is a single or double arm technique more advantageous in triple jumping triple jumpers employ either an asymmetrical single arm action or symmetrical double arm action in the takeoff of each phase of the jump this study investigated which technique is more beneficial in each phase using computer simulation kinematic data were obtained from an entire triple jump using a vicon automatic motion capture system a planar 13 segment torque driven subject specific computer simulation model was evaluated by varying torque generator activation timings using a genetic algorithm in order to match performance data the matching produced a close agreement between simulation and performance with differences of 3 8 2 7 and 3 1 for the hop step and jump phases respectively each phase was optimised for jump distance and an increase in jump distance beyond the matched simulations of 3 3 11 1 and 8 2 was obtained for the hop step and jump respectively the optimised technique used symmetrical shoulder flexion whereas the triple jumper had used an asymmetrical arm technique this arm action put the leg extensors into slower concentric conditions allowing greater extensor torques to be produced the main increases in work came at the joints of the stance leg but the largest increases in angular impulse came at the shoulder joints indicating the importance of both measures when assessing the impact of individual joint actions on changes in technique possible benefits of the double arm technique include cushioning the stance leg during impact raising the centre of mass of the body at takeoff facilitating an increase in kinetic energy at takeoff allowing a re orientation of the body during flight

multi soliton and double wronskian solutions of a 2 1 dimensional modified heisenberg ferromagnetic system a 2 1 dimensional modified heisenberg ferromagnetic system which arises in the motion of magnetization vector of the isotropic ferromagnet and biological pattern formation is investigated via the hirota bilinear method multi soliton solutions of such a system are derived it is proved that the system possesses the n soliton solutions expressed in terms of the double wronskian determinant head on and overtaking elastic interactions are exhibited elastic interaction behavior between the two solitons has been interpreted through the asymptotic analysis namely amplitude and velocity of each soliton remain unchanged except for the phase shift after the interaction inelastic interactions including the soliton fusion and fission between two solitons are shown during the soliton propagation for the product of two fields the soliton with the smaller amplitude can travel faster than with the larger while for the third field the soliton with the larger amplitude can travel faster than with the smaller on the other hand the soliton for the third field may exhibit the solitoff like property with respect to the three solitons head on elastic interaction can be found

constrained kp hierarchy and bi hamiltonian structures the kakomtsev petviashvili kp hierarchy is considered together with the evolutions of eigenfunctions and adjoint eigenfunctions constraining the kp flows in terms of squared eigenfunctions one obtains 1 1 dimensional integrable equations with scattering problems given by pseudo differential lax operators the bi hamiltonian nature of these systems is shown by a systematic construction of two general poisson brackets on the algebra of associated lax operators gauge transformations provide miura links to modified equations these systems are constrained flows of the modified kp hierarchy for which again a general description of their bi hamiltonian nature is given the gauge transformations are shown to be poisson maps relating the bi hamiltonian structures of the constrained kp hierarchy and the modified kp hierarchy the simplest realization of this scheme yields the akns hierarchy and its miura link to the kaup broer hierarchy

superposition principles associated with the moutard transformation an integrable discretization of a 2 1 dimensional sine gordon system superposition principles both linear and nonlinear associated with the moutard transformation are found on suitable reinterpretation these constitute an integrable discrete nonlinear system and its associated linear system further it is shown that in a particular form this system is an integrable discretization of a 2 1 dimensional sine gordon system solutions of the discrete nonlinear system are constructed by means of a discrete analogue of the moutard transformation included in these solutions are discrete analogues of the kink solutions of the continuous system

conserved quantities and symmetries of kp hierarchy conserved quantities and symmetries of the kp equation from the point of view of the sato theory that provides a unifying approach to soliton equations is studied conserved quantities are derived from the generalized lax equations some reductions of the kp hierarchy such as kdv boussinesq a coupled kdv and sawada kotera equation are also considered by expansion of the squared eigenfunctions of the lax equations in terms of the function symmetries of the kp equations are obtained the relationship of this procedure to the two dimensional recursion operator newly found by fokas and santini is discussed

method of squared eigenfunction potentials in integrable hierarchies of kp type the method of squared eigenfunction potentials sep is developed systematically to describe and gain new information about the kadomtsev petviashvili kp hierarchy and its reductions interrelation to the function method is discussed in detail the principal result which forms the basis of our sep method is the proof that any eigenfunction of the general kp hierarchy can be represented as a spectral integral over the baker akhiezer ba wave function with a spectral density expressed in terms of sep in fact the spectral representations of the adjoint ba functions can in turn be considered as defining equations for the kp hierarchy the sep method is subsequently used to show how the reduction of the full kp hierarchy to the constrained kp ckp rm hierarchies can be given entirely in terms of linear constraint equations on the pertinent functions the concept of sep turns out to be crucial in providing a description of ckp rm hierarchies in the language of the universal sato grassmannian and finding the non isospectral virasoro symmetry generators acting on the underlying functions the sep method is used to write down generalized binary darboux backlund transformations for constrained kp hierarchies whose orbits are shown to correspond to a new toda model on a square lattice as a result we obtain a series of new determinant solutions for the functions generalizing the known wronskian multi soliton solutions finally applications to random matrix models in condensed matter physics are briefly discussed

