divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities abstract it is shown that a lie point symmetry of the semilinear polyharmonic equations involving nonlinearities of power or exponential type is a variational divergence symmetry if and only if the equation parameters assume critical values the corresponding conservation laws for critical polyharmonic semilinear equations are established

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

the tent transformation can improve the convergence rate of quasi monte carlo algorithms using digital nets in this paper we investigate multivariate integration in reproducing kernel sobolev spaces for which the second partial derivatives are square integrable as quadrature points for our quasi monte carlo algorithm we use digital t m s nets over mathbb z 2 which are randomly digitally shifted and then folded using the tent transformation for this qmc algorithm we show that the root mean square worst case error converges with order 2 m 2 varepsilon for any 0 where 2m is the number of points a similar result for lattice rules has previously been shown by hickernell

dynamic stability and compensatory stepping responses during anterior gait slip perturbations in people with chronic hemiparetic stroke abstract to examine the control of dynamic stability and characteristics of the compensatory stepping responses to an unexpected anterior gait slip induced under the non involved limb in people with hemi paretic stroke pwhs and to examine any resulting adaptive changes in these on the second slip due to experience from prior slip exposure ten pwhs experienced overground slip s1 during walking on the laboratory walkway after 5 8 regular walking rw trials followed by a second consecutive slip trial s2 the slip outcome backward loss of balance blob and no loss of balance nlob and com state i e its com position and velocity stability were examined between the rw and s1 and s1 and s2 at touchdown td of non involved limb and at liftoff lo of the contralateral limb at td there was no difference in stability between rw and s1 however at lo subjects demonstrated a lower stability on s1 than rw resulting in a 100 backward loss of balance blob with compensatory stepping response recovery step rs 4 10 or aborted step as 6 10 on s2 although there was no change in stability at td there was a significant improvement in stability at lo with a 40 decrease in blob there was also a change in step strategy with a decrease in as response 60 to 35 p

the jackknife estimate of variance tukey s jackknife estimate of variance for a statistic s x 1 x 2 cdots x n which is a symmetric function of i i d random variables x i is investigated using an anova like decomposition of s it is shown that the jackknife variance estimate tends always to be biased upwards a theorem to this effect being proved for the natural jackknife estimate of operatorname var s x 1 x 2 cdots x n 1 based on x 1 x 2 cdots x n

center of mass velocity position predictions for balance control the purposes of this analysis were to predict the feasible movements during which balance can be maintained based on environmental contact force anatomical foot geometry and physiological muscle strength constraints and to identify the role of each constraint in limiting movement an inverted pendulum model with a foot segment was used with an optimization algorithm to determine the set of feasible center of mass cm velocity position combinations for movement termination the upper boundary of the resulting feasible region ran from a velocity of 1 1 s 1 normalized to body height at 2 4 foot lengths behind the heel to 0 45 s 1 over the heel to zero over the toe and the lower boundary from a velocity of 0 9 s 1 at 2 7 foot lengths behind the heel to zero over the heel forward falls would be initiated if states exceeded the upper boundary and backward falls would be initiated if the states fell below the lower boundary under normal conditions the constraint on the size of the base of support bos determined the upper and lower boundaries of the feasible region however friction and strength did limit the feasible region when friction levels were less than 0 82 when dorsiflexion was reduced more than 51 or when plantar flexion strength was reduced more than 35 these findings expand the long held concept that balance is based on cm position limits i e the horizontal cm position has to be confined within the bos to guarantee stable standing to a concept based on cm velocity position limits

optimal quasi monte carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions we investigate quasi monte carlo rules for the numerical integration of multivariate periodic functions from besov spaces s r p q b mathbb t d sp qrb td with dominating mixed smoothness 1 p

simplifying the form of lie groups admitted by a given differential equation rather general results are obtained for determining the nature of infinitesimal generators which can be admitted by a given differential equation simple criteria are given to determine whether or not 1 the infinitesimals of independent variables can depend only on independent variables and 2 the infinitesimal of the dependent variable can depend at most linearly on the dependent variable many examples are given a trivial consequence of this paper is that an admitted lie group for any linear partial differential equation of at least second order must have infinitesimals of independent variables depending only on independent variables and the infinitesimal of the dependent variable depends at most linearly on the dependent variable this latter result previously has only been proved for a second order linear pde in the last century sophus lie developed the theory of continuous groups lie groups of transformations he showed that such transformations can be characterized in terms of infinitesimal generators moreover lie gave an algorithm to find the infinitesimal generators admitted by a given differential equation de for any de the admittance of a lie group leads to the construction of a family of new solutions from any known solution the admittance of a lie group for any ordinary differential equation ode leads constructively to a reduction of its order plus quadratures if a partial differential equation pde is invariant under a lie group one can construct special families of solutions called invariant solutions or similarity solutions if a de can be derived from a variational principle then admittance of a lie group is a necessary condition in order to find conservation laws by means of noether s theorem for recent references on lie s algorithm to find infinitesimal generators admitted by a given de and various uses of lie groups for des see l 4 71 52

