the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

algebraic structure of a generalized coupled dispersionless system we study a physical model of the o 3 invariant coupled integrable dispersionless equations that describes the dynamic of a focused system within the background of a plane gravitational field the investigation is carried out both numerically and analytically and realized beneath some assumptions superseding the structure constant with the structure function implemented in lie algebra and quasigroup theory respectively the energy density and topological structures such as loop soliton are examined

nonisospectral scattering problems a key to integrable hierarchies we show that certain partial differential equations associated to nonisospectral scattering problems in 2 1 dimensions provide a key to associated integrable hierarchies of both ordinary and partial differential equations this is illustrated using an extension of a known second order and two new third order nonisospectral scattering problems these scattering problems allow us to derive new hierarchies of integrable partial differential equations in both 1 1 and 2 1 dimensions together with their underlying linear problems isospectral and nonisospectral and also new hierarchies of integrable ordinary differential equations again with their underlying linear problems

singularity structure analysis and hirota s bilinearisation of the davey stewartson equation the singularity structure aspects of the davey stewartson equation is investigated and it is shown that the system possesses the generalised painleve property in the sense of weiss tabor and carnevale 1983 further the associated backlund transformation in constructed and hirota s bilinearisation is obtained straightforwardly from the painleve analysis

the painleve property and backlund transformations for the sequence of boussinesq equations we investigate the sequence of boussinesq equations by the method of singular manifolds for the boussinesq equation which is known to possess the painleve property a backlund transformation is defined this backlund transformation which is formulated in terms of the schwarzian derivative obtains the system of modified boussinesq equations and the resulting miura type transformation the modified boussinesq equations are found to be invariant under a discrete group of symmetries acting on the dependent variables by linearizing the miura transformation and modified equations the lax pair is readily obtained furthermore by a result of fokas and anderson the recursion operators defining the sequence of higher order boussinesq equations may be constructed from the miura transformation this allows the recursive definition of backlund transformations for this sequence of equations the recursion operator is found to preserve the discrete symmetries of the modified boussinesq equations this leads to the conclusion that the sequences of boussinesq and modified boussinesq equations identically possess the painleve property are meromorphic we also find that by a simple reduction the sequences of caudrey dodd gibbon and kuperschmidt equations are contained within the boussinesq sequence rational solutions are iteratively constructed for the boussinesq equation and a criterion is proposed for the existence of rational solutions of general integrable systems

on a painleve test of a coupled system of boussinesq and schrodinger equations the complete integrability of a new system of nonlinear equations using the technique of painleve analysis has been investigated the system essentially represents a coupling of boussinesq and schrodinger equations through nonlinear terms while the arbitrariness of the expansion coefficients are proved for a particular branch in the formalism of weiss et al j math phys 24 522 1983 with the reduced ansatz of kruskal the consistency of the truncation is proved by a combination of the methodology due to weiss j math phys 25 13 2226 1984 and hirota lecture notes in physics vol 515 springer berlin 1976 on the other hand the backlund transformation for the equations are obtained via the truncation procedure without the use of kruskal s simplification

comparison of different calculations of three dimensional joint kinematics from video based system data when skin fixed marker trajectories are used to calculate 3d joint kinematics the measurement errors i e the difference between the trajectories of the external markers and those of the skeleton influence to some extent the accuracy of the results depending both on the calculation method and on the axes about which the rotations are expressed the purpose of this paper is to compare several expressions of joint angular variations two kinematic concepts are used to calculate the changes in the orientation of the distal segment versus the proximal one the first method consists of computing the components of the spatial attitude vector the second one deals with the determination of elementary rotations about successive axes for each of these methods two sets of three axes are tested to express the results the axes forming the reference frame affixed to the body segment adjacent to the joint named fixed axes and a set consisting of a first axis belonging to the proximal segment a third axis belonging to the distal segment and a second floating axis defined as the cross product between the two other ones named mobile axes to compare these four distinct expressions on the knee joint numerical simulations of perturbed skin marker trajectories are performed based on experimental data recorded by a motion analysis system during a normal gait cycle a significant difference is pointed out only for the internal external rotation angle for which the best expression from the viewpoint of sensitivity to experimental errors is obtained using the components of the attitude vector in a segment embedded reference frame