measurement of body segment parameters using dual energy x ray absorptiometry and three dimensional geometry an application in gait analysis abstract body segment parameters bsp are essential input for the computations in kinetics of motion applied in the field of biomechanics these data are usually obtained from population specific predictive equations which present limitations in being representative of the population under study more recently medical imaging techniques have been adopted but are limited to two dimensional 2 d measurements or required extensive tomographic images for three dimensional 3 d reconstruction we proposed an in vivo method to measure 3 d bsp using x ray imaging and 3 d exterior geometry criterion values of the bsp were determined using magnetic resonance imaging mri which has previously been validated errors for all bsp values were less than 2 when values derived from our method were compared to the criterion values we found no significant difference between our method and four selected bsp models in both stance and swing phase significant phase effects were observed for our method and other bsp models between stance and swing phase significant differences p

the simulation of aerial movement i the determination of orientation angles from film data abstract quantitative mechanical analyses of human movement require the time histories of the angles which specify body configuration and orientation when these angles are obtained from a filmed performance they may be used to evaluate the accuracy of a simulation model this paper presents a method of determining orientation angles and their rates of change from film data the stages used comprise the synchronization of data obtained from two camera views the determination of three dimensional coordinates of joint centres the calculation of an angle from a sequence of sine and cosine values and the curve fitting of angles using quintic splines for each state other possible approaches are discussed original procedures are presented for obtaining individual error estimates of both the film data and the calculated angles to permit the automatic fitting of quintic splines for interpolation and differentiation and for deriving the time history of an angle as a continuous function from a sequence of sine and cosine values the method is applied to a forward somersault with 1 1 2 twists and the average error estimate of 17 orientation angles is obtained as 2 1 degrees

kinematics estimation of straddled movements on high bar from a limited number of skin markers using a chain model to reduce the effects of skin movement artefacts and apparent joint dislocations in the kinematics of whole body movement derived from marker locations global optimisation procedures with a chain model have been developed these procedures can also be used to reduce the number of markers when self occlusions are hard to avoid this paper assesses the kinematics precision of three marker sets 16 11 and 7 markers for movements on high bar with straddled piked posture a three dimensional person specific chain model was defined with 9 parameters and 12 degrees of freedom and an iterative procedure optimised the gymnast posture for each frame of the three marker sets the time histories of joint angles obtained from the reduced marker sets were compared with those from the 16 marker set by means of a root mean square difference measure occlusions of medial markers fixed on the lower limb occurred when the legs were together and the pelvis markers disappeared primarily during the piked posture despite these occlusions reconstruction was possible with 16 11 and 7 markers the time histories of joint angles were similar the main differences were for the thigh mediolateral rotation and the knee flexion because the knee was close to full extension when five markers were removed the average angles difference was about 3 this difference increased to 9 for the seven marker set it is concluded that kinematics of sports movement can be reconstructed using a chain model and a global optimisation procedure for a reduced number of markers

darboux and binary darboux transformations for discrete integrable systems i discrete potential kdv equation the hirota miwa equation can be written in nonlinear form in two ways the discrete kp equation and by using a compatible continuous variable the discrete potential kp equation for both systems we consider the darboux and binary darboux transformations expressed in terms of the continuous variable and obtain exact solutions in wronskian and grammian form we discuss reductions of both systems to the discrete kdv and discrete potential kdv equation respectively and exploit this connection to find the darboux and binary darboux transformations and exact solutions of these equations

the existence of global attractors for the norm to weak continuous semigroup and application to the nonlinear reaction diffusion equations abstract in this paper first we introduce a new concept called the norm to weak continuous semigroup in a banach space and give a technical theorem to verify this notion of continuity then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup as an application we obtain the existence of the global attractor for a nonlinear reaction diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term the global attractors are obtained in l p h 0 1 and h 2 h 0 1 respectively a new a priori estimate method called asymptotic a priori estimate has been introduced since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in l p h 0 1 and h 2 h 0 1 the results in this part are new and appear to be optimal

segment inertial parameter evaluation in two anthropometric models by application of a dynamic linked segment model the estimation of segment inertial parameters sips is an important source of error in inverse dynamic analysis in most individual cases sips are derived from extrapolation of known sips of a certain population through regression equations proportional models another well known method is the use of mathematical approximation of the shape of human body segments combined with estimations of segment densities geometric models in the current study five males and five females performed four different lifting movements in the sagittal plane a full body linked segment model was applied twice to the same data set once using a proportional and once using a geometric anthropometric model as a full body linked segment model is an overdetermined system of equations four equations could be formed to test the summed effect of sip errors on the inverse dynamic analysis the overall performance in terms of coefficients of correlation was better for the geometric model as compared to the proportional model when a back lifting movement was performed the equations indicated systematic errors in the proportional model however when a leg lifting movement was performed the equations indicated systematic errors in the geometric model therefore analyzing only one kind of movement does not suffice to draw conclusions with respect to the reliability of an anthropometric model

the effect of increasing strength and approach velocity on triple jump performance the triple jump is an athletic event comprising three phases in which the optimal phase ratio the proportion of each phase to the total distance jumped is unknown this study used a planar whole body torque driven computer simulation model of the ground contact parts of all three phases of the triple jump to investigate the effect of strength and approach velocity on optimal performance the strength and approach velocity of the simulation model were each increased by up to 30 in 10 increments from baseline data collected from a national standard triple jumper increasing strength always resulted in an increased overall jump distance increasing approach velocity also typically resulted in an increased overall jump distance but there was a point past which increasing approach velocity without increasing strength did not lead to an increase in overall jump distance increasing both strength and approach velocity by 10 20 and 30 led to roughly equivalent increases in overall jump distances distances ranged from 14 05m with baseline strength and approach velocity up to 18 49m with 30 increases in both optimal phase ratios were either hop dominated or balanced and typically became more balanced when the strength of the model was increased by a greater percentage than its approach velocity the range of triple jump distances that resulted from the optimisation process suggests that strength and approach velocity are of great importance for triple jump performance

