on the periodic schrodinger boussinesq system abstract we study the local and global well posedness of the periodic boundary value problem for the nonlinear schrodinger boussinesq system the existence of periodic traveling wave solutions as well as the orbital stability of such solutions are also considered

interaction equations for short and long dispersive waves abstract we show the time local well posedness for a system of nonlinear dispersive equations for the water wave interaction formula it is shown that for any initial data u0 v0 hs r hs 1 2 r s 0 the solution for the above equation uniquely exists in a subset ofc t t hs c t t hs 1 2 and depends continuously on the data by virtue of a special structure of the nonlinear coupling the solution is stable under a singular limiting process

brief paper accuracy analysis of bias eliminating least squares estimates for errors in variables systems the bias eliminating least squares bels method is one of the consistent estimators for identifying dynamic errors in variables systems in this paper we investigate the accuracy properties of the bels estimates an explicit expression for the normalized asymptotic covariance matrix of the estimated parameters is derived and supported by some numerical examples

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

an improved algorithm for computing topological entropy a new algorithm is presented for computing the topological entropy of a unimodal map of the interval the accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed

nonlinear stability of periodic traveling wave solutions to the schrodinger and the modified korteweg de vries equations abstract this work is concerned with stability properties of periodic traveling waves solutions of the focusing schrodinger equation i u t u x x u 2 u 0 posed in r and the modified korteweg de vries equation u t 3 u 2 u x u x x x 0 posed in r our principal goal in this paper is the study of positive periodic wave solutions of the equation 3 0 called dnoidal waves a proof of the existence of a smooth curve of solutions with a fixed fundamental period l 2 2 l 2 h per 0 l is given it is also shown that these solutions are nonlinearly stable in the energy space h per 1 0 l and unstable by perturbations with period 2l in the case of the schrodinger equation

computing the topological entropy of maps we give an algorithm for determining the topological entropy of a unimodal map of the interval given its kneading sequence we also show that this algorithm converges exponentially in the number of letters of the kneading sequence

piecewise invertible dynamical systems the aim of the paper is the investigation of piecewise monotonic maps t of an interval x the main tool is an isomorphism of x t with a topological markov chain with countable state space which is described by a 0 1 transition matrix m the behavior of the orbits of points in x under t is very similar to the behavior of the paths of the markov chain every irreducible submatrix of m gives rise to a t invariant subset l of x such that l is the set x of all limit points of the orbit of an x x the topological entropy of l is the logarithm of the spectral radius of the irreducible submatrix which is a l 1 operator besides these sets l there are two t invariant sets y and p such that for all x x the set x is either contained in one of the sets l or in y or in p the set p is a union of periodic orbits and y is contained in a finite union of sets y with y x and has topological entropy zero this isomorphism of x t with a topological markov chain is also an important tool for the investigation of t invariant measures on x results in this direction which are published elsewhere are described at the end of the paper furthermore a part of the proofs in the paper is purely topological without using the order relation of the interval x so that some results hold for more general dynamical systems x t

on the estimation of topological entropy we study a method for estimating the topological entropy of a smooth dynamical system our method is based on estimating the logarithmic growth rates of suitably chosen curves in the system we present two algorithms for this purpose and we analyze each according to its strengths and pitfalls we also contrast these with a method based on the definition of topological entropy using n spanning sets

low regularity global well posedness for the zakharov and klein gordon schrodinger systems we prove low regularity global well posedness for the id zakharov system and the 3d klein gordon schrodinger system which are systems in two variables u r d x x r t c and n r d x x r t r the zakharov system is known to be locally well posed in u n l 2 x h and the klein gordon schrodinger system is known to be locally well posed in u n l 2 x l 2 here we show that the zakharov and klein gordon schrodinger systems are globally well posed in these spaces respectively by using an available conservation law for the l 2 norm of u and controlling the growth of n via the estimates in the local theory

computing the topological entropy of maps of the interval with three monotone pieces an algorithm is presented for computing the topological entropy of a piecewise monotone map of the interval having three monotone pieces the accuracy of the algorithm is discussed and some graphs of the topological entropy obtained using the algorithm are displayed some of the ideas behind the algorithm have application to piecewise monotone functions with more than three monotone pieces