3 d attitude representation of human joints a standardization proposal abstract in view of the singularities asymmetries and other adverse properties of existing three dimensional definitions for joint and segment angles the present paper proposes a new convention for unambiguous and easily interpretable 3 d joint angles based on the concept of the attitude vector as derived from euler s theorem the suggested standard can be easily explained to non mathematically trained clinicians is readily implemented in software and can be simply related to classical cardanic eulerian angles for planar rotations about a coordinate system s axes the proposed convention coincides with the cardanic convention the attitude vector dispenses with the gimbal lock and non orthogonality disadvantages of cardanic eulerian conventions therefore its components have better metrical properties and they are less sensitive to measurement errors and to coordinate system uncertainties than cardanic eulerian angles a sensitivity analysis and a physical interpretation of the proposed standard are given and some experimental results that demonstrate its advantages

the structure of wtc expansions and applications we construct generalized painleve expansions with logarithmic terms for a general class of non integrable scalar equations and describe their structure in detail these expansions were introduced without logarithms by weiss tabor carnevale wtc 1983 the construction of the formal solutions is shown to involve semi invariants of binary forms and tools from invariant theory are applied to the determination of the type of logarithmic terms that are required for the most general singular series the structure of the series depends strongly on whether 1 is or is not a resonance the convergence of these series is obtained as a consequence of the general results of littman and kichenassamy 1993 the results are illustrated on a family of fifth order models for water waves and other examples we also give necessary and sufficient conditions for 1 to be a resonance

on the painleve property of the so 2 1 invariant non linear σ model it is shown that the 1 1 dimensional so 2 1 invariant non linear sigma model possesses the painleve p property consequently the nature of the backlund transformation is discussed

rotation sequence is an important factor in shoulder kinematics application to the elite players flat serves the aim of this study was to test three different rotation sequences yxy zxy and xzy on the shoulder kinematics rotations of the humerus relative to the thorax during an original movement such as the tennis flat serve fs nine elite male and female players performed a minimum of five flat serves an optoelectronic motion analysis system was used to record the movements segment kinematics during each fs was reconstructed from the spatial trajectories of the markers according to isb recommendations for each rotation sequence three angles were reported for the shoulder joint each corresponding to a rotation component around a defined axis the occurrence of gimbal lock gl and angle amplitude coherences were examined from these three rotation sequences tested it appears that the xzy sequence was the only decomposition not to suffer from gl moreover the rotation sequence xzy was found to be coherent for all rotation components thus these results show that the best rotation sequence from both gl and amplitude coherence points of view is xzy to describe the shoulder kinematics during the tennis serve

the hirota s direct method and the tanh coth method for multiple soliton solutions of the sawada kotera ito seventh order equation abstract in this work the sawada kotera ito seventh order equation is studied the tanh coth method is applied to obtain soliton solution of this equation the hirota s direct method combined with the simplified hereman s method are applied to determine the n soliton solutions for this equation the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

painleve test of coupled gross pitaevskii equations a painleve p test of the coupled gross pitaevskii equations has been carried out with the result that the coupled equations pass the p test only if a special relation containing system parameters masses and scattering lengths is satisfied computer algebra is applied to evaluate the j 4 compatibility condition for admissible external potentials the appearance of an arbitrary real potential embedded in the external potentials is shown to be the consequence of the coupling the connection with recent experiments related to the stability of two component bose einstein condensates of rb atoms is discussed

