the effects of phase noise on trellis coded modulation over gaussian and fading channels in this paper error performance bounds are derived for 8 psk trellis coded modulation tcm over gaussian and fading channels in the presence of phase noise coherent demodulation combined with both phase locked loop pll and transparent tone in band technique ttib for phase recovery is assumed the analysis is then applied to a number of ungerboeck 8 psk trellis codes and the results for the bit error rate ber performance obtained both analytically and by monte carlo simulation are presented the derived bounds can be directly extended to any m psk trellis code

sharp systolic inequalities for reeb flows on the three sphere the systolic ratio of a contact form alpha on the three sphere is the quantity begin aligned rho mathrm sys alpha frac t min alpha 2 mathrm vol s 3 alpha wedge d alpha end aligned where t min alpha is the minimal period of closed reeb orbits on s 3 alpha a zoll contact form is a contact form such that all the orbits of the corresponding reeb flow are closed and have the same period our first main result is that rho mathrm sys le 1 in a neighbourhood of the space of zoll contact forms on s 3 with equality holding precisely at zoll contact forms this implies a particular case of a conjecture of viterbo a local middle dimensional non squeezing theorem and a sharp systolic inequality for finsler metrics on the two sphere which are close to zoll ones our second main result is that rho mathrm sys is unbounded from above on the space of tight contact forms on s 3

packing stability for symplectic 4 manifolds abstractthe packing stability in symplectic geometry was rst noticed bybiran bir97 the symplectic obstructions to embed several balls into amanifold disappear when their size is small enough this phenomenonis known to hold for all closed manifolds with rational symplectic class see bir99 for the 4 dimensional case and bh11 bh13 for higherdimensions as well as for all ellipsoids bh13 in this note we show that packing stability holds for all closed andseveral open symplectic 4 manifolds 1 introduction in bir97 bir99 biran discovered the packing stability phenomenon insome symplectic 4 manifolds the symplectic obstructions to pack nidenti cal balls disappear when nbecomes large enough he later generalized thisresult to every closed symplectic 4 manifold with rational symplectic class h 2 m q in this paper we generalize these results in several directions by applyingthe singular in ation technique developed in ops13b mo13 we generalizebiran s packing stability to all symplectic 4 manifolds and also to a class ofopensymplectic 4 manifolds includingellipsoids anddomainswe call pseudo balls for these manifolds we establish not just packing stability but strongpacking stability which we de ne now the de nition is in the spirit ofbiran s rst results on the subject bir97 throughout b will denote anopen ball of capacity see de nition 1 3 and we will write u

hofer s question on intermediate symplectic capacities roughly twenty five years ago hofer asked can the cylinder b 2 1 times mathbb r 2 n 1 be symplectically embedded into b 2 n 1 r times mathbb r 2 for some r 0 we show that this is the case if r geq sqrt 2 n 1 2 n 2 2 we deduce that there are no intermediate capacities between 1 capacities first constructed by gromov in 1985 and n capacities answering another question of hofer in 2008 guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

a stability property of symplectic packing we prove that for any closed symplectic 4 manifold m with h 2 m q there exists a number n 0 such that for every n n 0 m admits full symplectic packing by n equal balls we also indicate how to compute this n 0 our approach is based on donaldson s symplectic submanifold theorem and on tools from the framework of taubes theory of gromov invariants

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

the asymptotics of ech capacities in a previous paper the second author used embedded contact homology ech of contact three manifolds to define ech capacities of four dimensional symplectic manifolds in the present paper we prove that for a four dimensional liouville domain with all ech capacities finite the asymptotics of the ech capacities recover the symplectic volume this follows from a more general theorem relating the volume of a contact three manifold to the asymptotics of the amount of symplectic action needed to represent certain classes in ech the latter theorem was used by the first and second authors to show that every contact form on a closed three manifold has at least two embedded reeb orbits

recent progress on symplectic embedding problems in four dimensions we survey some recent progress on understanding when one four dimensional symplectic manifold can be symplectically embedded into another in 2010 mcduff established a number theoretic criterion for the existence of a symplectic embedding of one four dimensional ellipsoid into another this result is related to previously known criteria for when a disjoint union of balls can be symplectically embedded into a ball numerical invariants defined using embedded contact homology give general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases

infinite dimensional symplectic capacities and a squeezing theorem for hamiltonian pde s we study partial differential equations of hamiltonian form and treat them as infinite dimensional hamiltonian systems in a functional phase space ofx dependent functions in this phase space we construct an invariant symplectic capacity and prove a version of gromov s non squeezing theorem we give an interpretation of the theorem in terms of the energy transition to high frequencies problem

the dynamics on three dimensional strictly convex energy surfaces we show that a hamiltonian flow on a three dimensional strictly convex energy surface s c r4 possesses a global surface of section of disc type it follows in particular that the number of its periodic orbits is either 2 or oc by a recent result of j franks on area preserving homeomorphisms of an open annulus in the plane the construction of this surface of section is based on partial differential equations of cauchy riemann type for maps from punctured riemann surfaces into r x s3 equipped with special almost complex structures

the sphere packing problem in dimension 24 building on viazovska s recent solution of the sphere packing problem in eight dimensions we prove that the leech lattice is the densest packing of congruent spheres in twenty four dimensions and that it is the unique optimal periodic packing in particular we find an optimal auxiliary function for the linear programming bounds which is an analogue of viazovska s function for the eight dimensional case

new obstructions to symplectic embeddings in this paper we establish new restrictions on the symplectic embeddings of basic shapes in symplectic vector spaces by refining an embedding technique due to guth we also show that they are sharp

design of turbo coded modulation for the awgn channel with tikhonov phase error we design 1 b symbol hz parallel concatenated turbo coded modulation pctcm for the additive white gaussian noise awgn channel with tikhonov phase error constituent recursive convolutional codes are optimized so that the turbo codes have low error floors and low convergence thresholds the pairwise error probability based on the maximum likelihood decoding metric is used to select codes with low error floors we also present a gaussian approximation method that accurately predicts convergence thresholds for pctcm codes on the awgn tikhonov channel simulation results show that the selected codes perform within 0 6 db of constellation constrained capacity and have no detectable error floor down to bit error rates of 10 sup 6

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

trellis coded mpsk with reference phase errors with trellis coded mpsk schemes reference phase errors have a major impact on the system performance this paper analyzes the interrelation among the coded modulation format the reference phase tracker and the carrier phase noise a tight upper bound to the error probability of a maximum likelihood decoder is introduced this bound reveals eight new distance type functions which along with the wellknown minimum euclidean distance characterize the coded modulation scheme relationships between the new distance type functions and the various system parameters as well as the irreducible probability of error are pointed out numerical results for uncoded qpsk and three ungerboeck encoded 8 psk schemes showy that excessive smoothing of the reference phase in presence of carder phase noise can degrade the performance of coded 8 psk modulation considerably

numerical characterization of the kahler cone of a compact kahler manifold the goal of this work is to give a precise numerical description of the kahler cone of a compact kahler manifold our main result states that the kahler cone depends only on the intersection form of the cohomology ring the hodge structure and the homology classes of analytic cycles if x is a compact kahler manifold the kahler cone k of x is one of the connected components of the set p of real 1 1 cohomology classes which are numerically positive on analytic cycles i e y p 0 for every irreducible analytic set y in x p dim y this result is new even in the case of projective manifolds where it can be seen as a generalization of the well known nakai moishezon criterion and it also extends previous results by campana peternell and eyssidieux the principal technical step is to show that every nef class which has positive highest self intersection numberx n 0 contains a kahler current this is done by using the calabi yau theorem and a mass concentration technique for monge ampere equations the main result admits a number of variants and corollaries including a description of the cone of numerically effective 1 1 classes and their dual cone another important consequence is the fact that for an arbitrary deformation x s of compact kahler manifolds the kahler cone of a very general fibre xt is independent of t i e invariant by parallel transport under the 1 1 component of the gauss manin connection

symplectic embeddings of polydisks if p and p are symplectic polydisks of radii r 1 r n and r 1 r n respectively then we prove that p symplectically embeds in p provided that c n r 1 r 1 and c n r 1 r n r 1 r n up to a constant factor these conditions are optimal

contact geometry of the restricted three body problem we show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value action of the first lagrange point and for energies slightly above it this opens up the possibility of using the technology of contact topology to understand this particular dynamical system 2011 wiley periodicals inc

on the topological properties of symplectic maps in this paper we show that symplectic maps have surprising topological properties in particular we construct an interesting metric for the symplectic diffeomorphism groups which is related but not obviously to the topological properties of symplectic maps and phase space geometry we also prove a certain number of generalised symplectic fixed point theorems and give an application to a hamiltonian system