effect of arm swing direction on forward and backward jump performance this study quantified and compared how the directional differences in arm swing affected mechanical and physiological parameters during forward and backward jumping seven subjects maximally performed three types of forward and backward squat jumps no arm swing fj bj forward arm swing fjf bjf and backward arm swing fjb bjb from a force platform all performances were captured with a 3 d motion capture system electromyograms emgs of the lower extremity muscles were obtained variables were calculated by combining kinematic and kinetic data the jump displacement and center of mass velocity at take off were significantly larger in fjf than in fj or fjb and larger in bjb than in bj or bjf suggesting that the best performance was obtained by employing the same arm swing direction as a given jump direction the total work by three lower and two upper extremity joints was significantly larger in fjf than in fj or fjb and larger in bjb than in bj or bjf for the lower extremity joints hip work was the greatest in fjf and bjb the integrated emg of the biceps femoris when the hip power was produced was significantly larger in fjf and bjb than under other conditions these results suggest that if the arm swing direction is the same as a given jump direction the activation level of the hip extensor is greater to counter large loads which make the hip joint flex during the push off phase which result in increased hip extension torque power and work

darboux and binary darboux transformations for the nonautonomous discrete kp equation it is shown how darboux and binary darboux transformations for a nonautonomous discrete kp equation can be obtained from fermion analysis this equation is obtained by considering a generalized miwa transformation it is also shown to be linked to the discrete kp equation by a special gauge transformation the darboux and binary darboux transformations are used to discuss general classes of solutions in the form of casorati and gramm type determinants n soliton solutions are discussed as well

1 1 dimensional hamiltonian systems as symmetry constraints of the kadomtsev petviashvili equation the authors consider linear problems associated with the kadomtsev petviashvili equation they prove that the linear problems are 1 1 dimensional hamiltonian systems under the symmetry constraints moreover they find that the hamiltonian flows of the linear problems are commutative

extensions of the matrix gelfand dickey hierarchy from generalized drinfeld sokolov reduction thep p matrix version of ther kdv hierarchy has been recently treated as the reduced system arising in a drinfeld sokolov type hamiltonian symmetry reduction applied to a poisson submanifold in the dual of the lie algebra widehat gl pr 1 here a series of extensions of this matrix gelfand dickey system is derived by means of a generalized drinfeld sokolov reduction defined for the lie algebra widehat gl pr s 1 using the natural embeddinggl pr glpr s fors any positive integer the hierarchies obtained admit a description in terms of ap p matrix pseudo differential operator comprising anr kdv type positive part and a non trivial negative part this system has been investigated previously in thep 1 case as a constrained kp system in this paper the previous results are considerably extended and a systematic study is presented on the basis of the drinfeld sokolov approach that has the advantage that it leads to local poisson brackets and makes clear the conformal w algebra structures related to the kdv type hierarchies

the constraint on potential and decomposition for 2 1 dimensional integrable systems besides a sufficient condition a necessary condition is given to determine some kind of consistent constraint on the potential of a 2 1 dimensional integrable system which cannot be obtained from the sufficient condition under this kind of constraint on the potential a 2 1 dimensional integrable system can be decomposed into two commuting 1 1 dimensional integrable systems and can be further decomposed into three commuting finite dimensional integrable hamiltonian systems the bkp hierarchy is taken as an illustrative example

global attractors for one dimensional p laplacian equation abstract we study the existence of the l 2 r w 1 p r global attractor for an evolution p laplacian equation under additional restrictions on force and source terms we improve the result of a kh khanmamedov existence of a global attractor for the parabolic equation with nonlinear laplacian principal part in an unbounded domain j math anal appl 316 2006 601 615 and correct the result of m yang c sun c zhong existence of a global attractor for a p laplacian equation in r n nonlinear anal 66 2007 1 13 in the one dimensional case

dynamics for a class of non autonomous degenerate p laplacian equations abstract in this paper we investigate a class of non autonomous degenerate p laplacian equations t u div a x u p 2 u u f u g x t in where a x is allowed to vanish on a nonempty closed subset with lebesgue measure zero g x t l l o c p r d 1 p a and an unbounded domain in r n we first establish the well posedness of these equations by constructing a compact embedding then we show the existence of the minimal pullback d attractor and prove that it indeed attracts the d class in l 2 norm for any 0 our results extend some known ones in previously published papers

existence of a global attractor for a p laplacian equation in rn abstract in this paper we prove the existence of the l 2 r n w 1 p r n l q r n global attractor for the p laplacian equation u t div u p 2 u u p 2 u f u g with a more general nonlinear term f f 1 a x f 2 in r n where a l 1 r n l r n and f 1 f 2 satisfy the arbitrary q order polynomial growth condition without any restriction on q p q 2 p 2

gauge transformations of constrained kp flows new integrable hierarchies integrable systems in 1 1 dimensions arise from the kp hierarchy as symmetry reductions involving square eigenfunctions exploiting the residual gauge freedom in these constraints new integrable systems are derived they include generalizations of the hierarchy of the kundu eckhaus equation and higher order extensions of the yajima oikawa and melnikov hierarchies constrained modified kp flows yield further integrable equations such as the hierarchies of the derivative nls equation the gerdjikov ivanov equation and the chen lee liu equation

optimizing the determination of the body center of mass the position or trajectory of the body center of mass com is often a parameter of interest when studying posture or movement for instance in balance control studies the body com can be related to the ground reaction force or to the base of support since small displacements of the body com are important in balance control studies it is essential to obtain valid estimates of the body com the main source of error in the determination of the body com is the estimation of the masses and centers of mass of the body segments especially the determination of the trunk com is prone to error in the current study five subjects maintained three postures differing in trunk angle during a few seconds the relation between the center of pressure of the ground reaction force and the vertical projection of the body com during the postures was used to optimize the trunk com position additionally the subjects performed two lifting movements the validity of the body com trajectory estimation during the lifting movements both with and without optimized trunk com was checked by relating the external moment of the ground reaction force with respect to the body com to the rate of change of the angular momentum of the whole body it was shown that the correspondence between the external moment and the rate of change of the angular momentum improved after optimization of the trunk com this suggests that the body com trajectory estimation can be improved by the proposed optimization procedure

the effects of initial conditions and takeoff technique on running jumps for height and distance this study used a subject specific model with eight segments driven by joint torques for forward dynamics simulation to investigate the effects of initial conditions and takeoff technique on the performance of running jumps for height and distance the torque activation profiles were varied in order to obtain matching simulations for two jumping performances one for height and one for distance by an elite male high jumper resulting in a simulated peak height of 1 98 m and a simulated horizontal distance of 4 38 m the peak height reached horizontal distance travelled by the mass centre for the same corresponding initial conditions were then maximised by varying the activation timings resulting in a peak height of 2 09 m and a horizontal distance of 4 67 m in a further two optimizations the initial conditions were interchanged giving a peak height of 1 82 m and a horizontal distance of 4 04 m the four optimised simulations show that even with similar approach speeds the initial conditions at touchdown have a substantial effect on the resulting performance whilst the takeoff phase is clearly important unless the approach phase and the subsequent touchdown conditions are close to optimal then a jumper will be unable to compensate for touchdown condition shortcomings during the short takeoff phase to achieve a performance close to optimum

global attractors for degenerate semilinear parabolic equations abstract let be a smooth bounded domain in r n n 2 we consider the long time behavior of solutions to the following problem u t div x u f u g in r u 0 on r u x 0 u 0 x in where u 0 g l 1 the diffusion coefficient x is measurable nonnegative and is allowed to have a finite number of zeroes at some points we provide the existence and uniqueness results for the problem then we establish some asymptotic regularity results on the solution and consider its long time behavior the existence of a global attractor is obtained in the proper space

box and ball system as a realization of ultradiscrete nonautonomous kp equation cellular automata which are realized by dynamics of several kinds of balls in an infinite array of boxes are investigated they show soliton patterns even in the case when each box has arbitrary capacity the analytical expression for the soliton patterns are obtained using ultradiscretization of the nonautonomous discrete kp equation

the kaup broer system and trilinear odes of painleve type the kaup broer hierarchy can be considered as a certain reduction of the kp hierarchy upon introducing the function the kaup broer system can be formulated in trilinear form giving rise to wronskian solutions in this paper several odes of the painleve type obtained through reductions of the kaup broer system are considered those odes take a trilinear form which allows a linearization

comparison of male and female lower limb segment inertial properties many studies have examined human segmental inertial parameters but these studies have focused more on male rather than female data the purpose of this study was to determine the lower limb segmental inertial parameters for a large sample n 1500 of both males and females the participants in this study were those measured as part of a survey of the anthropometry of us army personnel the sample comprised 1774 males mean height 1 756 0 079 m mean mass of 78 49 0 11 kg and mean age of 27 21 6 81 years and 2208 females mean height 1 629 0 072 m mean mass of 62 01 0 08 kg and mean age of 26 18 5 70 years anthropometric measurements were used to determine the inertial properties of the lower limb segments by modeling them as series of geometric solids an analysis of variance revealed that the normalized inertial parameters for each of the segments were statistically significantly different p 0 001 between the two groups the time for each segment to swing through the range of motion of the swing phase of gait produced shorter swing times for the male segments the differences between the segmental inertial properties for the sexes have implications for how these parameters are customized to experimental subjects

the appropriate use of regression equations for the estimation of segmental inertia parameters linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct in many cases theoretical relationships between such quantities are known and can be used as a basis for non linear regression equations this study compares linear and non linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of chandler et al chandler et al 1975 investigation of inertial properties of the human body amrl technical report 74 137 wright patterson air force base oh right limb data were used to derive the equations while left limb data were used as a cross validation sample to evaluate the inertia estimates calculated from the equations for the limb segments the standard error estimates had average values of 21 for the linear equations and 13 for the non linear equations data on a 10 yr old boy was used to compare the two approaches outside the sample range the mean percentage residuals were 286 for the linear equations and 20 for the non linear equations a set of non linear equations is provided

darboux transformations and the discrete kp equation this paper presents two results first it is shown how the discrete kp equation arises from a superposition principle associated with the darboux transformation of the two dimensional toda system then darboux transformations and binary darboux transformations are derived for the discrete kp equation and it is shown how these may be used to construct exact solutions