the sine gordon equations complete and partial integrability the sine gordon equation in one space one time dimension is known to possess the painleve property and to be completely integrable it is shown how the method of singular manifold analysis obtains the backlund transform and the lax pair for this equation a connection with the sequence of higher order kdv equations is found the modified sine gordon equations are defined in terms of the singular manifold these equations are shown to be identically painleve also certain rational solutions are constructed iteratively the double sine gordon equation is shown not to possess the painleve property however if the singular manifold defines an affine minimal surface then the equation has integrable solutions this restriction is termed partial integrability the sine gordon equation in n 1 variables n space 1 time where n is greater than one is shown not to possess the painleve property the condition of partial integrability requires the singular manifold to be an einstein space with null scalar curvature the known integrable solutions satisfy this constraint in a trivial manner finally the coupled kdv or hirota satsuma equations possess the painleve property the associated modified equations are derived and from these the lax pair is found

factorization of operators ii we extend the methods of a previous paper j math phys 21 2508 1980 factorizing the general scalar third order differential operator and obtain a miura transformation for the boussinesq equation we give a general factorized eigenvalue problem we also give a hamiltonian structure associated with the factorized eigenvalue problem we derive several isospectral flows some of klein gordon type

nonlinear schrodinger equation painleve test backlund transformation and solutions the authors demonstrate that the nonlinear schrodinger equation passes the painleve test and construct a backlund transformation and solutions within this approach the connection with the hirota bilinear formalism is discussed also the heisenberg ferromagnet equation which is gauge equivalent to the nonlinear schrodinger equation is studied

on the normal subgroups of we give a characterization theorem for the e a normalized subgroups of g2 a where a is any commutative ring this is the last of the simple chevalley demazure group schemes for which such a theorem is lacking introduction in this paper we prove a theorem 3 6 which characterizes the e a normalized subgroups of g2 a for an arbitrary commutative ring a the theorem brings to completion the larger project of finding characterization theorems for e a normalized subgroups of simple chevalley demazure group schemes g a of rank 2 over arbitrary commutative rings the bulk of t he project was done by vaserstein in his essential paper 16 there he proved the standard characterization theorem given by a ladder corresponding to an ideal for all commutative rings for all g of rank 2 except those of types b2 c2 and g2 vaserstein also suggested in that paper that previous work by abe 1 and abe suzuki 3 could be improved to yield more this was accomplished by abe in 2 wherein he showed that e a normalized subgroups of g a could be characterized by ladders determined by admissible pairs of ideals with the exception that for g of type b2 c2 or g2 rings a having residue class fields of two elements must be excluded our paper 8 subsequently succeeded in removing this restriction for g of type c2 and so also for g of type b2 by recognizing that the presence of residue fields of two elements required lowering the bottom rung of the ladder this left only the case g of type g2 to be finished the present paper does so by applying the lower bottom rung idea of 8 see also 7 to this case we now give a more explicit description of our results let a be an arbitrary commutative ring and denote by g2 a the group of type g2 defined over a the main theorem 3 6 is that a subgroup n of g2 a is e a normalized if and only if c j j c n c g j j for a pair of ideals j j satisfying the condition j3 c j c j here j3 denotes the ideal of a generated by all elements of the form x3 and 3x for all x in j so that j j is an admissible pair in the sense of abe the bracketing groups c j j and g j j are defined in section 1 below in essence c j j is the mixed commutator group e a e j j where e j j is the e a normalized subgroup generated by all elements x j with a long and received by the editors april 1 1997 and in revised form may 22 1997 1991 mathematics sutbject classification primary 20h05 secondary 20g35 research partially supported by nsa grant mda 904 94 h 2008 and nsf grant dms 9622899 1999 american mathematical society

