comments on a new construction of 16 qam golay complementary sequences and extension for 64 qam golay sequences for original article by c v chong see ibid vol 49 no 11 p 2953 2959 nov 2003 some corrections are given for the sequence pairing descriptions of 16 qam golay complementary sequences in chong venkataramani and tarokh s paper together with a related correction for lee and golomb s 64 qam golay sequence construction lee and golomb obtained 496 808 and 976 offset pairs for length 2m 64 qam golay sequences m 2 3 4 we obtained 724 972 and 1224 offset pairs adding w 1 to case iii in lee and golomb s construction gives some additional offset pairs others are new and exist for m ges 3 only descriptions of new offset pairs and enumeration for all first order offset pairs are proposed as conjectures an example is given to show that there exist other 64 qam golay sequences not within this construction

construction of ofdm m qam sequences with low peak to average power ratio we present a technique to derive m quadrature amplitude modulation qam signals from quaternary phase shift keying qpsk constellations when m 2 sup n and n is an even number by utilizing qpsk golay sequences we have constructed m qam sequences with low peak to mean envelope power ratios several upper bounds for these m qam sequences were derived

can chaotic quantum energy levels statistics be characterized using information geometry and inference methods abstract in this paper we review our novel information geometrodynamical approach to chaos igac on curved statistical manifolds and we emphasize the usefulness of our information geometrodynamical entropy ige as an indicator of chaoticity in a simple application furthermore knowing that integrable and chaotic quantum antiferromagnetic ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies respectively we apply our igac to present an alternative characterization of such systems remarkably we show that in the former case the ige exhibits asymptotic logarithmic growth while in the latter case the ige exhibits asymptotic linear growth at this stage of its development igac remains an ambitious unifying information geometric theoretical construct for the study of chaotic dynamics with several unsolved problems however based on our recent findings we believe that it could provide an interesting innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos

novel 16 qam and 64 qam near complementary sequences with low pmepr in ofdm systems in this paper we first propose a novel construction of 16 quadrature amplitude modulation qam near complementary sequences with low peak to mean envelope power ratio pmepr in orthogonal frequency division multiplexing ofdm systems the proposed 16 qam near complementary sequences can be constructed by utilizing novel nonlinear offsets where the length of the sequences is n 2 m the family size of the newly constructed 16 qam near complementary sequences is 8 times m 2 times 4 m 1 and the pmepr of these sequences is proven to satisfy pmepr 2 4 thus the proposed construction can generate a number of 16 qam near complementary sequences with low pmepr resulting in the improvement of the code rate in ofdm systems furthermore we also propose a novel construction of 64 qam near complementary sequences with low pmepr which is the first proven construction of 64 qam near complementary sequences the pmeprs of two types of the proposed 64 qam near complementary sequences are proven to satisfy that pmepr 3 62 or pmepr 2 48 respectively the family size of the newly constructed 64 qam near complementary sequences is 64 times m 2 times 4 m 1

peak power reduction of ofdm signals with sign adjustment it has recently been shown that significant reduction in the peak to mean envelope power pmepr can be obtained by altering the sign of each subcarrier in a multicarrier system with n subcarriers however finding the best sign not only requires a search over 2n possible signs but also may lead to a substantial rate loss for small size constellations in this paper we first propose a greedy algorithm to choose the signs based on p norm minimization and prove that the resulting pmepr is guaranteed to be less than c log n where c is a constant independent of n for any n this approach has lower complexity in each iteration compared to the derandomization approach of while achieving similar pmepr reduction we further improve the performance of the proposed algorithm by enlarging the search space using pruning simulation results show that pmepr of a multicarrier signal with 128 subcarriers can be reduced to within 1 6 db of the pmepr of a single carrier system in the second part of the paper we address the rate loss by proposing a block coding scheme in which only one sign vector is chosen for k different modulating vectors the sign vector can be computed using the greedy algorithm in n iterations we show that the multi symbol encoding approach can reduce the rate loss by a factor of k while achieving the pmepr of c logkn i e only logarithmic growth in k simulation results show that the rate loss can be made smaller than 10 at the cost of only 1 db increase in the resulting pmepr for a system with 128 subcarriers

