not zero then y is a fibre space over a smooth affine curve c i e we have a surjective morphism from y to c such that the general fibre is smooth and irreducible such that every fibre satisfies the same vanishing condition if an irreducible smooth fibre is not affine then the kodaira dimension of x is oc and the d dimension of x is 1 we also discuss sufficient conditions from the behavior of fibres or higher direct images to guarantee the global vanishing of hodge cohomology and the affineness of y

critical exponents for branching annihilating random walks with an even number of offspring recently takayasu and tretyakov phys rev lett 68 3060 1992 studied branching annihilating random walks baws with n 1 char21 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation in this article i study the baw with n 4 using time dependent simulations and finite size scaling obtaining precise estimates for various critical exponents the results are consistent with the conjecture ensuremath beta ensuremath nu mathrm ensuremath perp 1 2 ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp 7 4 ensuremath gamma 0 ensuremath delta 2 7 ensuremath eta 0 and mathrm ensuremath delta mathit h 9 2 these critical exponents characterize respectively the dependence of the order parameter ensuremath beta ensuremath nu mathrm ensuremath perp and relaxation time ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp on system size the growth of fluctuations ensuremath gamma close to the critical point the long time behavior of the probability of survival ensuremath delta and average number of particles ensuremath eta when starting at time zero with just two particles and finally the decay of the order parameter mathrm ensuremath delta mathit h at the critical point in the presence of an external source

a nadel vanishing theorem for metrics with minimal singularities on big line bundles abstract the purpose of this paper is to establish a nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we apply the theory of harmonic integrals and generalize enoki s proof of kollar s injectivity theorem moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics

analytic trapezoidal fourier p element for vibrating plane problems a trapezoidal fourier p element for the in plane vibration analysis of two dimensional elastic solids is presented trigonometric functions are used as enriching functions instead of polynomials to avoid ill conditioning problems the element matrices are analytically integrated in closed form with the additional fourier degrees of freedom d o f s the accuracy of the computed natural frequencies is greatly increased one element can predict many modes accurately since a triangle can be divided into three trapezoidal elements the range of application is much wider than the previously derived rectangular fourier p element numerical examples show that convergence is very fast with respect to the number of trigonometric terms comparison of natural modes calculated by the trapezoidal fourier p element and the conventional finite elements is carried out the results show that the trapezoidal fourier p element produces much higher accurate modes than the conventional finite elements with the same number of d o f s for a benchmark problem the condition number of the mass matrix using legendre p element increases rapidly and it becomes non positive with 22 terms the condition numbers of the fourier p element matrices are consistently much lower than those of the legendre p element

distribution of zeros of random and quantum chaotic sections of positive line bundles we study the limit distribution of zeros of certain sequences of holomorphic sections of high powers m n of a positive holomorphic hermitian line bundle l over a compact complex manifold m our first result concerns random sequences of sections using the natural probability measure on the space of sequences of orthonormal bases s n j of h 0 m l n we show that for almost every sequence s n j the associated sequence of zero currents 1 n z s n j tends to the curvature form of l thus the zeros of a sequence of sections s n h 0 m l n chosen independently and at random become uniformly distributed our second result concerns the zeros of quantum ergodic eigenfunctions where the relevant orthonormal bases s n j of h 0 m l n consist of eigensections of a quantum ergodic map we show that also in this case the zeros become uniformly distributed

l 2 properties of the overline partial and the overline partial neumann operator on spaces with isolated singularities let x be a hermitian complex space of pure dimension with only isolated singularities and pi m rightarrow x a resolution of singularities let omega subset subset x be a domain with no singularities in the boundary omega omega setminus mathrm sing x and omega pi 1 omega we relate l 2 properties of the overline partial and the overline partial neumann operator on omega to properties of the corresponding operators on omega where the situation is classically well understood outside some middle degrees there are compact solution operators for the overline partial equation on omega exactly if there are such operators on the resolution omega and the overline partial neumann operator is compact on omega exactly if it is compact on omega