a model of the soft tissue artefact rigid component when using stereophotogrammetry and skin markers the reconstruction of skeletal movement is affected by soft tissue artefact sta this may be described by considering a marker cluster as a deformable shape undergoing a geometric transformation formed by a non rigid change in size and shape and a rigid component translation and rotation displacements a modal decomposition of the sta relative to an appropriately identified basis allows the separation of these components this study proposes a mathematical model of the sta that embeds only its rigid component and estimates the relevant six mode amplitudes as linear functions of selected proximal and distal joint rotations during the analysed task this model was successfully calibrated for thigh and shank using simultaneously recorded pin and skin marker data of running volunteers the root mean square difference between measured and model estimated sta rigid component was 1 1 0 8 mm median inter quartile range over 3 subjects 5 trials 33 markers coordinates and it was mostly due to the wobbling not included in the model knee joint kinematics was estimated using reference pin marker data and skin marker data both raw and compensated with the model estimated sta sta compensation decreased inaccuracy on average from 6 to 1 for flexion extension from 43 to 18 for the other two rotations and from 69 to 25 for the linear displacements thus the proposed mathematical model provides an sta estimate which can be effectively used within optimal bone pose and joint kinematics estimators for artefact compensation and for simulations aimed at their comparative assessments

on the one and two dimensional toda lattices and the painleve property the toda lattice and the two dimensional toda lattice 2 dtl are shown to possess a type of painleve property that is based on the use of separate singular manifolds for each dependent variable the isospectral problem for the 2 dtl found by both mikhailov and by fordy and gibbons can be simply and logically derived from this analysis some remarks are made about the connection between our work and independent work of kametaka and airhault on the relationship between the toda lattice and the second painleve transcendent

the e 2 a sections of mathrm sl 2 a in this paper we characterize the normal subgroups of sl 2 a for commutative rings a in a class which includes the arithmetic dedekind domains with infinitely many units and all rings satisfying the first stable range condition the characterization works as follows given an ideal j of a a group u of units in a j and an additive subgroup p of a closed under certain operations a structure we have dubbed a radix there is a canonically defined normal subgroup g j u p of sl 2 a these subgroups are generic in the sense that the commutators sl 2 a g j u p are all of the commutators of sl 2 a with normal subgroups of sl 2 a and a subgroup n is normal in sl 2 a if and only if sl 2 a g j u p c n c g j u p for one of these generic groups this is proved in the main theorem 3 1 3 the proof is accomplished by using results of bass milnor and serre 4 vaserstein 37 and liehl 17 in conjunction with the theory developed in sections 1 and 2 also invaluable is a refinement of the method of reduction introduced in 8 and 9 it appears in the proof of theorem 3 1 2 and is what makes it possible to reduce the question for arithmetic dedekind domains to the case of proper homomorphic images all of which are finite rings and satisfy the

on subgroups of gl2 over banach algebras and von neumann regular rings which are normalized by elementary matrices abstract let a be an associative ring with 1 and let e 2 a be the group generated by all elementary 2 by 2 matrices over a in this paper we describe all normal subgroups of e 2 a for all von neumann regular rings a as well as for a wide class of rings a containing all banach algebras for banach algebras a the answer involves quasi ideals of a which replace ideals of a in the similar results for gl n a n 3 obtained previously by the second author

a comparison between joint coordinate system and attitude vector for multi segment foot kinematics the joint angles of multi segment foot models have been primarily described using two mathematical methods the joint coordinate system and the attitude vector this study aimed to determine whether the angles obtained through these two descriptors are comparable and whether these descriptors have similar sensitivity to experimental errors six subjects walked eight times on an instrumented walkway while the joint angles among shank hindfoot medial forefoot and lateral forefoot were measured the angles obtained using both descriptors and their sensitivity to experimental errors were compared there was no overall significant difference between the ranges of motion obtained using both descriptors however median differences of more than 6 were noticed for the medial lateral forefoot joint for all joints and rotation planes both descriptors provided highly similar angle patterns median correlation coefficient r 0 90 except for the medial lateral forefoot angle in the transverse plane median r 0 77 the joint coordinate system was significantly more sensitive to anatomical landmarks misplacement errors however the absolute differences of sensitivity were small relative to the joints ranges of motion in conclusion the angles obtained using these two descriptors were not identical but were similar for at least the shank hindfoot and hindfoot medial forefoot joints therefore the angle comparison across descriptors is possible for these two joints comparison should be done more carefully for the medial lateral forefoot joint moreover despite different sensitivities to experimental errors the effects of the experimental errors on the angles were small for both descriptors suggesting that both descriptors can be considered for multi segment foot models