global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid we consider the two dimensional motion of several non homogeneous rigid bodies immersed in an incompressible non homogeneous viscous fluid the fluid and the rigid bodies are contained in a fixed open bounded set of r 2 the motion of the fluid is governed by the navier stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies the time variation of the fluid domain due to the motion of the rigid bodies is not known a priori so we deal with a free boundary value problem the main novelty here is the demonstration of the global existence of weak solutions for this problem more precisely the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary we give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero

chaos based on riemannian geometric approach to abelian higgs dynamical system based on the riemannian geometric approach we study chaos of the abelian higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous abelian gauge field and higgs field using the global indicator of chaos formulated by the sectional curvature of the ambient manifold we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the lyapunov exponents in the conventional and phenomenological approach we confirm that the mechanism of chaos is a parametric instability of the system by analyzing a close relation between the sectional curvature and the gaussian curvature we point out that the toda brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition

new constructions of general qam golay complementary sequences a construction of general quadrature amplitude modulation qam golay complementary sequences based on quadrature phase shift keying golay davis jedwab sequences gdj sequences is described existing constructions of 16 and 64 qam golay sequences are extended to 4q qam sequences of length 2m for q 1 m 2 this construction gives m 1 42 q 1 m 1 4 q 1 2q 1 m 2 4 m 1 golay complementary sequences a previous offset pair enumeration conjecture for 64 qam golay sequences is proved as a special case of the enumeration for 4q qam golay sequences when used for orthogonal frequency division multiplexing signals the peak to mean envelope power ratio upper bound is shown to be 6 2q 1 2q 1 approaching 6 as the qam constellation size increases

near complementary sequences with low pmepr for peak power control in multicarrier communications new families of near complementary sequences are presented for peak power control in multicarrier communications a framework for near complementary sequences is given by an explicit boolean expression and an equivalent matrix structure the framework transforms seed pairs to near complementary sequences by the aid of golay complementary sequences new families of near complementary sequences of various lengths and pmepr 4 are then presented where the sequences are constructed by the framework employing the seeds of shortened and extended golay complementary pairs the families present in a constructive way a large number of sequences of pmepr 4 for the lengths 100 of 24 28 30 34 36 48 56 60 62 66 68 72 and 96 where no golay pairs have been reported the sequence families can find potential applications for peak power control requiring codewords or sequences of various lengths as well as low peak to mean envelope power ratio pmepr

the effect of microscopic correlations on the information geometric complexity of gaussian statistical models abstract we present an analytical computation of the asymptotic temporal behavior of the information geometric complexity igc of finite dimensional gaussian statistical manifolds in the presence of microcorrelations correlations between microvariables we observe a power law decay of the igc at a rate determined by the correlation coefficient it is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in the absence of microcorrelations this finding uncovers an important connection between micro correlations and macro complexity in gaussian statistical dynamical systems

a modified lagrange galerkin method for a fluid rigid system with discontinuous density in this paper we propose a new characteristics method for the discretization of the two dimensional fluid rigid body problem in the case where the densities of the fluid and the solid are different the method is based on a global weak formulation involving only terms defined on the whole fluid rigid domain to take into account the material derivative we construct a special characteristic function which maps the approximate rigid body at the k 1 th discrete time level into the approximate rigid body at k th time convergence results are proved for both semi discrete and fully discrete schemes

a new construction of 16 qam golay complementary sequences we present a new construction of 16 qam golay sequences of length n 2 sup m the number of constructed sequences is 14 12m m 2 4 sup m 1 when employed as a code in an orthogonal frequency division multiplexing ofdm system this set of sequences has a peak to mean envelope power ratio pmepr of 3 6 by considering two specific subsets of these sequences we obtain new codes with pmepr bounds of 2 0 and 2 8 and respective code sizes of 2 2m m 2 4 sup m 1 and 4 4m m 2 4 sup m 1 these are larger than previously known codes for the same pmepr bounds

micro motions of a 2 d swimming model governed by multiplicative controls abstract the goal of this paper is to derive a formula for the micro motions of a simplified model of an object swimming by itself in a 2 d stokes fluid mathematics wise the model equations are described by a nonlinear coupled hybrid system of fluid equations and integro differential equations we view this swimming motion as one governed by multiplicative controls such problems are of interest in biological and engineering applications dealing with propulsion systems in fluids

convergence of the lagrange galerkin method for the equations modelling the motion of a fluid rigid system in this paper we consider a lagrange galerkin scheme to approximate a two dimensional fluid rigid body problem the equations of the system are the navier stokes equations in the fluid part coupled with ordinary differential equations for the dynamics of the rigid body in this problem the equations of the fluid are written in a domain whose variation is one of the unknowns we introduce a numerical method based on the use of characteristics and on finite elements with a fixed mesh our main result asserts the convergence of this scheme

well posedness of 2 d and 3 d swimming models in incompressible fluids governed by navier stokes equations abstract we introduce and investigate the wellposedness of two models describing the self propelled motion of a small bio mimetic swimmer in the 2 d and 3 d incompressible fluids modeled by the navier stokes equations it is assumed that the swimmer s body consists of finitely many subsequently connected parts identified with the fluid they occupy linked by the rotational and elastic forces the swimmer employs the change of its shape inflicted by respective explicit internal forces as the means for self propulsion in a surrounding medium similar models were previously investigated in 15 16 17 18 19 where the fluid was modeled by the liner nonstationary stokes equations such models are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids and air

motion of an elastic solid inside an incompressible viscous fluid the motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature mathematically such motion is described by a pde system that couples the parabolic and hyperbolic phases the latter inducing a loss of regularity which has left the basic question of existence open until now in this paper we prove the existence and uniqueness of such motions locally in time when the elastic solid is the linear kirchhoff elastic material the solution is found using a topological fixed point theorem that requires the analysis of a linear problem consisting of the coupling between the time dependent navier stokes equations set in lagrangian variables and the linear equations of elastodynamics for which we prove the existence of a unique weak solution we then establish the regularity of the weak solution this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases our functional framework is optimal and provides the a priori estimates necessary for us to employ our fixed point procedure

on cosets of the generalized first order reed muller code with low pmepr golay sequences are well suited for use as codewords in orthogonal frequency division multiplexing ofdm since their peak to mean envelope power ratio pmepr in q ary phase shift keying psk modulation is at most 2 it is known that a family of polyphase golay sequences of length 2m organizes in m 2 cosets of a q ary generalization of the first order reed muller code rmq 1 m in this paper a more general construction technique for cosets of rm q 1 m with low pmepr is established these cosets contain so called near complementary sequences the application of this theory is then illustrated by providing some construction examples first it is shown that the m 2 cosets of rmq 1 m comprised of golay sequences just arise as a special case second further families of cosets of rmq 1 m with maximum pmepr between 2 and 4 are presented showing that some previously unexplained phenomena can now be understood within a unified framework a lower bound on the pmepr of cosets of rmq 1 m is proved as well and it is demonstrated that the upper bound on the pmepr is tight in many cases finally it is shown that all upper bounds on the pmepr of cosets of rmq 1 m also hold for the peak to average power ratio papr under the walsh hadamard transform wht

control at a distance of the motion of a rigid body immersed in a two dimensional viscous incompressible fluid abstract we consider the motion of a rigid body immersed in a two dimensional viscous incompressible fluid with navier slip with friction conditions at the solid boundary the fluid solid system occupies the whole plane we prove the small time global exact controllability of the position and velocity of the solid when the control takes the form of a distributed force supported in a compact subset with nonvoid interior of the fluid domain away from the body the strategy relies on the introduction of a small parameter we consider fast and strong amplitude controls for which the navier stokes rigid body system behaves like a perturbation of the euler rigid body system by the means of a multi scale asymptotic expansion we construct a controlled solution to the navier stokes rigid body system thanks to some controlled solutions to euler rigid body type systems and by using that the influence of the boundary layer on the solid motion turns out to be sufficiently small

generic controllability of 3d swimmers in a perfect fluid we address the problem of controlling a dynamical system governing the motion of a 3d weighted shape changing body swimming in a perfect fluid the rigid displacement of the swimmer results from the exchange of momentum between prescribed shape changes and the flow with the total impulse of the fluid swimmer system being null at every time we prove the following tracking results i synchronized swimming up to an arbitrarily small change of its density any swimmer can approximately follow any given trajectory while in addition undergoing approximately any given shape changes in this statement the control consists in arbitrarily small superimposed deformations ii freestyle swimming up to an arbitrarily small change of its density any swimmer can approximately track any given trajectory by suitably combining at most five basic movements that can be generically chosen no macro shape changes are prescribed in this statement

quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and jacobi fields abstract we characterize the complexity of geodesic paths on a curved statistical manifold m s through the asymptotic computation of the information geometric complexity v m s and the jacobi vector field intensity j m s the manifold m s is a 2 l dimensional gaussian model reproduced by an appropriate embedding in a larger 4 l dimensional gaussian manifold and endowed with a fisher rao information metric g with non trivial off diagonal terms these terms emerge due to the presence of a correlational structure embedding constraints among the statistical variables on the larger manifold and are characterized by macroscopic correlational coefficients r k first we observe a power law decay of the information geometric complexity at a rate determined by the coefficients r k and conclude that the non trivial off diagonal terms lead to the emergence of an asymptotic information geometric compression of the explored macrostates on m s finally we observe that the presence of such embedding constraints leads to an attenuation of the asymptotic exponential divergence of the jacobi vector field intensity

a new construction of 64 qam golay complementary sequences in this correspondence we present a new construction for 64 qam golay sequences of length n 2 sup m for integer m the peak envelope power pep of 64 qam golay sequences is shown to be bounded by 4 66n the new construction of 64 qam golay sequences of length n 2 sup m is based on our earlier construction of new offsets of 16 qam golay sequences which are also presented here the total number of offsets of 64 qam golay sequences is 496 for m 2 808 for m 3 and 976 for m 4 obtained by computer search we also computed the pep distribution for 64 qam golay sequences for m 2 m 3 and m 4

the interaction between quasilinear elastodynamics and the navier stokes equations the interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations coupled to one another along the moving material interface through the continuity of the velocity and traction vectors we prove the existence and uniqueness locally in time of strong solutions in sobolev spaces for quasilinear elastodynamics coupled to the incompressible navier stokes equations unlike our approach in 5 for the case of linear elastodynamics we cannot employ a fixed point argument on the nonlinear system itself and are instead forced to regularize it by a particular parabolic artificial viscosity term we proceed to show that with this specific regularization we obtain a time interval of existence which is independent of the artificial viscosity together with a priori estimates we identify the global solution in both phases as well as the interface motion as a weak limit in strong norms of our sequence of regularized problems

a new construction of 16 qam near complementary sequences we present a new 16 qam near complementary sequence construction where the length of the sequences is n 2m the 16 qam near complementary sequences are constructed by nonlinear offsets but the peak to mean envelope power ratio bounds for these 16 qam near complementary sequences is as low as 2 4 the number of newly constructed 16 qam near complementary sequences is m 2 4m 1

an initial and boundary value problem modeling of fish like swimming in this paper we consider an initial and boundary value problem that models the self propelled motion of solids in a bidimensional viscous incompressible fluid the self propelling mechanism consisting of appropriate deformations of the solids is a simplified model of the propulsion mechanism of fish like swimmers the governing equations consist of the navier stokes equations for the fluid coupled to newton s laws for the solids since we consider the case in which the fluid solid system fills a bounded domain we have to tackle a free boundary value problem the main theoretical result in the paper asserts the global existence and uniqueness up to possible contacts of strong solutions of this problem the second novel result of this work is the provision of a numerical method for the fluid solid system this method provides a simulation of the simultaneous displacement of several swimmers and is tested on several examples

existence of weak solutions for the motion of rigid bodies in a viscous fluid we study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of r d d 2 or 3 with dirichlet boundary conditions by introducing an appropriate weak formulation for the complete problem we prove existence of solutions for initial velocities in h 1 0 omega in the absence of collisions solutions exist for all time in dimension 2 whereas in dimension 3 the lifespan of solutions is infinite only for small enough data