the geometry of symplectic energy non squeezing theorem which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form r2 x b2 where b2 is a 2 disc this led to hofer s discovery of symplectic capacities which give a way of measuring the size of subsets in symplectic manifolds recently hofer found a way to measure the size or energy of symplectic diffeomorphisms by looking at the total variation of their generating hamiltonians this gives rise to a bi invariant pseudo norm on the group ham m of compactly supported hamiltonian symplectomorphisms of the manifold m the deep fact is that this pseudo norm is a norm in other words the only symplectomorphism on m with zero energy is the identity map up to now this had been proved only for sufficiently nice symplectic manifolds and by rather complicated analytic arguments in this paper we consider a more geometric version of this energy which was first considered by eliashberg and hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary we prove by a simple geometric argument that both versions of energy give rise to genuine norms on all symplectic manifolds roughly speaking we show that if there were a symplectomorphism of m which had too little energy one could embed a large ball into a thin cylinder m x

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

remarks on seshadri constants which is called the seshadri constant of l at x here the infimum is taken over all irreducible curves c passing through x and mx c is the multiplicity of c at x for example if l is very ample then e l x 1 there has been recant interest in trying to give lower bounds for this invariant at a general point ein and lazarsfeld el show that if x is a surface then e l x 1 for very general x x in higher dimension n 3 ein kuchle and lazarsfeld ekl prove that e l x 1 n for a very general point we say that a point x x is very general if x is in the complement x z of z a countably union of proper subvarieties examples of miranda show that e l x can take arbitrarily small values in codimension two i e codim z 2 even for an ample line bundle one may expect that this general bounds are not optimal an elementary observation see remark 1 below for the proof shows that e l x n ln a natural question is are there conditions which guarantee equality even in relative simple cases it turns out to be hard to give an answer recently xu xu improved the surface bound given by ein and lazarsfeld he showed that if l2 3 4 4 5 for a given integer 1

metric and isoperimetric problems in symplectic geometry introduction 411 1 some basic results in symplectic topology 413 2 capacity and symplectic reduction 414 3 volume estimates for lagrange submanifolds 416 3 1 the case of r 417 3 2 deformations of the zero section in cotangent bundles 419 3 3 generalization to the case of cp 422 4 an application to billiards 423 5 geometry of convex sets and periodic orbits 425 6 compensated compactness and closure of the symplectic group 426 appendix a a summary of symplectic geometry through generating functions 427 appendix b john s ellipsoid 428 references 430

phase noise effects on turbo trellis coded over m ary coherent channels the effect of the phase noise on the performance of bandwidth efficient coded modulation is studied to this end the average mutual information ami for specific constellations such as 8 phase shift keying and 16 quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white gaussian noise channel the ami not only quantifies the effect of the phase noise from an information theoretic viewpoint but also serves as an estimate for a permissible amount of the phase noise for a given signal to noise ratio the bit error rate ber performance of a near optimal turbo trellis coded modulation scheme is then investigated over such a channel for this purpose an optimal branch metric which best fits the channel characteristics is derived furthermore simple branch metrics referred to as suboptimal simplified and gaussian metrics are derived which may offer the tradeoff between ber performance and computational complexity numerical analysis shows that a near optimal coded modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis coded modulation scheme

interval methods for verifying structural optimality of circle packing configurations in the unit square the paper is dealing with the problem of finding the densest packings of equal circles in the unit square recently a global optimization method based exclusively on interval arithmetic calculations has been designed for this problem with this method it became possible to solve the previously open problems of packing 28 29 and 30 circles in the numerical sense tight guaranteed enclosures were given for all the optimal solutions and for the optimum value the present paper completes the optimality proofs for these cases by determining all the optimal solutions in the geometric sense namely it is proved that the currently best known packing structures result in optimal packings and moreover apart from symmetric configurations and the movement of well identified free circles these are the only optimal packings the required statements are verified with mathematical rigor using interval arithmetic tools

punctured holomorphic curves and lagrangian embeddings we use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and maslov class with boundary on lagrangian submanifolds of nonpositive curvature applications include the proof of audin s conjecture on the maslov class of lagrangian tori in linear symplectic space the construction of a new symplectic capacity obstructions to lagrangian embeddings into uniruled symplectic manifolds a quantitative version of arnold s chord conjecture and estimates on the size of weinstein neighbourhoods the main technical ingredient is transversality for the relevant moduli spaces of punctured holomorphic curves with tangency conditions