a triangular fourier p element for the analysis of membrane vibrations abstract a triangular fourier p element for the analysis of membrane vibrations is presented the element s transverse displacement is written in terms of dimensionless area co ordinates and is described by three linear shape functions plus a variable number of trigonometric shape functions the three nodal displacements and the amplitudes of the trigonometric functions on the three edges and in the interior of the element respectively are used as generalized co ordinates inter element compatibility is achieved by matching the generalized co ordinates at the three nodes and the three edges results are obtained for a right isosceles triangular and a square membranes and comparisons are made with exact and linear triangular finite element solutions the results of both membranes confirm that the solutions converge very fast from above to the exact values as the number of trigonometric terms is increased and highly accurate values are obtained with the use of a very few terms the results also show that the triangular fourier p element produces a much higher accuracy than the linear triangular finite element with fewer system degrees of freedom

monge ampere equations in big cohomology classes we define non pluripolar products of an arbitrary number of closed positive 1 1 currents on a compact kahler manifold x given a big 1 1 cohomology class on x i e a class that can be represented by a strictly positive current and a positive measure on x of total mass equal to the volume of and putting no mass on pluripolar sets we show that can be written in a unique way as the top degree self intersection in the non pluripolar sense of a closed positive current in we then extend kolodziedj s approach to sup norm estimates to show that the solution has minimal singularities in the sense of demailly if has l 1 e density with respect to lebesgue measure if is smooth and positive everywhere we prove that t is smooth on the ample locus of provided is nef using a fixed point theorem we finally explain how to construct singular kahler einstein volume forms with minimal singularities on varieties of general type

on uniruled degenerations of algebraic varieties with trivial canonical divisor we give a uniruledness criterion on degenerate fibers in a family of varieties whose general fiber has a numerically trivial canonical divisor the criterion is related with the so called non nef locus of the canonical divisor of the total space

phase transitions on fractals iii infinitely ramified lattices for pt ii see ibid vol 17 p 435 1984 in the first two papers of this series the authors considered self similar fractal lattices with a finite order of ramification r in the present paper they study physical models defined on a family of fractals with r infinity in order to characterise the geometry of these systems they need the connectivity q and the lacunarity l in addition to the fractal dimensionality d it is found that discrete symmetry spin models on these lattices undergo a phase transition at tc 0 an approximate renormalisation group scheme is constructed and used to find the dependence of tc and the critical exponents on the geometrical factors they also solve the problem of resistor networks on these fractals and discuss its consequences concerning spin models with continuous symmetry

a geometric effective nullstellensatz the purpose of this paper is to present a geometric theorem which clarifies and extends in several directions work of brownawell kollar and others on the effective nullstellensatz specifically we work on an arbitrary smooth complex projective variety x with the previous classical results corresponding to the case when x is projective space in this setting we prove a local effective nullstellensatz for ideal sheaves and a corresponding global division theorem for adjoint type bundles we also make explicit the connection with the intersection theory of fulton and macpherson finally constructions involving products of prime ideals that appear in earlier work are replaced by geometrically more natural conditions involving orders of vanishing along subvarieties much of the previous activity in this area has been algebraic in nature and seems perhaps not well known in detail among geometers therefore we have felt it worthwhile to include here a rather extended introduction we start with an overview of the questions and earlier work on them then we present the set up and statement of our main theorem we conclude with a series of examples which can be read before the general result of what it yields in special cases

on a non vanishing conjecture of kawamata and the core of an ideal we show under suitable hypothesis which are sharp in a certain sense that the core of an m primary ideal in a regular local ring of dimension d is equal to the adjoint or multiplier ideal of its d th power this generalizes the fundamental formula for the core of an integrally closed ideal in a two dimensional regular local ring due to huneke and swanson we also find a generalization of this result to singular non regular settings which we show to be intimately related to the problem of finding non zero sections of ample line bundles on projective varieties in particular we show that a graded analog of our formula for core would imply a remarkable conjecture of kawamata predicting that every adjoint ample line bundle on a smooth variety admits a non zero section