an explicit construction of optimal order quasi monte carlo rules for smooth integrands in a recent paper by the authors it is shown that there exists a quasi monte carlo qmc rule which achieves the best possible rate of convergence for numerical integration in a reproducing kernel hilbert space consisting of smooth functions in this paper we provide an explicit construction of such an optimal order qmc rule our approach is to exploit both the decay and the sparsity of the walsh coefficients of the reproducing kernel simultaneously this can be done by applying digit interlacing composition due to dick to digital nets with large minimum hamming and niederreiter rosenbloom tsfasman metrics due to chen and skriganov to our best knowledge our construction gives the first qmc rule which achieves the best possible convergence in this function space

on the paper symmetry analysis of wave equation on sphere by h azad and m t mustafa abstract using the scalar curvature of the product manifold s 2 r and the complete group classification of nonlinear poisson equation on pseudo riemannian manifolds we extend the previous results on symmetry analysis of homogeneous wave equation obtained by h azad and m t mustafa h azad m t mustafa symmetry analysis of wave equation on sphere j math anal appl 333 2007 1180 1188 to nonlinear klein gordon equations on the two dimensional sphere

duality theory and propagation rules for generalized digital nets digital nets are used in quasi monte carlo algorithms for approximating high dimensional integrals over the unit cube hence one wants to have explicit constructions of digital nets of high quality in this paper we consider the so called propagation rules for digital nets which state how one can obtain a new digital net of different size from existing digital nets this way one often can generate digital nets of higher quality than were previously known here we generalize existing propagation rules for classical digital nets to generalized digital nets as introduced by dick

special conformal groups of a riemannian manifold and lie point symmetries of the nonlinear poisson equation abstract we obtain a complete group classification of the lie point symmetries of nonlinear poisson equations on generic pseudo riemannian manifolds m using this result we study their noether symmetries and establish the respective conservation laws it is shown that the projection of the lie point symmetries on m are special subgroups of the conformal group of m in particular if the scalar curvature of m vanishes the projection on m of the lie point symmetry group of the poisson equation with critical nonlinearity is the conformal group of the manifold we illustrate our results by applying them to the thurston geometries

limits of recovery against slip induced falls while walking abstract slip induced falls in gait often have devastating consequences the purposes of this study were 1 to select the determinants that can best discriminate the outcomes recoveries or falls of an unannounced slip induced in gait and to find their corresponding threshold i e the limits of recovery which can clearly separate these two outcomes and 2 to verify these results in a subset of repeated slip trials based on the data collected from 69 young subjects during a slip induced in gait nine different ways of combining the center of mass com stability the hip height and its vertical velocity were investigated with the aid of logistic regression the results revealed that the com stability s and limb support represented by the quotient of hip vertical velocity to hip height s hip recorded at the instant immediately prior to the recovery step touchdown were sufficiently sensitive to account for all 100 variance in falls and specific enough to account for nearly all 98 3 variability in recoveries this boundary s hip 0 22 s 0 25 which quantifies the risk of falls in the stability limb support quotient s s hip domain was fully verified using second slip and third slip trials n 76 with classification of falls at 100 and recoveries at 98 6 the severity of an actual fall is likely to be greater further below the boundary while the likelihood of a fall diminishes above it finally the slope of the boundary also indicates the tradeoff between the stability and limb support whereby high stability can compensate for the insufficiency in limb support or vice versa

higher order qmc petrov galerkin discretization for affine parametric operator equations with random field inputs we construct quasi monte carlo methods to approximate the expected values of linear functionals of petrov galerkin discretizations of parametric operator equations which depend on a possibly infinite sequence of parameters such problems arise in the numerical solution of differential and integral equations with random field inputs we analyze the regularity of the solutions with respect to the parameters in terms of the rate of decay of the fluctuations of the input field if p in 0 1 denotes the summability exponent corresponding to the fluctuations in affine parametric families of operators then we prove that deterministic interlaced polynomial lattice rules of order alpha lfloor 1 p rfloor 1 in s dimensions with n points can be constructed using a fast component by component algorithm in mathcal o alpha s n log n alpha 2 s 2 n operations to achieve a convergence rate of mathcal o n 1 p with the implied constant independent of s this dimension independen

the dirichlet problem for the kohn laplacian on the heisenberg group ii for x y t rn rn r denote xj xj 2yj t yj yj 2xj t and l 14 j 1nxj2 yj2 t when n 2q la represents the action of the kohn laplacian b on q forms on the heisenberg group for n n we construct a parametrix for the dirichlet problem in smooth domains d near non characteristic points of d a point w of d is non characteristic if one of x1 xn y1 yn is transverse to d at w this yields sharp local estimates in the dirichlet problem in the appropriate non isotropic lipschitz classes the main new tool is a convolution calculus of pseudo differential operators that can be applied to the relevant layer potentials for which the usual asymptotic composition formula is false characteristic points are treated in part ii