analysis of optimum detector of trellis coded mpsk in phase noise channels this paper presents a novel analytical expression which approximates the bit error rate ber of the joint phase and symbol maximum a posteriori jmap sequence estimator for trellis code modulation tcm with m ary phase shift keying mpsk modulation any arbitrary phase noise model i e not limited to the wiener process and either a matched or mismatched decoder first we derived convenient closed form expressions for approximating the pairwise error probability of two code sequences for both matched and mismatched decoders since the expressions are formulated either in the time or in the frequency domain it is possible to indicate the contribution of every frequency in the phase noise spectrum we then applied the union bound on the code sequence pairwise errors the analytical expression was tight usually 1db for mpsk constellations with m 4 and code rates 0 5 once developed the expressions will assist designers to consider the influence on receiver performance of the code characteristics decoder implementation and rf synthesizer phase noise it further enables joint optimization of the rf synthesizer the code and the decoder for achieving the lowest error rate or other design targets

symplectic geometry and topology this is a review of the ideas underlying the application of symplectic geometry to hamiltonian systems the paper begins with symplectic manifolds and their lagrangian submanifolds covers contact manifolds and their legendrian submanifolds and indicates the first steps of symplectic and contact topology

the embedding capacity of 4 dimensional symplectic ellipsoids this paper calculates the function c a whose value at a is the inmum of the size of a ball that contains a symplectic image of the ellipsoide 1 a here a 1 is the ratio of the area of the large axis to that of the smaller axis the structure of the graph of c a is surprisingly rich the volume constraint implies that c a is always greater than or equal to the square root of a and it is not hard to see that this is equality for large a however for a less than the fourth power 4 of the golden ratio c a is piecewise linear with graph that alternately lies on a line through the origin and is horizontal we prove this by showing that there are exceptional curves in blow ups of the complex projective plane whose homology classes are given by the continued fraction expansions of ratios of fibonacci numbers on the interval 4 7 we nd c a a 1 3 for a 7 the function c a coincides with the square root except on a nite number of intervals where it is again piecewise linear the embedding constraints coming from embedded contact homology give rise to another capacity function cech which may be computed by counting lattice points in appropriate right angled triangles according to hutchings and taubes the functorial properties of embedded contact homology imply that cech a c a for all a we show here that cech a c a for all a

the topology of the space of symplectic balls in rational 4 manifolds we study in this paper the rational homotopy type of the space of symplectic embeddings of the standard ball b4 c r4 into 4 dimensional rational symplectic manifolds where c r2 is the capacity of the standard ball of radius r we compute the rational homotopy groups of that space when the 4 manifold has the form m s2 s2 0 0 where 0 is the area form on the sphere with total area 1 and belongs to the interval 1 2 we show that when is 1 this space retracts to the space of symplectic frames for any value of c however for any given 1 2 the rational homotopy type of that space changes as c crosses the critical parameter 1 which is the difference of areas between the two s2 factors we prove moreover that the full homotopy type of that space changes only at that value that is that the restriction map between these spaces is a homotopy equivalence as long as these values of c remain either below or above that critical value the same methods apply to all other values of and other rational 4 manifolds as well the methods rely on two different tools the study of the action of symplectic groups on the stratified space of almost complex structures developed by gromov abreu and mcduff and the analysis of the relations between the group corresponding to a manifold m the group corresponding to its blow up m and the space of symplectic embedded balls in m

fixed point and convergence theorems for different classes of generalized nonexpansive mappings in cat 0 spaces in this paper we prove the existence of common fixed points in cat 0 spaces for three different classes of generalized nonexpansive mappings including a quasi nonexpansive single valued mapping a pointwise asymptotically nonexpansive mapping and a multivalued mapping satisfying the conditions e and c l for some email protected 0 1 moreover we introduce an iterative process for these mappings and prove convergence and strong convergence theorems for such an iterative process in cat 0 spaces

from symplectic measurements to the mahler conjecture in this note we link symplectic and convex geometry by relating two seemingly different open conjectures a symplectic isoperimetric type inequality for convex domains and mahler s conjecture on the volume product of centrally symmetric convex bodies more precisely we show that if for convex bodies of fixed volume in the classical phase space the hofer zehnder capacity is maximized by the euclidean ball then a hypercube is a minimizer for the volume product among centrally symmetric convex bodies

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free