determination of subject specific model parameters for visco elastic elements the determination of subject specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively this study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot ground interface kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper stiffness and damping coefficients of the visco elastic elements in the model were varied until the difference between simulation and performance was minimised percentage differences of 6 and 9 between the simulated and recorded performances were obtained in the jumps for height and distance respectively when the parameters obtained from the jump for height were used in a simulation of the jump for distance and vice versa there was poor agreement with the recorded jump on the other hand a common set of visco elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8 made up of 7 and 10 between simulation and performance that was almost as good as the individual matches simulations were not overly sensitive to perturbations of the common set of visco elastic parameters it is concluded that subject specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations

a note on p laplacian parabolic problems in rn abstract in this work we study the asymptotic behavior of parabolic p laplacian problems of the form u t div d u p 2 u a u p 2 u b u in l 2 r n where n 1 p 2 d l r n m d x 0 a e in r n 0 b l 2 r n l 2 r n is a globally lipschitz map and a r n r is a non negative continuous function we prove under suitable assumptions on a the existence of a global attractor in l 2 r n for each positive finite diffusion coefficient and we show that the family of attractors behaves upper semicontinuously with respect to positive finite diffusion parameters

backlund transformations for the kp and mkp hierarchies with self consistent sources using gauge transformations for the corresponding generating pseudo differential operators ln in terms of eigenfunctions and adjoint eigenfunctions we construct several types of auto backlund transformations for the kp hierarchy with self consistent sources kphscs and mkp hierarchy with self consistent sources mkphscs respectively the backlund transformations from kphscs to mkphscs are also constructed in this way

the simulation of aerial movement iv a computer simulation model a computer simulation model of human airborne movement is described the body is modelled as 11 rigid linked segments with 17 degrees of freedom which are chosen with a view to modelling twisting somersaults the accuracy of the model is evaluated by comparing the simulation values of the angles describing somersault tilt and twist with the corresponding values obtained from film data of nine twisting somersaults the maximum deviations between simulation and film are found to be 0 04 revolutions for somersault seven degrees for tilt and 0 12 revolutions for twist it is shown that anthropometric measurement errors from which segmental inertia parameters are calculated have a small effect on a simulation whereas film digitization errors can account for a substantial part of the deviation between simulation and film values

exploration of the validity of the two dimensional sagittal plane assumption in modeling the standing long jump most previous standing long jump studies have been based on the assumption of two dimensional sagittal plane motion with bilateral symmetry the purpose of this study was to investigate the validity of this assumption standing long jump trials were collected using six adult male participants each participant stood with a foot on each of two force plates and performed eight standing long jumps for maximal distance inverse dynamics analyses were performed for two dimensional 2d and three dimensional 3d models and joint moments powers and work values were compared the differences between these models with respect to the validity of the common planar jumping assumption were analyzed good agreement was observed between 2d and 3d methods for the lower body with minimal differences in sagittal plane moments power and work for the ankle knee and lower back there were significant but relatively small differences in the sagittal plane kinematics and kinetics at the hip for the upper body the results contradicted the sagittal plane assumption in that significant moments and power were generated about the abduction adduction axis of the shoulder and a similar amount of work was performed about both abduction adduction and flexion extension axes of the shoulder the elbow also showed significant differences in power and work these results indicate that an assumption of planar motion should be sufficient for many studies of the standing long jump that only examine lower body movement however for studies that include upper body motion diagnosing injury risk or investigating gender differences a 3d model may be more appropriate

constructing lump like solutions of the hirota miwa equation we construct special solutions of the hirota miwa equation for which the function is a polynomial in the independent variables three different methods are presented direct construction obtained also as a limit of the soliton solutions and the derivation of the solutions in two different determinant forms namely grammian and casorati introducing the appropriate ansatz we write the hirota miwa equation in a nonlinear form for a single variable in terms of the latter the solutions obtained are rational and are reminiscent of the lump solutions for the continuous analogue of the hirota miwa equation namely the kp equation

role of arm motion in the standing long jump the role of arm motion on the performance of the standing long jump was investigated three males performed a series of jumps with free jfa and with restricted jra arm motion to determine if arm swing improves jumping distance the subjects jumped off a force platform and the motion of the body segments were recorded with a four camera passive motion capture system jumping performance was defined as the horizontal displacement of the toe between the initial and landing td positions the subjects jumped 21 2 further on an average with arm movement 2 09 0 03 m than without 1 72 0 03 m seventy one percent of the increase in performance in jfa was attributable to a 12 7 increase in the take off to velocity of the center of gravity cg increases in the horizontal displacement of the cg before to and in the horizontal position of the toe with respect to the cg at td accounted for the remaining 29 of the improvement in jumping distance the added balance and control provided by the arms throughout the jumping motion contributed to performance improvement in jfa the subjects were able to remedy excessive forward rotation about the cg by swinging the arms backwards during the flight phase without the freedom to swing the arms during flight the subjects had to eliminate any excessive forward rotation while still in contact with the ground this tendency in jra was manifest in the premature decline in the vertical ground reaction force vgrf and the development of a counterproductive backward rotating moment about the cg just before to

darboux theorems and wronskian formulas for integrable systems i constrained kp flows abstract generalizations of the classical darboux theorem are established for pseudo differential scattering operators of the form l i 0 n u i i i 1 m i 1 i i iteration of the darboux transformations leads to a gauge transformed operator with coefficients given by wronskian formulas involving a set of eigenfunctions of l nonlinear integrable partial differential equations are associated with the scattering operator l which arise as a symmetry reduction of the multicomponent kp hierarchy with a suitable linear time evolution for the eigenfunctions the darboux transformation is used to obtain solutions of the integrable equations in terms of wronskian determinants