deformations of canonical singularities m reid defined the concept of canonical singularities as those which appear on canonical models of algebraic varieties whose canonical rings are finitely generated from the view point of the classification theory of algebraic varieties it is expected that small deformations of a variety which has only canonical singularities have only canonical singularities the main result of this paper states that this is the case

l2 estimates on p convex riemannian manifolds abstract in this paper we establish various l 2 estimates for the exterior differential operator on p convex riemannian manifolds in the sense of harvey and lawson as applications we establish a carleman type estimate which is uniform with respect to both weight functions and domains and we also obtain topological restrictions for a riemannian manifold to be p convex

curvature of vector bundles associated to holomorphic fibrations let l be a semi positive line bundle over a kahler manifold x fibered over a complex manifold y assuming the fibers are compact and nonsingular we prove that the hermitian vector bundle e over y whose fibers over points y are the spaces of global sections over xy to l kx y endowed with the l2 metric is semi positive in the sense of nakano we also discuss various applications among them a partial result on a conjecture of griffiths on the positivity of ample bundles

free vibration analysis of plate using finite strip fourier p element a finite strip fourier p element for the in plane vibration analysis of plate is presented trignometric functions are used as enriching functions instead of polynomials to avoid ill conditioning problems with the additional fourier degrees of freedom dofs and reduce dimensions the accuracy of the computed natural frequencies is greatly increased numerical examples show that convergence is very fast with respect to the number of trignometric terms comparison of natural frequencies calculated by the finite strip fourier p element the fourier p element the finite strip and the conventional finite elements is carried out the results show that the finite strip fourier p element can obtain much higher accurate modes than the fourier p element the finite strip and the conventional finite elements

invariance of plurigenera in this paper we give a proof of the following long conjectured result on the invariance of the plurigenera main theorem let p x d be a smooth projective family of compact complex manifolds parametrized by the open unit 1 disk d assume that the bers xt py1 t t 2 d are of general type then for every positive integer m the plurigenus dimc c xt mkxt is independent of t 2 d where kxt is the canonical line bundle of xt

uniform bounds and symbolic powers on smooth varieties the purpose of this note is to show how one can use multiplier ideals toestablish effective uniform bounds on the multiplicative behavior of certainfamilies of ideal sheaves on a smooth algebraic variety in particular weprove a quick but rather surprising result concerning the symbolic powersof radical ideals on such a variety let

reentrant phase diagram of branching annihilating random walks with one and two offspring we investigate the phase diagram of branching annihilating random walks with one and two offspring in one dimension a walker can hop to a nearest neighbor site or branch with one or two offspring with relative ratio two walkers annihilate immediately when they meet in general this model exhibits a continuous phase transition from an active state into the absorbing state vacuum at a finite hopping probability we map out the phase diagram by monte carlo simulations that shows a reentrant phase transition from vacuum to an active state and finally into vacuum again as the relative rate of the two offspring branching process increases this reentrant property apparently contradicts the conventional wisdom that increasing the number of offspring will tend to make the system more active we show that the reentrant property is due to the static reflection symmetry of two offspring branching processes and the conventional wisdom is recovered when the dynamic reflection symmetry is introduced instead of the static one c 1995 the american physical society

universality split in absorbing phase transition with conserved field on fractal lattices the universality split in absorbing phase transition between the conserved lattice gas clg model and the conserved threshold transfer process cttp is investigated on a checkerboard fractal and on a sierpinski gasket the critical exponents theta beta nu and z which are associated with respectively the density of active particles in time the order parameter the temporal correlation length and the dynamics of active particles are elaborately measured for two models on selected fractal lattices the exponents for the clg model are found to be distinctly different from those of the cttp model on a checkerboard fractal whereas the two models exhibit the same critical behavior on a sierpinski gasket indicating that the universality split between the two models occurs only on a checkerboard fractal such a universality split is attributed from the dominant hopping mechanisms caused by the intrinsic properties of the underlying fractal lattice

discontinuous galerkin finite element in time for solving periodic differential equations the dynamics of rotating systems can be modeled by ordinary differential equations with periodic time varying coefficients and forcing discontinuous galerkin dg methods which are known to be higher order accurate a stable and locally conservative are used to solve such equations in this work dg methods are shown to find the steady state periodic solution of a constant coefficient structural dynamics problem with periodic forcing and b helicopter rotor rigid blade flapping equation which is a parametric ordinary differential equation with periodic time varying coefficients and periodic forcing convergence of the numerical solution obtained is studied for both the above equations while h and p are refined separately it is found that the dg method works well for these problems and allows the development of an element level error estimate which can be used to monitor convergence and hence develop adaptive schemes it is clear from the results that even though higher order polynomials result in much faster convergence with reduced computational effort it also results in deterioration of the numerical performance for p 12 two adaptive strategies based on the element level displacement jump norm i e h and hp refinement are proposed and demonstrated on problems with higher harmonic forcing primary controls and parametric variations

comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates this paper presents a comprehensive comparison study between the discrete singular convolution dsc and the well known global method of generalized differential quadrature gdq for vibration analysis so as to enhance the understanding of the dsc algorithm the dsc method is implemented through lagrange s delta sequence kernel dsc lk which utilizes local lagrange polynomials to calculate weighting coefficients whereas the gdq requires global ones moreover it is shown that the treatments of boundary conditions and the use of grid systems are different in the two methods comparison study is carried out on 21 rectangular plates of different combinations of simply supported s clamped c and transversely supported with nonuniform elastic rotational restraint e edges and five rectangular plates of mixed supporting edges some of which with a range of aspect ratios and rotational spring coefficients all the results of the dsc lk agree very well with both those in the literature and newly computed gdq results furthermore it is observed that the dsc lk performs much better for plates vibrating at higher order eigenfrequencies unlike the gdq the dsc lk is numerically stable for problems which require a large number of grid points

free vibration analysis of circular and annular sectorial thin plates using curve strip fourier p element abstract a curve strip fourier p element for free vibration analysis of circular and annular sectorial thin plates is presented the element transverse displacement is described by a fixed number of polynomial shape functions plus a variable number of trigonometric shape functions the polynomial shape functions are used to describe the element s nodal displacements and the trigonometric shape functions are used to provide additional freedom to the edges and the interior of the element with the additional fourier degrees of freedom dof and reduce dimensions the accuracy of the computed natural frequencies is greatly increased results are obtained for a number of circular and annular sectorial thin plates and comparisons are made with exact the curve strip fourier p element the proposed fourier p element and the finite strip element the results clearly show that the curve strip fourier p element produces a much higher accuracy than the proposed fourier p element the finite strip element

extinction survival and dynamical phase transition of branching annihilating random walk we analyze statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate numerical results for one two and three dimensions and for the sierpinski gasket are assessed in view of the mean field theory predictions universality classes are found to depend on the number of offsprings in space dimension less than 3

relative critical exponents non vanishing and metrics with minimal singularities in this article we establish a very general non vanishing statement as well as several properties of metrics with minimal singularities of adjoint bundles our arguments combine the proof of the classical non vanishing theorem due to v shokurov as well as many ideas from y t siu s analytic proof of the finite generation of the canonical ring an important tool is the notion of relative critical exponent of two closed positive currents with respect to a measure

bergman kernels and the pseudoeffectivity of relative canonical bundles a criterion for the pseudoeffectivity of twisted relative canonical bundles of surjective projective maps

absorbing phase transition in conserved lattice gas model on fractal lattices we study the continuous phase transition of the conserved lattice gas clg model from an active phase into an absorbing phase on two fractal lattices i e on a checkerboard fractal and on a sierpinski gasket in the clg model a particle is assumed to be active if any of the neighboring sites are occupied by a particle and inactive if all neighboring sites are empty we estimate critical exponents theta beta nu and nu perpendicular characterizing respectively the density of active particles in time the order parameter the temporal and spatial correlation lengths near the critical point and the results are confirmed by off critical scaling and finite size scaling the order parameter exponent beta on a checkerboard fractal appears to lie between the one dimensional 1d value and two dimensional 2d value of the clg model while that on a sierpinski gasket lies between the 1d and 2d values of the conserved threshold transfer process such a difference is manifested based on the intrinsic properties of the underlying fractal lattices

hierarchical finite element analyses of geometrically non linear vibration of beams and plane frames geometrically non linear vibrations of beams and plane frameworks are analyzed by the hierarchical finite element method hfem two main points are of interest the first is to compare polynomials trigonometric functions and beam eigenfunctions as displacement shape functions for beam hierarchical finite elements the second is to examine the suitability of the hfem for time domain non linear analyses

extension of sections via adjoint ideals we prove theorems on extending sections of line bundles from divisors to the ambient space inspired by various results of siu kawamata and especially hacon mckernan and takayama we include applications to basepoint freeness to the invariance of analogues of plurigenera and of part of the boundary of the pseudo effective cone in families and to a slightly simplified approach to results of hacon mckernan towards the existence of flips

extension theorems non vanishing and the existence of good minimal models we prove an extension theorem for effective purely log terminal pairs x s b of non negative kodaira dimension kappa k x s b ge 0 the main new ingredient is a refinement of the ohsawa takegoshi l 2 extension theorem involving singular hermitian metrics

families of conic kahler einstein metrics let p x rightarrow y be an holomorphic surjective map between compact kahler manifolds and let d be an effective divisor on x with generically simple normal crossings support and coefficients in 0 1 provided that the adjoint canonical bundle k x y d y of the generic fiber is ample we show that the current obtained by glueing the fiberwise conic kahler einstein metrics on the regular locus of the fibration is positive moreover we prove that this current is bounded outside the divisor and that it extends to a positive current on x

a solution of an l 2 extension problem with an optimal estimate and applications in this paper we prove an l 2 extension theorem with an optimal estimate in a precise way which implies optimal estimate versions of various well known l 2 extension theorems as applications we give proofs of a conjecture of suita on the equality condition in suita s conjecture the so called l conjecture and the extended suita conjecture as other applications we give armative answer to a question by ohsawa about limiting case for the extension operators between the weighted bergman spaces and we present a relation of our result to berndtsson s important result on log plurisubharmonicity of the bergman kernel

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

well defined set of exponents for a pair contact process with diffusion recently it was suggested that a pair contact process with diffusion pcpd might represent an independent new universality class different from the directed percolation dp and the parity conservation pc class the dynamics in the pcpd are usually controlled by two independent parameters the critical exponents for the pcpd are known to have different values for varying values of the two independent parameters however once the diffusion and annihilation or coagulation rate in the pcpd is tuned in a way that the process without offspring production is exactly solvable a well defined set of the exponents for the pcpd is obtained then dynamics are controlled by only one independent parameter the obtained critical exponents are different than those of dp and pc the critical exponents satisfy the generalized hyperscaling relation within numerical errors

scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension we analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field phys rev lett 85 1803 2000 we determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in d 2 3 4 5 dimensions a comparison of our results and those obtained from a mean field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four

division theorems for the koszul complex abstract we establish a twisted version of skoda s estimate for the koszul complex from which we get global division theorems for the koszul complex this generalizes skoda s division theorem we also show how to use skoda triples to produce division theorems for the koszul complex

universal finite size scaling behavior and universal dynamical scaling behavior of absorbing phase transitions with a conserved field we analyze numerically three different models exhibiting an absorbing phase transition we focus on the finite size scaling as well as the dynamical scaling behavior an accurate determination of several critical exponents allows one to validate certain hyperscaling relations using these hyperscaling relations it is possible to express the avalanche exponents of a self organized critical system in terms of the ordinary exponents of a continuous absorbing phase transition

boundedness of pluricanonical maps of varieties of general type using the techniques of 20 and 10 we prove that certain log forms may be lifted from a divisor to the ambient variety as a consequence of this result following 22 we show that for any positive integer n there exists an integer rn such that if x is a smooth projective variety of general type and dimension n then phi rk x colon x dasharrow mathbb p h 0 mathcal o x rk x is birational for all r rn