explicit constructions of quasi monte carlo rules for the numerical integration of high dimensional periodic functions in this paper we give explicit constructions of point sets in the s dimensional unit cube yielding quasi monte carlo algorithms which achieve the optimal rate of convergence of the worst case error for numerically integrating high dimensional periodic functions in the classical measure p alpha of the worst case error introduced by korobov the convergence for every even integer alpha ge 1 is of cal o n min alpha d log n s alpha 2 where d is a parameter of the construction which can be chosen arbitrarily large and n is the number of quadrature points this convergence rate is known to be the best possible up to some log n factors we prove the result for the deterministic and also a randomized setting the construction is based on a suitable extension of digital t m s nets over the finite field mathbb z b

asymptotics for some green kernels on the heisenberg group and the martin boundary on decrit completement le comportement asymptotique pour la solution fondamentale de l operateur de la chaleur

can stability really predict an impending slip related fall among older adults the primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices obtained during normal walking among community dwelling older adults one hundred and eighty seven community dwelling older adults participated in the study after walking regularly for 20 strides on a walkway participants were subjected to an unannounced slip during gait under the protection of a safety harness full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates stability variables including feasible stability region measurement margin of stability the maximum floquet multiplier the lyapunov exponents short and long term and the variability of gait parameters including the step length step width and step time were calculated for each subject sensitivity of predicting slip outcome fall vs recovery was examined for each stability variable using logistic regression results showed that the feasible stability region measurement predicted fall incidence among these subjects with the highest sensitivity 68 4 except for the step width with an sensitivity of 60 2 no other stability variables could differentiate fallers from those who did not fall for the sample included in this study the findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible stability region measurement or variability of the step width

walsh spaces containing smooth functions and quasi monte carlo rules of arbitrary high order we define a walsh space which contains all functions whose partial mixed derivatives up to order delta ge 1 exist and have finite variation in particular for a suitable choice of parameters this implies that certain sobolev spaces are contained in these walsh spaces for this walsh space we then show that quasi monte carlo rules based on digital t alpha s sequences achieve the optimal rate of convergence of the worst case error for numerical integration this rate of convergence is also optimal for the subspace of smooth functions explicit constructions of digital t alpha s sequences are given hence providing explicit quasi monte carlo rules which achieve the optimal rate of convergence of the integration error for arbitrarily smooth functions

tight error bounds for rank 1 lattice sampling in spaces of hybrid mixed smoothness we consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank 1 lattice moreover the main result is the fact that any non linear reconstruction algorithm taking function values on any integration lattice of size m has a dimension independent lower bound of 2 alpha 1 2 m alpha 2 when considering the optimal worst case error with respect to function spaces of hybrid mixed smoothness alpha 0 on the d torus we complement this lower bound with upper bounds that coincide up to logarithmic terms these upper bounds are obtained by a detailed analysis of a rank 1 lattice sampling strategy where the rank 1 lattices are constructed by a component by component method the lattice group structure allows for an efficient approximation of the underlying function from its sampled values using a single one dimensional fast fourier transform this is one reason why these algorithms keep attracting significant interest we compare our results to recent almost optimal methods based upon samples on sparse grids

predicted threshold against backward balance loss in gait the purpose of this study was to determine the minimum forward center of mass com velocity required to prevent backward loss of balance in gait as function of the initial com position we hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing to investigate this issue we constructed a seven link nine degree of freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions 1 the posture at the beginning of swing phase i e at toe off and 2 symmetric bipedal standing in particular for a range of possible com positions posterior to the base of support bos simulated annealing was used to search for the minimum velocity that could carry the com into the bos and avoid backward loss of balance we found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing in general the minimal com velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing and the difference could approach 30 or more when the com started 0 5 and 1 0 foot lengths behind the bos these discrepancies suggest that simpler biomechanical models while being more efficient and easier to employ may not always be adequate for exploring stability limits of humans

lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity laplacian abstract using the classical lie method we obtain the full lie point symmetry group of the aronsson equation in two independent variables some group invariant solutions of this equation are found and a conjecture on the lie point symmetry group of the aronsson equation in r n is presented

group classification of semilinear kohn laplace equations abstract we study the lie point symmetries of semilinear kohn laplace equations on the heisenberg group h 1 and obtain a complete group classification of these equations

predicted threshold against backward balance loss following a slip in gait the purpose of this study was to use a 7 link moment actuated human model to predict at liftoff of the trailing foot in gait the threshold of the center of mass com velocity relative to the base of support bos required to prevent backward balance loss during single stance recovery from a slip five dynamic optimization problems were solved to find the minimum com velocities that would allow the simulation to terminate with the com above the bos when the com started 0 25 0 5 0 75 1 0 and 1 25 foot lengths behind the heel of the stance foot i e behind the bos the initial joint angles of the model were based on averaged data from experimental trials foot ground contact was modeled using 16 visco elastic springs distributed under the stance foot slipping was modeled by setting the sliding coefficient of friction of these springs to 0 02 the forward velocity of the com necessary to avoid a backward balance loss is nearly two times larger under slip conditions under non slip conditions the predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking in all trials in which a subject s com had a velocity below the predicted threshold the subject s recovery foot landed posterior to the slipping foot as predicted finally combining experimental data with optimization we verified that the 7 link model could more accurately predict gait stability than a 2 link model