on the painleve property of nonlinear field equations in 2 1 dimensions the davey stewartson system with the purpose of clarifying some aspects of the complete integrability of nonlinear field equations a singular point analysis is performed of the davey stewartson system which can be considered as an extension in 2 1 dimensions of the nonlinear schrodinger equation it is found that the system under consideration possesses the painleve property and allows a set of backlund transformations obtained by truncating the series expansions of the solutions about the singularity manifold

infinite dimensional symmetry algebras and an infinite number of conserved quantities of the 2 1 dimensional davey stewartson equation an infinite dimensional symmetry algebra of the davey stewartson equation is explicitly presented it is shown that this algebra is a gauge generalization of the symmetry transformation for the schrodinger equation and that the virasoro algebra appears as the subalgebra an infinite number of conserved quantities associated with the transformations are also obtained

assessment of anatomical frame variation effect on joint angles a linear perturbation approach although the interpretability and reliability of joint kinematics depends strongly on the accuracy and precision of determining the anatomical frame af orientation the exact dependency of joint angle error on af misalignment is still not clear to fully understand the behavior this study uses linear perturbations to quantify joint angle error due to known modifications of the afs where the joint angles are calculated according to the cardanic convention the result is a functional representation of joint angle error with dependence on nominal joint angles and on the orientations of the alternative afs relative to the nominal afs the results are validated using numerical analysis on knee joint angle data during walking the derived relationship elucidates results from previous work studying this effect and allows af differences to be inferred by joint angle curves when multiple sets of joint angle curves are collected simultaneously

the analytic structure of dynamical systems and self similar natural boundaries abstract in this paper we investigate the analytic complex time structure of the movable singularities for several dynamical systems in general it is found that there exists a direct connection between the occurencce of a certain type of multiple valuedness of the singularities and the existence of a class of remarkable self similar natural boundaries for these systems an asymptotic description of the distribution of singularities in the natural boundary is developed this provides a description of the fine scale structure of these natural boundaries that agrees closely with the numerical calculations

on the normal subgroups ofgl 2 a in this paper we determine the normal subgroups of gl 2 a for a a commutative local ring the papers of klingenberg a lacroix 3 and our paper 1 constitute the previous work on this problem as a consequence of our results we are able to describe the normal subgroups of gl 2 a for all artinian rings a hence in particular for all finite rings a if n is a subset of gl 2 a we denote by i n the level ideal of n that is the smallest ideal of a such that n consists of scalar matrices modulo i n for j an ideal of a gc 2 a j te gl 2 a 1 i t e j is the normal subgroup consisting of all matrices which are scalars modulo j while sl 2 a j te gl 2 a 1 det t 1 and tz imod j is the principal congruence subgroup for j klingenberg proved that if i e a and the residue field of a is not g8 3 then a subgroup n of gl 2 a is normal if and only if sl 2 a z n en equivalently n is normal if and only if sl 2 a j e nc gc 2 a j for some ideal j in which case j z n his paper also shows that this criterion for normality holds in gl n a for n 3 without any hypotheses on the local ring a our paper 1 characterizes normal subgroups of gl 2 a for any ring a with 6 a since every local ring is an sr ring this leaves only the case of local rings in which 2 is not a unit i e in which the residue field has characteristic 2 lacroix in 3 deals with local rings in which the residue field has characteristic 2 but is not gi 2 obtaining the same normality criterion as klingenberg this leaves open the case of local rings with residue field ge 2 we shall use the method of reduction employed in cl to give a normality criterion for subgroups of gl 2 a for a a local ring with gj 2 as residue field moreover the method will allow us to recapture the results of klingenberg and lacroix with great efficiency thus we will be able to 395 0021 8693 90 3 00