canonical singular hermitian metrics on relative canonical bundles we introduce a new class of canonical analytic zariski decompositions azd s in short called the supercanonical azd s on the canonical bundles of smooth projective varieties with pseudoeffective canonical classes we study the variation of the supercanonical azd hat h rm can under projective deformations and give a new proof of the invariance of plurigenera

a sector fourier p element applied to free vibration analysis of sectorial plates abstract a sector fourier p element is presented and applied to free vibration analysis of sectorial plates an important feature of this element is that it can describe the geometry of a sectorial plate exactly and is therefore suitable for this type of plate the element is formulated in terms of a fixed number of cubic polynomial shape functions plus a variable number of trigonometric hierarchical shape functions the cubic polynomial shape functions are used to describe the element s nodal d o f and the trigonometric hierarchical shape functions are used to give additional freedom to the edges and the interior of the element results are obtained for a number of sectorial plates with various boundary conditions and comparisons are made with exact and 16 d o f sector finite element solutions the results show that the solutions converge very quickly from above to the exact values as the number of trigonometric terms is increased and highly accurate values are obtained with the use of very few terms the results also show that the sector fourier p element gives a much higher accuracy than the 16 d o f sector finite element with far fewer system d o f

siu s lemma optimal l 2 extension and applications to twisted pluricanonical sheaves we prove a general version of siu s lemma for plurisubharmonic functions with nontrivial multiplier ideal sheaves and use it to prove an optimal l 2 extension theorem and an optimal l frac 2 m extension theorem for kahler fibrations these results are used to prove the positivity of twisted relative pluricanonical bundles and their direct images for kahler fibrations and to answer a comparison question about singular metrics of twisted pluricanonical bundles

a nadel vanishing theorem via injectivity theorems the purpose of this paper is to establish nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we generalize kollar s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics by making use of the theory of harmonic integrals moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles

the multiplier ideals of a sum of ideals we prove that if a b o x are nonzero sheaves of ideals on a complex smooth variety x then for every q we have the following relation between the multiplier ideals of a b and a b i x a b i x a i x b a similar formula holds for the asymptotic multiplier ideals of the sum of two graded systems of ideals we use this result to approximate at a given point arbitrary multiplier ideals by multiplier ideals associated to zero dimensional ideals this is applied to compare the multiplier ideals associated to a scheme in different embeddings

on invariance of plurigenera for foliations on surfaces let x be a smooth algebraic surface a foliation f on x is roughly speaking a subline bundle t f of the tangent bundle of x the dual of t f is called the canonical bundle of the foliation k f in the last few years birational methods have been successfully used in order to study foliations more precisely geometric properties of the foliation are translated into properties of the canonical bundle of the foliation one of the most important invariants describing the properties of a line bundle l is its kodaira dimension kappa l which measures the growth of the global sections of l and its tensor powers the kodaira dimension of a foliation f is defined as the kodaira dimension of its canonical bundle kappa k f in their fundamental works brunella and mcquillan give a classfication of foliations on surfaces on the model of enriques kodaira classification of surfaces the next step is the study of the behaviour of families of foliations brunella proves that for a family of foliations x t f t of dimension one on surfaces satisfying certain hypotheses of regularity the kodaira dimension of the foliation does not depend on t by analogy with siu s invariance of plurigenera it is natural to ask whether for a family of foliations x t f t the dimensions of global sections of the canonical bundle and its powers depend on t in this talk we will discuss to which extent an invariance of plurigenera for foliations is true and under which hypotheses on the family of foliations it holds

phase transitions on fractals i quasi linear lattices magnetic spin models and resistor networks are studied on certain self similar fractal lattices which are described as quasi linear because they share a significant property of the line finite portions can be isolated from the rest by removal of two points sites in all cases there is no long range order at finite temperature the transition at zero temperature has a discontinuity in the magnetisation and the associated magnetic exponent is equal to the fractal dimensionality d when the lattice reduces to a non branching curve the thermal exponent v 1 y is equal to d when the lattice is a branching curve y is related respectively to the dimensionality of the single channel segments of the curve for the ising model or to the exponent describing the resistivity for models with continuous spin symmetry