on the squared eigenfunction symmetry of the toda lattice hierarchy the squared eigenfunction symmetry for the toda lattice hierarchy is explicitly constructed in the form of the kronecker product of the vector eigenfunction and the vector adjoint eigenfunction which can be viewed as the generating function for the additional symmetries when the eigenfunction and the adjoint eigenfunction are the wave function and the adjoint wave function respectively then after the fay like identities and some important relations about the wave functions are investigated the action of the squared eigenfunction related to the additional symmetry on the tau function is derived which is equivalent to the adler shiota van moerbeke formulas

global attractors for weighted p laplacian equations with boundary degeneracy using a new a priori estimate method which is introduced by zhong et al j differ equations 223 2 367 2006 10 1016 j jde 2005 06 008 we establish the existence of a global attractor in l2 and lq q 2 respectively for weighted p laplacian equations with boundary degeneracy and without any restriction on the growing order of the nonlinearity

understanding how an arm swing enhances performance in the vertical jump this investigation was conducted to examine the various theories that have been proposed to explain the enhancement of jumping performance when using an arm swing compared to when no arm swing is used twenty adult males were asked to perform a series of maximal vertical jumps while using an arm swing and again while holding their arms by their sides force motion and electromyographical data were recorded during each performance participants jumped higher 0 086 m in the arm swing compared to the no arm swing condition and was due to increased height 28 and velocity 72 of the center of mass at take off the increased height at take off was due to the elevation of the arm segments the increased velocity of take off stemmed from a complex series of events which allowed the arms to build up energy early in the jump and transfer it to the rest of the body during the later stages of the jump this energy came from the shoulder and elbow joints as well as from extra work done at the hip this energy was used to i increase the kinetic and potential energy of the arms at take off ii store and release energy from the muscles and tendons around the ankle knee and hip joint and iii pull on the body through an upward force acting on the trunk at the shoulder it was concluded that none of the prevailing theories exclusively explains the enhanced performance in the arm swing jump but rather the enhanced performance is based on several mechanisms operating together

kp constraints from reduced multi component hierarchies the m vector k constrained kadomtsev petviashvili kp hierarchy is shown to be a pseudo reduction of the m 1 component kp hierarchy to facilitate the implementation of this reduction on the level of the solutions the typical multi component kp solutions are mapped onto solutions of a toda molecule type equation from which wronskian and grammian solutions for the constrained kp hierarchy follow the reduction of the associated linear systems is discussed and its importance for the choice of bilinear representation of the reduced systems is explained

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

moment of inertia of whole body using an oscillating table in adolescent boys abstract this study measured the moment of inertia of the body using the oscillating table method and saw how it is affected by age and body size one hundred and seventeen subjects of junior and senior high school boys of ages 13 18 participated in this study moment of inertia was measured in two postures of supine imx and recumbent imy positions both imx and imy account for the range from 5 6 to 14 0 kg m2 and 4 2 to 13 5 kg m2 respectively and correlate linearly to body height ht and body weight w the values of i my i mx becomes 93 6 and 95 2 independent of age and body size the difference between imx and imy might be affected by projection areas on the frontal from the sagittal area of the body the multiple regression analysis of ht2 and w with regard to im was performed to obtain the following multiple regression equations i mx 3 44 ht 2 0 144 w 8 04 r 0 973 i my 3 52 ht 2 0 125 w 7 78 r 0 972 when imx and imy were estimated using these equations the standard deviation of error which calculates the percent differences between the estimated and measured values amounted to 5 in imx and imy the results suggest that with japanese boys there is a relationship between the postures and body size height or weight independent of age

evolutionary weighted p laplacian with boundary degeneracy abstract the paper concerns the well posedness problem of an evolutionary weighted p laplacian with boundary degeneracy different from the classical theory for linear equations it is shown that the degenerate portion of the boundary should be decomposed into two parts the strongly degenerate boundary on which the equation exhibits hyperbolic characteristics and the weakly degenerate boundary on which the equation still exhibits parabolic characteristics we formulate reasonably the boundary value condition and establish the existence and uniqueness theorems

conserved quantities of generalized periodic box ball systems constructed from the ndkp equation we investigate periodic box ball systems pbbss with several kinds of balls and box capacity greater than or equal to one conserved quantities of the pbbss are constructed from those of the nonautonomous discrete kp ndkp equation using the lax representation of the ndkp equation

reducing ground reaction forces in gymnastics landings may increase internal loading the aim of this study was to use a subject specific seven link wobbling mass model of a gymnast and a multi layer model of a landing mat to determine landing strategies that minimise ground reaction forces grf and internal forces subject specific strength parameters were determined that defined the maximum voluntary torque angle angular velocity relationship at each joint these relationships were used to produce subject specific lumped linear muscle models for each joint muscle activation histories were optimised using a simplex algorithm to minimise grf or bone bending moments for forward and backward rotating vault landings optimising the landing strategy to minimise each of the grf reduced the peak vertical and horizontal grf by 9 for the backward rotating vault and by 8 and 48 for the forward rotating vault compared to a matching simulation however most internal loading measures bone bending moments joint reaction forces and muscle forces increased compared to the matching simulation optimising the landing strategy to minimise the peak bone bending moments resulted in reduced internal loading measures and in most cases reduced grf bone bending moments were reduced by 27 during the forward rotating vault and by 2 during the backward rotating vault landings when compared to the matching simulations it is possible for a gymnast to modify their landing strategy in order to minimise internal forces and lower grf however using a reduction in grf due to a change in landing strategy as a basis for a reduction in injury potential in vaulting movements may not be appropriate since internal loading can increase

optimum phase ratio in the triple jump the purpose of this study was to develop and validate a method to determine the optimum phase ratio that yields the longest actual distance for a given triple jumper two hypotheses were tested a for any given triple jumper the greater the gain in the vertical velocity the greater the loss in the horizontal velocity and b there is no single optimum phase ratio for all triple jumpers kinematic data were collected for four elite male triple jumpers it was found that the loss in the horizontal velocity during a support phase has a significant positive linear correlation with the gain in the vertical velocity during the same support phase the slope of the regression line was referred to as the horizontal to vertical velocity conversion factor based on this relationship an optimization model for the longest actual distance was developed to determine the optimum phase ratio for each of the four subjects the optimization results showed that there was an optimum phase ratio for the longest actual distance for each triple jumper the results of a validity test showed that the model predicted the actual distance with a degree of fair accuracy the results of sensitivity analysis showed that the optimum phase ratio for a given athlete was a function of the horizontal to vertical velocity conversion factor and the horizontal velocity at the touchdown of the hop these results support the two hypotheses of this study

q special functions with q 1 and their application to discrete integrable systems solutions for certain discrete integrable systems are constructed by using integral solutions for hypergeometric q difference systems with q 1 we apply a solution for lauricella s d type hypergeometric q difference system with q 1 to construct a solution for the discrete kp hierarchy furthermore an integral solution of a q difference analogue of bessel s equation is newly introduced and applied to construct a solution for a q difference analogue of the cylindrical toda equation with q 1

a theoretical analysis of preferred pedaling rate selection in endurance cycling one objective of this study was to investigate whether neuromuscular quantities were associated with preferred pedaling rate selection during submaximal steady state cycling from a theoretical perspective using a musculoskeletal model with an optimal control analysis specific neuromuscular quantities of interest were the individual muscle activation force stress and endurance to achieve this objective a forward dynamic model of cycling and optimization framework were used to simulate pedaling at three different rates of 75 90 and 105 rpm at 265 w the pedaling simulations were produced by optimizing the individual muscle excitation timing and magnitude to reproduce experimentally collected data the results from these pedaling simulations indicated that all neuromuscular quantities were minimized at 90 rpm when summed across muscles in the context of endurance cycling these results suggest that minimizing neuromuscular fatigue is an important mechanism in pedaling rate selection a second objective was to determine whether any of these quantities could be used to predict the preferred pedaling rate by using the quantities with the strongest quadratic trends as the performance criterion to be minimized in an optimal control analysis these quantities were analyzed to assess whether they could be further minimized at 90 rpm and produce normal pedaling mechanics the results showed that both the integrated muscle activation and average endurance summed across all muscles could be further minimized at 90 rpm indicating that these quantities cannot be used individually to predict preferred pedaling rates

effect of low pass filtering on joint moments from inverse dynamics implications for injury prevention analyses of joint moments are important in the study of human motion and are crucial for our understanding of e g how and why acl injuries occur such analyses may be affected by artifacts due to inconsistencies in the equations of motion when force and movement data are filtered with different cut off frequencies the purpose of this study was to quantify the effect of these artifacts and compare joint moments calculated with the same or different cut off frequency for the filtering of force and movement data 123 elite handball players performed sidestep cutting while the movement was recorded by eight 240 hz cameras and the ground reaction forces were recorded by a 960 hz force plate knee and hip joint moments were calculated through inverse dynamics with four different combinations of cut off frequencies for signal filtering movement 10 hz force 10 hz 10 10 movement 15 hz force 15 hz movement 10 hz force 50 hz 10 50 movement 15 hz force 50 hz the results revealed significant differences especially between conditions with different filtering of force and movement mean sd peak knee abduction moment for the 10 10 and 10 50 condition were 1 27 0 53 and 1 64 0 68 nm kg respectively ranking of players based on knee abduction moments were affected by filtering condition out of 20 players with peak knee abduction moment higher than mean 1 sd with the 10 50 condition only 11 were still above mean 1 sd when the 10 10 condition was applied hip moments were very sensitive to filtering cut off mean sd peak hip flexion moment was 3 64 0 75 and 5 92 1 80 under the 10 10 and 10 50 conditions respectively based on these findings force and movement data should be processed with the same filter conclusions from previous inverse dynamics studies where this was not the case should be treated with caution

path description of conserved quantities of generalized periodic box ball systems we investigate conserved quantities of periodic box ball systems pbbs with arbitrary kinds of balls and box capacity greater than or equal to 1 we introduce the notion of nonintersecting paths on the two dimensional array of boxes and give a combinatorial formula for the conserved quantities of the generalized pbbs using these paths

on a non abelian hirota miwa equation a generalization of the hirota miwa equation to an abstract non abelian associative algebra is considered this system is integrable in the sense that it arises as compatibility condition for a linear system and has solutions constructed by means of the application of an arbitrary number of darboux transformations these solutions are in general expressed in terms of quasideterminants

multi soliton and pfaffian solutions of a 2 1 dimensional nonlinear evolution equation via the jaulent miodek hierarchy abstract under investigation in this paper is a 2 1 dimensional nonlinear evolution equation generated by the jaulent miodek hierarchy via the hirota bilinear method multi soliton solutions of such equation are obtained soliton propagation and interactions are analyzed and both the elastic and inelastic interactions are seen with some parameters selected furthermore it is proved that the equation possesses the n soliton solutions expressed in terms of gramm type pfaffian and can be written in the form of a pfaffian identity

the am 1 automata related to crystals of symmetric tensors a soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra uq am 1 is introduced it is a crystal theoretic formulation of the generalized box ball system in which capacities of boxes and carriers are arbitrary and inhomogeneous scattering matrices of two solitons coincide with the combinatorial r matrices of uq am 1 1 a piecewise linear evolution equation of the automaton is identified with an ultradiscrete limit of the nonautonomous discrete kadomtsev petviashivili equation a class of n soliton solutions is obtained through the ultradiscretization of soliton solutions of the latter

long time behavior for quasilinear parabolic equations involving weighted p laplacian operators abstract in this paper we study the first initial boundary value problem for a class of quasilinear degenerate parabolic equations involving weighted p laplacian operators the long time behavior of solutions to that problem is considered via the concept of global attractors for multi valued semiflows

the simulation of aerial movement ii a mathematical inertia model of the human body a mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described the human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements a stadium solid is introduced for modelling the torso segments using perimeter and width measurements this procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used inertia parameter values may be obtained for body models of up to 20 segments errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes

determination of a new uniform thorax density representative of the living population from 3d external body shape modeling body segment parameters bsp for each body s segment are needed for biomechanical analysis to provide population specific bsp precise estimation of body s segments volume and density are needed widely used uniform densities provided by cadavers studies did not consider the air present in the lungs when determining the thorax density the purpose of this study was to propose a new uniform thorax density representative of the living population from 3d external body shape modeling bi planar x ray radiographies were acquired on 58 participants allowing 3d reconstructions of the spine rib cage and human body shape three methods of computing the thorax mass were compared for 48 subjects 1 the dempster uniform density method currently in use for bsps calculation using dempster density data 2 the personalized method using full description of the thorax based on 3d reconstruction of the rib cage and spine and 3 the improved uniform density method using a uniform thorax density resulting from the personalized method for 10 participants comparison was made between the body mass obtained from a force plate and the body mass computed with each of the three methods the dempster uniform density method presented a mean error of 4 8 in the total body mass compared to the force plate vs 0 2 for the personalized method and 0 4 for the improved uniform density method the adjusted thorax density found from the 3d reconstruction was 0 74g cm 3 for men and 0 73g cm 3 for women instead of the one provided by dempster 0 92g cm 3 leading to a better estimate of the thorax mass and body mass

a finite toda representation of the box ball system with box capacity a connection between the finite ultradiscrete toda lattice and the box ball system is extended to the case where each box has its own capacity and a carrier has a capacity parameter depending on time in order to consider this connection new carrier rules size limit for solitons and recovery of balls and a concept expansion map are introduced a particular solution to the extended system of a special case is also presented

maximising somersault rotation in tumbling performing complex somersaulting skills during the flight phase of tumbling requires the generation of linear and angular momenta during the approach and takeoff phases this paper investigates how approach characteristics and takeoff technique affect performance with a view to maximising somersault rotation in tumbling a five segment planar simulation model customised to an elite gymnast was used to produce a simulation which closely matched a recorded performance of a double layout somersault by the elite gymnast three optimisations were carried out to maximise somersault rotation with different sets of initial conditions using the same initial linear and angular momentum as the double layout somersault and varying the joint torque activation timings allowed a double straight somersault to be performed with 19 more rotation potential than the actual performance increasing the approach velocity to a realistic maximum of 7 ms 1 resulted in a 42 reduction in rotation potential when the activation timings were unchanged but allowed a triple layout somersault to be performed with an increase of 31 in rotation potential when activation timings were re optimised increasing also the initial angular momentum to a realistic maximum resulted in a 4 reduction in rotation potential when the activation timings were unchanged but allowed a triple straight somersault to be performed with a further increase of 9 in rotation potential when activation timings were re optimised it is concluded that the limiting factor to maximising somersault rotation is the ability to generate high linear and angular velocities during the approach phase coupled with the ability to adopt consonant activation timings during the takeoff phase

an algebraic description of generalized k constraints the generalized k constrained kp hierarchy is shown to correspond to a so called pseudo reduction of the two dimensional toda lattice hierarchy described in a free fermion approach which is adapted to the case of two singularities in the spectral parameter range wronskian solutions are discussed and in particular soliton solutions are recovered through a reduction of the toda solitons

body segment inertial parameter estimation for the general population of older adults the practical determination of accurate body segment inertial parameters for the general older adult population remains a problem especially in estimating these parameters for women and accounting for variations in body type a method is presented for determining the mass and center of mass location of the body segments of individuals within the general population of older adults effects of sex and body type on older adult mass distribution are accounted for using 32 easily obtainable body measurements the method is based on existing results from different data sources and employs a combination of validated estimation approaches including body mass and segment length proportions linear and nonlinear regression equations and a mathematical model of the trunk the method was applied to a validation sample of healthy community dwelling older adults 29 men 50 women predicted body mass was 96 7 4 8 and 95 7 3 7 of measured body mass in the men and women respectively the estimates of body segment mass and trunk center of mass location for the sample population approximate those reported in the literature supporting the validity of the described method by producing practical subject specific estimates of body segment inertial parameters the method should allow more accurate biomechanical analyses of the older adult population

on solutions of constrained kadomtsev petviashvili equations grammians we show the existence of grammian type solutions for the vector k constrained kadomtsev petviashvili kp equations to introduce the method we give a novel proof for the presence of grammian solutions for the bilinear l modified kp hierarchies