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

analytic structure of the henon heiles hamiltonian in integrable and nonintegrable regimes the solutions of the henon heiles hamiltonian are investigated in the complex time plane the use of the painleve property i e the property that the only movable singularities exhibited by the solution are poles enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes these boundaries have a remarkable self similar structure whose form changes as a function of the nonlinear coupling

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract recent work on joint kinematics indicates that the finite centroid centre of rotation and the finite helical axis axis of rotation screw axis twist axis are highly susceptible to measurement errors when they are experimentally determined from landmark position data this paper presents an analytical model to describe these effects under isotropic conditions for the measurement errors and for the spatial landmark distribution it appears that the position and direction errors are inversely proportional to the rotation magnitude and that they are much more error prone than the relatively well determined rotation and translation magnitudes furthermore the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis for the planar centroid the use of rigid body constraints results in considerable precision improvement relative to the classical finite reuleaux method for centroid reconstruction these analytical results can be used to define suitable measurement configurations and they are used in this paper to explain experimental results on rontgenphotogrammetrically acquired in vitro wrist joint movement

the bi hamiltonian structure of some nonlinear fifth and seventh order differential equations and recursion formulas for their symmetries and conserved covariants using a bi hamiltonian formulation we give explicit formulas for the conserved quantities and infinitesimal generators of symmetries for some nonlinear fifth and seventh order nonlinear partial differential equations among them the caudrey dodd gibbon sawada kotera equation and the kupershmidt equation we show that the lie algebras of the symmetry groups of these equations are of a very special form among the c vector fields they are generated from two given commuting vector fields by a recursive application of a single operator furthermore for some higher order equations those multisoliton solutions which for t asymptotically decompose into traveling wave solutions are characterized as eigenvector decompositions of certain operators

aspects of the painleve property for partial differential equations abstract aspects of the painleve property are reviewed special attention is paid to the connection with hirota s method the formulation of a painleve type property suitable for differential difference equations and certain results concerning the self dual yang mills equations

new symmetry reductions and exact solutions of the davey stewartson system i reductions to ordinary differential equations in this article symmetry reductions and exact solutions are presented for the 2 1 dimensional davey stewartson ds system which has the completely integrable dsi and dsii systems as special cases these symmetry reductions are obtained using the direct method originally developed by clarkson and kruskal to study symmetry reductions of the boussinesq equation which involves no group theoretic techniques the ds system is reduced directly to ordinary differential equations with no intermediate step using these reductions exact solutions of the ds system including some expressible in terms of the second and fourth painleve equations and elementary functions are obtained

painleve analysis and integrability of coupled non linear schrodinger equations considering a system of coupled non linear schrodinger nls equations the authors discuss the integrability properties through painleve p analysis for the two coupled nls equations they show that there exists a pair of parametric values possessing the p property for which the associated backlund transformation bt and the hirota bilinearisation are constructed these parametric choices are identical to those of zakharov and schulman 1982 who established the integrability in terms of motion invariants finally they extend the p analysis to the n coupled nls system and identify two parametric choices possessing the p property which are natural generalisations of the two coupled nls cases

symplectic commutator subgroups abstract this paper expands on the work of douglas costa and gordon keller costa and keller used a structure called the commutator subgroup to find the normal subgroups of special linear groups and symplectic groups it is often difficult to determine which matrices are in the commutator subgroup they create a homomorphism on the special linear group which provides us with a formula on the entries of a matrix in that group in order to tell us whether or not a matrix is in the commutator subgroup this information is not only useful in finding normal subgroups but in studying power residue symbols this paper creates a homomorphism on the symplectic group sp 2 m 2 a for a commutative ring a that provides us with a formula on the entries of an element of that group which tells us whether or not the matrix is in the commutator subgroup this homomorphism is also extended to one on ep 2 m 2 a s the elementary group generated by elementaries whose off daigonal entries come from s for s a particular kind of ideal and jordan ideal

modified singular manifold expansion application to the boussinesq and mikhailov shabat systems we present a modified treatment of the singular manifold method as an improved variant of the painleve analysis for partial differential equations with two branches in the painleve expansion we illustrate the method by fully applying it to the classical boussinesq system and to the mikhailov shabat system

on soliton solutions of the kaup kupershmidt equation i direct bilinearisation and solitary wave abstract in this first of two papers designated i and ii physica d 137 2000 34 a direct procedure is given for bilinearising the kaup kupershmidt and sawada kotera equations it is found that whereas the sawada kotera equation can be written in bilinear form in two distinct ways which are shown to be equivalent the kaup kupershmidt equation has a single bilinear representation this distinguishing feature which has previously received no explanation has consequences for obtaining the soliton solutions of these two closely related fifth order integrable equations the anomalous solitary wave of the kaup kupershmidt equation is reconstructed and a simplified approach to obtaining its n soliton solutions is proposed this provides the basis for constructing these solutions explicitly in ii

on classes of integrable systems and the painleve property the caudrey dodd gibbon equation is found to possess the painleve property investigation of the backlund transformations for this equation obtains the kuperschmidt equation a certain transformation between the kuperschmidt and caudrey dodd gibbon equation is obtained this transformation is employed to define a class of p d e s that identically possesses the painleve property for equations within this class backlund transformations and rational solutions are investigated in particular the sequences of higher order kdv caudrey dobb gibbon and kuperschmidt equations are shown to possess the painleve property

error propagation from kinematic data to modeled muscle tendon lengths during walking kinematic data from 3d gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle tendon lengths during walking however kinematic data are subject to soft tissue artifacts sta referring to skin marker displacements during movement sta are known to significantly affect the computation of joint kinematics and would therefore also have an effect on muscle tendon lengths which are derived from the segmental positions the present study aimed to introduce an analytical approach to calculate the error propagation from sta to modeled muscle tendon lengths skin marker coordinates were assigned uncorrelated isotropic error functions with given standard deviations accounting for sta two different musculoskeletal models were specified one with the joints moving freely in all directions and one with the joints constrained to rotation but no translation using reference kinematic data from two healthy boys mean age 9 y 5 m the propagation of sta to muscle tendon lengths was quantified for semimembranosus gastrocnemius and soleus the resulting average sd ranged from 6 to 50 of the normalized muscle tendon lengths during gait depending on the muscle the sta magnitudes and the musculoskeletal model these results highlight the potential impact sta has on the biomechanical analysis of modeled muscle tendon lengths during walking and suggest the need for caution in the clinical interpretation of muscle tendon lengths derived from joint kinematics

a solidification procedure to facilitate kinematic analyses based on video system data abstract when video based motion analysis systems are used to measure segmental kinematics the major source of error is the displacement of skin fixed markers relative to the underlying skeletal structure such displacements cause the marker representation of the segment to deform thereby decreasing the accuracy of subsequent three dimensional kinematic calculations we have developed a two step solidification procedure to address this problem first the mean rigid shape is computed which best represents the time varying marker configuration of each segment second a least squares minimization is used to replace the measured marker coordinates with those corresponding to the best fit mean rigid shape rigid body theory can then be applied unambiguously to perform kinematic analyses to evaluate this approach we defined an unperturbed three dimensional reference movement using kinematic data from the swing phase of gait after perturbing the marker coordinates with artificial noise the rotation matrix and translation vector absolute and relative movement between each pair of successive images were computed using 1 reference frames fixed directly to the perturbed marker coordinates 2 a least squares minimization procedure found in the literature and 3 the proposed solidification procedure the least squares and solidification procedures produced extremely similar results which relative to the direct calculation reduced kinematic errors on average by 20 25 when the maximum distance between markers was small e g

on jordan ideals and matrix rings abstract for a a commutative ring and a m 2 a results by costa and keller characterize certain ep 2 a normalized subgroups of the symplectic group sp 2 a via structures utilizing jordan ideals and the notion of radices the following work creates a jordan ideal structure theorem for z 2 graded rings a 0 a 1 and a z 2 graded matrix algebra the major theorem is a generalization of costa and keller s previous work on matrix algebras over commutative rings

a correction for axis misalignment in the joint angle curves representing knee movement in gait analysis this paper derives a simple mathematical model relating changes in the orientations of the two cartesian coordinate systems involved in recording knee movement and the varus valgus and the internal external rotation angles for describing the knee s motion rotation matrices are given for changing the orientations of the two cartesian coordinate systems in such a way that the quadratic variations in the varus valgus and in the external internal angles are minimal these estimated rotation matrices are used to correct for axis misalignment the correction is calibrated by considering the impact of the new orientation of the thigh cartesian coordinate system on the hip joint angles the procedure is applied to kinematic data collected on normal subjects the uncertainty about the specification of the thigh cartesian coordinate system is shown to explain some of the between subject variability in the varus valgus and in the internal external rotation angles curves

variable coefficient davey stewartson system with a kac moody virasoro symmetry algebra we study the symmetry group properties of the variable coefficient davey stewartson vcds system the lie point symmetry algebra with a kac moody virasoro kmv structure is shown to be isomorphic to that of the usual constant coefficient ds system if and only if the coefficients satisfy some conditions these conditions turn out to coincide with those for the vcds system to be transformable to the ds system by a point transformation the equivalence group of the vcds system is applied to pick out the integrable subsystems from a class of non integrable ones additionally the full symmetry group of the ds system is derived explicitly without exponentiating its symmetry algebra lump solutions rationally localized in all directions in 2 introduced by ozawa for the ds system are shown to hold even for the vcds system precisely when the system belongs to the integrable class i e equivalent to the ds system these solutions can be used for establishing exact blow up solutions in finite time in the s

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

three dimensional three wave interactions a bilinear approach we consider the three dimensional three wave resonance equation using a bilinear approach to investigate a broad class of solutions solutions are obtained in a grammian form and their relationship to kaup s solutions examined

nonclassical symmetries as special solutions of heir equations in phys d 78 1994 124 we have found that iterations of the nonclassical symmetries method give rise to new nonlinear equations which inherit the lie point symmetry algebra of the given equation in the present paper we show that special solutions of the right order heir equation correspond to classical and nonclassical symmetries of the original equations an infinite number of nonlinear equations which possess nonclassical symmetries are derived

integrability characteristics of two dimensional generalizations of nls type equations a recent procedure based on truncated painleve expansions is used to derive lax pairs darboux transformations and various soliton solutions for integrable 2 1 generalizations of nls type equations in particular diverse classes of solutions are found analogous to the dromion instanton lump and ring soliton solutions derived recently for 2 1 korteweg de vries type equations the nizhnik novikov veselov equation and the 2 1 broer kaup system

lie transformations nonlinear evolution equations and painleve forms we present the results of a systematic investigation of invariance properties of a large class of nonlinear evolution equations under a one parameter continuous lie group of transformations it is shown that in general the corresponding invariant variables the subclass of which is the usual similarity variables lead to ordinary differential equations of painleve type in the case of inverse scattering transform solvable equations as conjectured by ablowitz ramani and segur this is found to be also true for certain higher spatial dimensional versions such as the kadomtsev petviashivilli two dimensional sine gordon and ernst equations for the nonsolvable equations considered here this invariance study leads to ordinary differential equations with movable critical points

painleve conjecture revisited the discovery of new integrable two dimensional hamiltonian systems is reported the analytic structure of the solutions makes necessary the generalization of the painlev e conjecture a widely used integrability criterion such a generalization is presented which the authors believe should replace the usual conjecture for two dimensional hamiltonian systems it is indeed compatible with all the systems already found and in addition leads to still new integrable cases