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

calculating topological entropy the attempt to find effective algorithms for calculating the topological entropy of piecewise monotone maps of the interval having more than three monotone pieces has proved to be a difficult problem the algorithm introduced here is motivated by the fact that if f 0 1 0 1 is a piecewise monotone map of the unit interval into itself thenh f limn 1 n log var f n where h f is the topological entropy off and var f n is the total variation off n we show that it is not feasible to use this formula directly to calculate numerically the topological entropy of a piecewise monotone function because of the slow convergence however a close examination of the reasons for this failure leads ultimately to the modified algorithm which is presented in this paper we prove that this algorithm is equivalent to the standard power method for finding eigenvalues of matrices with shift of origin in those cases for which the function is markov and present encouraging experimental evidence for the usefulness of the algorithm in general by applying it to several one parameter families of test functions

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

computing the topological entropy for piecewise monotonic maps on the interval a new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented it uses a transition matrix associated with the transformation for this matrix we give a spectral theorem this can be used for an estimation of the accuracy of the algorithm

a procedure for determining rigid body transformation parameters for many biomechanical applications it is necessary to determine the parameters which describe the transformation of a rigid body from one reference frame to another these parameters are a scaling factor an attitude matrix and a translation vector the paper presents a new procedure for the determination of these parameters incorporating the work of arun et al ieee trans pattern anal machine intell 9 698 700 1987 but expanding their analysis to allow for the determination of a scale factor the scalar weighting of the least squares problem and the problem of obtaining the incorrect determinant when determining the attitude matrix the procedure which requires the coordinates of three or more non collinear points is based around the singular value decomposition and provides a least squares estimate of the rigid body transformation parameters examples are presented of the use of this procedure for determining the attitude of a rigid body and for osteometric scaling when used for osteometric scaling mirror transformations are possible therefore a right hand specimen can be scaled to the left hand side of another specimen

influence of geometrical distribution of common points on the accuracy of coordinate transformation geometrical distribution of common points is of significance for coordinate transformation as the transformation parameters are computed through common points whose coordinates are known common points can be divided into a calculating set and a testing set whose geometrical distribution can be described by internal and external distribution parameters the former contains the number of points the reference coordinate and the coordinate difference the latter is defined as the overlapping degree between both sets both a rotation matrix and a translation vector are involved in the transformation parameters and could be evaluated by 3 approaches i e the coordinate error method the rms error method and the error method of relative euclidean distance an invalidation of the third method has been proven that evaluating indexes will remain invariant for a fixed testing set regardless of variation in the calculating set according to the classification of geometrical distribution of common points the influences of internal and external distribution parameters on the accuracy of coordinate transformation are related to the number of points symmetrical distribution and the overlapping degree which will be formulated and summarized in detail finally the above conclusions can be verified and proven by computer simulation and practical experiment respectively

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

topological entropy of one dimensional maps approximations and bounds we present a method for computing the topological entropy of one dimensional maps as an approximation scheme the algorithm converges rapidly and provides both upper and lower bounds

cauchy problem of schrodinger improved boussinesq systems on the torus in this paper we will study the local well posedness of schrodinger improved boussinesq system with additive noise in td d 1 and we will also study the global well posedness of dimension 1 case with the initial data u0 v1 v2 l2 l2 l2 almost surely gaining some exponential growth of l2 norm of v

on the schrodinger boussinesq system with singular initial data abstract we study the existence of local and global solutions for coupled schrodinger boussinesq systems with initial data in weak l r spaces these spaces contain singular functions with infinite l 2 mass such as homogeneous functions of negative degree moreover we analyze the self similarity and radial symmetry of solutions by considering initial data with the right homogeneity and radially symmetric respectively since functions in weak l r with r 2 have local finite l 2 mass the solutions obtained can be physically realized moreover for initial data in h s local solutions belong to h s which shows that the constructed data solution map in weak l r recovers h s regularity

computing the topological entropy of general one dimensional maps a matrix theoretic method for computing the topological entropy of continuous piecewise monotonic maps of the interval is presented the method results in a constructive procedure which is easily implemented on the computer examples for families of unimodal nonunimodal and discontinuous maps are presented

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation