a linear code for the sawtooth and cat maps abstract the sawtooth maps are a one parameter set of piecewise linear area preserving maps on the torus for positive integer values of the parameter k they are automorphisms of the torus known as the cat maps we present a symbolic dynamics for these maps in which the symbols are integers this code is related to a practical problem of the stabilisation of a system which is perturbed by impulses the code is linear in the sense that an orbit and its code are linearly related so it is not difficult to obtain a good approximation to one from the other in practice a stationary stochastic process for generating the code is given explicitly the theory uses green function methods which are also used to study ordered periodic orbits and cantori the problems of using a similar code for arbitrary area preserving twist maps on the torus are briefly discussed

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

hodge metrics and positivity of direct images building on fujita griffiths method of computing metrics on hodge bundles we show that the direct image of an adjoint semi ample line bundle by a projective submersion has a continuous metric with griffiths semi positive curvature this shows that for every holomorphic semi ample vector bundle e on a complex manifold and every positive integer k the vector bundle se dete has a continuous metric with griffiths semi positive curvature if e is ample on a projective manifold the metric can be made smooth and griffiths positive

information theoretic characterization of quantum chaos hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a hamiltonian system from increasing we demonstrate numerically that hypersensitivity to perturbation is present in the following quantum maps the quantum kicked top the quantum baker s map the quantum lazy baker s map and the quantum sawtooth and cat maps

strong convergence of an iterative method for nonexpansive and accretive operators abstract let x be a banach space and a an m accretive operator with a zero consider the iterative method that generates the sequence x n by the algorithm x n 1 n u 1 n j r n x n where n and r n are two sequences satisfying certain conditions and j r denotes the resolvent i r a 1 for r 0 strong convergence of the algorithm x n is proved assuming x either has a weakly continuous duality map or is uniformly smooth

chaos for liouville probability densities using the method of symbolic dynamics we show that a large class of classical chaotic maps exhibits exponential hypersensitivity to perturbation i e a rapid increase with time of the information needed to describe the perturbed time evolution of the liouville density the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation the exponential rate of growth of the ratio of information to entropy is given by the kolmogorov sinai entropy of the map these findings generalize and extend results obtained for the baker s map r schack and c m caves phys rev lett 69 3413 1992

approximation of a zero point of accretive operator in banach spaces abstract this paper introduces a composite iteration scheme for approximating a zero point of accretive operator in the framework of uniformly smooth banach spaces and the reflexive banach space which has a weak continuous duality map respectively strong convergence of the composite iteration scheme x n defined by y n n x n 1 n j r n x n x n 1 n u 1 n y n where j r n is the resolvent of m accretive operator a and u c is an arbitrary but fixed element in c and sequences n in 0 1 n in 0 1 is established under certain appropriate assumptions on the sequences n n and r n that x n defined by the above iteration scheme converges to a zero point of a is proved the results improve and extend results of t h kim h k xu and some others

the bakerian lecture 1987 quantum chaology bounded or driven classical systems often exhibit chaos exponential instability that persists but their quantum counterparts do not nevertheless there are new regimes of quantum behaviour that emerge in the semiclassical limit and depend on whether the classical orbits are regular or chaotic and this motivates the following definition definition quantum chaology is the study of semiclassical but nonclassical behaviour characteristic of systems whose classical motion exhibits chaos this is illustrated by the statistics of energy levels on scales comparable with the mean level spacing of order h n for n freedoms these fall into universality classes for classically chaotic systems the statistics are those of random matrices real symmetric or complex hermitian depending on the presence or absence of time reversal symmetry for classically regular ones the statistics are poisson on larger scales of order h i e classically small but semiclassically large universality breaks down these phenomena are being explained by representing spectra in terms of classical closed orbits universal spectral behaviour has its origin in very long orbits non universal behaviour depends only on short ones

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

approximating solution of 0 t x for an h accretive operator in banach spaces abstract we firstly study the inclusion problem of 0 t x for an h accretive operator introduced in yaping fang nanjing huang h accretive operators and resolvent operator technique for solving variational inclusions in banach spaces appl math lett 17 2004 647 653 in banach spaces and obtain strong convergence theorems and weak convergence theorems simultaneously we analyze the relations between m accretive operators and h accretive operators and give some numerical examples to explain main results the main results presented in this paper mainly extend and improve the results of tomas dominguez benavides genaro lopez acedo hong kun xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 and hong kun xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 from m accretive operators to h accretive operators

convergence of composite iterative methods for finding zeros of accretive operators abstract strong convergence theorems on composite iterative schemes by the viscosity approximation methods for finding a zero of an accretive operator are established in banach spaces the main results generalize the recent corresponding results of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 ceng et al l c ceng a r khan q h ansari j c yao strong convergence of composite iterative schemes for zeros of m accretive operators in banach spaces nonlinear anal 70 2009 1830 1840 kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 to viscosity methods in a strictly convex and reflexive banach space having a uniformly g teaux differentiable norm our results also improve the corresponding results of t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory appl 2006 2006 1 10 s kamimura w takahashi approximation solutions of maximal monotone operators in hilbert spaces j approx theory 106 2000 226 240 p e mainge viscosity methods for zeroes of accretive operators j approx theory 140 2 2006 127 140 k nakajo strong convergence to zeros of accretive operators in banach spaces j nonlinear convex anal 7 2006 71 81

unknown quantum states the quantum de finetti representation we present an elementary proof of the quantum de finetti representation theorem a quantum analog of de finetti s classical theorem on exchangeable probability assignments this contrasts with the original proof of hudson and moody z wahrschein verw geb 33 343 1976 which relies on advanced mathematics and does not share the same potential for generalization the classical de finetti theorem provides an operational definition of the concept of an unknown probability in bayesian probability theory where probabilities are taken to be degrees of belief instead of objective states of nature the quantum de finetti theorem in a closely analogous fashion deals with exchangeable density operator assignments and provides an operational definition of the concept of an unknown quantum state in quantum state tomography this result is especially important for information based interpretations of quantum mechanics where quantum states like probabilities are taken to be states of knowledge rather than

semiclassical properties and chaos degree for the quantum baker s map we study the chaotic behavior and the quantum classical correspondence for the baker s map correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale the quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model the correspondence between classical and quantum chaos degrees is considered

the classical limit for a class of quantum baker s maps we show that the class of quantum baker s maps defined by schack and caves have the proper classical limit provided the number of momentum bits approaches infinity this is done by deriving a semi classical approximation to the coherent state propagator

strong convergence of a new composite iterative method for equilibrium problems and fixed point problems in this paper we propose a new composite iterative method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings in a hilbert space it is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings our results improve and extend the corresponding ones announced by many others

anosov actions on noncommutative algebras an axiomatic framework for a quantum mechanical extension to the theory of anosov systems is constructed and it is shown that this retains some of the characteristic features of its classical counterpart e g nonvanishing lyapunov exponents a vectorial k property and exponential clustering the effects of quantization are investigated on two prototype examples of anosov systems namely the iterations of an automorphism of the torus the arnold cat model and the free dynamics of a particle on a surface of negative curvature it emerges that the anosov property survives quantization in the case of the former model but not of the latter one finally we show that the modular dynamics of a relativistic quantum field on the rindler wedge of minkowski space is that of an anosov system

representability of chern weil forms in this paper we look at two naturally occurring situations where the following question arises when one can find a metric so that a chern weil form can be represented by a given form the first setting is semi stable hartshorne ample vector bundles on complex surfaces where we provide evidence for a conjecture of griffiths by producing metrics whose chern forms are positive the second scenario deals with a particular rank 2 bundle related to the vortex equations over a product of a riemann surface and the sphere

invariant connections and vortices we study the vortex equations on a line bundle over a compact kahler manifold these are a generalization of the classical vortex equations over 2 we first prove an invariant version of the theorem of donaldson uhlenbeck and yau relating the existence of a hermitian yang mills metric on a holomorphic bundle to the stability of such a bundle we then show that the vortex equations are a dimensional reduction of the hermitian yang mills equation using this fact and the theorem above we give a new existence proof for the vortex equations and describe the moduli space of solutions

segre forms and kobayashi lubke inequality starting from the description of segre forms as direct images of powers of the first chern form of the anti tautological line bundle on the projectivized bundle of a holomorphic hermitian vector bundle we derive a version of the pointwise kobayashi lubke inequality

iterative approximation for a zero of accretive operator and fixed points problems in banach space abstract in this paper we introduced an iteration scheme for viscosity approximation for a zero of accretive operator and fixed points problems in a reflexive banach space with weakly continuous duality mapping a new iterative sequence is introduced and strong convergence of the algorithm xn is proved the results improve and extend the results of hu and liu l hu and l liu a new iterative algorithm for common solutions of a finite family of accretive operators nonlinear anal 70 2009 2344 2351 and some others

approximation common zero of two accretive operators in banach spaces the purpose of this paper is to introduce a new iterative method that is the combination of the proximal point algorithm viscosity approximation method and alternating resolvent method for finding the common zeros of two accretive operators in banach spaces and we will prove the strong convergence theorems for the iterative algorithms and give the example of the main theorems the results of this paper are improvements and extensions of the corresponding ones announced by many others

strong convergence of composite iterative schemes for a countable family of nonexpansive mappings in banach spaces abstract in this paper we propose a new modified viscosity approximation method for approximating common fixed points for a countable family of nonexpansive mappings in a banach space we prove strong convergence theorems for a countable family nonexpansive mappings in a reflexive banach space with uniformly gateaux differentiable norm under some control conditions these results improve and extend the results of jong soo jung j s jung convergence on composite iterative schemes for nonexpansive mappings in banach spaces fixed point theory and appl 2008 2008 14 pp article id 167535 further we apply our result to the problem of finding a zero of an accretive operator and extend the results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 ceng et al l c ceng a r khan q h ansari j c yao strong convergence of composite iterative schemes for zeros of m accretive operators in banach space nonlinear anal 70 2009 1830 1840 and chen and zhu r chen z zhu viscosity approximation methods for accretive operator in banach space nonlinear anal 69 2008 1356 1363

cohomological aspects of abelian gauge theory we discuss some aspects of cohomological properties of a two dimensional free abelian gauge theory in the framework of the brst formalism we derive the conserved and nilpotent brst and co brst charges and express the hodge decomposition theorem in terms of these charges and a conserved bosonic charge corresponding to the laplacian operator it is because of the topological nature of free u 1 gauge theory that the laplacian operator goes to zero when equations of motion are exploited we derive two sets of topological invariants which are related to each other by a certain kind of duality transformation and express the lagrangian density of this theory as the sum of terms that are brst and co brst invariants mathematically this theory captures together some of the key features of witten and schwarz type topological field theories

new topological field theories in two dimensions it is shown that two 1 1 dimensional 2d free abelian and self interacting non abelian gauge theories without any interaction with matter fields belong to a new class of topological field theories tfts these new theories capture together some of the key features of witten and schwarz types of tft because they are endowed with symmetries that are reminiscent of the schwarz type theories but their lagrangian density has the appearance of the witten type theories the topological invariants for these theories are computed on a 2d compact manifold and their recursion relations are obtained these new theories are shown to provide a class of tractable field theoretical models for the hodge theory in two dimensions of flat minkowski spacetime where there are no propagating degrees of freedom associated with the 2d gauge boson

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

strong convergence of viscosity approximation methods for finding zeros of accretive operators in banach spaces abstract in this paper we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in banach spaces then we establish strong convergence theorems for the composite iterative scheme the main theorems improve and generalize the recent corresponding results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 as well as aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 benavides et al t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 chen and zhu r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory and appl 2006 2006 1 10 and kamimura and takahashi s kamimura w takahashi approximation solutions of maximal monotone operators in hilberts spaces j approx theory 106 2000 226 240

strong convergence of composite iterative schemes for zeros of m accretive operators in banach spaces abstract we introduce a new composite iterative scheme to approximate a zero of an m accretive operator a defined on uniform smooth banach spaces and a reflexive banach space having a weakly continuous duality map it is shown that the iterative process in each case converges strongly to a zero of a the results presented in this paper substantially improve and extend the results due to ceng et al l c ceng h k xu j c yao strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators taiwanese j math in press kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 our work provides a new approach for the construction of a zero of m accretive operators