nonexistence and uniqueness of positive solutions of yamabe type equations on nonpositively curved manifolds we prove nonexistence and uniqueness of positive c2 solutions of the elliptic equation u a x u k x u 0 1 on a nonpositively curved complete manifold m g 0 introduction let m g be a complete noncompact riemannian manifold of dimension m 3 and let a x k x be assigned continuous functions on m the aim of this paper is to determine conditions involving the asymptotic behavior of a k and the geometry of m g in order to guarantee nonexistence and eventually uniqueness of positive c solutions of the elliptic equation u a x u k x u 0 0 1 on m for some constant 1 this problem has geometrical roots indeed up to an inessential multiplicative positive constant in front of the choice m 2 m 2 in 0 1 produces the well known yamabe equation relating the scalar curvature a x of g to that k x of the conformally deformed metric gu u 4 m 2 g u 0 in this case a fairly accurate general existence result satisfying the further request of completeness of gu has been given in rrv1 for negative scalar curvatures in the present investigation as naturally expected on a riemannian manifold the geometry is controlled via curvature conditions to be more precise we have fixed our attention on the two most typical cases i riem m g 0 and ii riem m g b2 for some constant b 0 here riem m g denotes the sectional curvature thus r with its canonical metric pertains to case i and in this special setting under the further assumption a x 0 a number of results have been obtained for instance by ni n lin l and more recently by cheng and lin c l however our methods beside having a geometrical flavor differ from those of the above authors mainly because while in r standard symmetrization techniques are at hand on a general manifold such an approach is obviously not feasible furthermore the appearance of the linear term in 0 1 plays a role in connection with k x which to our knowledge has not been thoroughly analysed even in euclidean space as received by the editors march 6 1995 1991 mathematics subject classification primary 53c21 58g03

multiple solutions of nonlinear schrodinger equations via flow invariance and morse theory we prove the existence of multiple bound states of the nonlinear schrodinger equation u v x u f u here the linear potential v is continuous and bounded from below and the nonlinearity f is of asymptotically linear type we show that under certain assumptions on the spectrum of the schrodinger operator v and the asymptotic behaviour of f u u the above equation has at least four non trivial solutions two of them sign changing

comparison between emg to force processing and kinetic analysis for the calf muscle moment in walking and stepping abstract in emg to force processing the force of a muscle or the corresponding muscle moment with respect to the joint is determined from emg and muscle length by means of a model of the muscle s contractile and elastic properties in kinetic analysis the joint moment is calculated from the ground reaction force and the positions and accelerations of the body segments by means of newtonian equations based on a rigid body segment model these two fundamentally different methods have been compared by determining simultaneously the calf muscle moment and the total ankle moment in walking at slow moderate and fast speed and in stepping up and down a low bench as long as there is no activity of other muscles the moments obtained by either method should be identical the analysis was restricted to such periods as assessed from the emg of tibialis anterior in each experimental condition three steps were analyzed in five subjects of 21 22 yr in comparison with the results of kinetic analysis emg processing shows differences between 7 and 54 nm r m s with an average of 22 nm r m s normalized with respect to the r m s value of the moment itself the differences amount to 0 13 0 51 with an average of 0 22 in the majority of cases there was no systematic deviation between emg processing and kinetic analysis and the r m s difference was of the same order of magnitude as determined previously in ergometer experiments

least squares identification of the dynamic relation between the electromyogram and joint moment the dynamic relation between surface emg of an agonist and isometric joint moment is important in models for the prediction of dynamic joint moment from emg an efficient approach for determining the best fitting linear transfer function relating emg and isometric moment using a least squares approach is presented and illustrated for a second order model

superlinear systems of second order ode s abstract we discuss the existence of positive solutions of the system u f t u v u v in 0 1 v g t u v u v in 0 1 u 0 u 1 v 0 v 1 0 where the nonlinearities f and g satisfy a superlinearity condition at both 0 and our main result is the proof of a priori bounds for the eventual solutions as an application we consider the dirichlet problem in an annulus for systems of semilinear elliptic equations with nonlinearities depending on the gradient as well as a second application we consider fourth order elastic beam equations with dependence also on the derivatives u u u

existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero we study the existence of changing sign solutions of an elliptic semilinear boundary value problem which arises as a limiting equation of the two species lotka volterra competing equations system using variational methods and a result of d aujourd hui we find conditions which are both sufficient and necessary for this existence problem

feasibility of estimating isokinetic knee torque using a neural network model many studies have investigated the relationships between electromyography emg and torque production a few investigators have used adjusted learning algorithms and feed forward artificial neural networks anns to estimate joint torque in the elbow this study sought to estimate net isokinetic knee torque using ann models isokinetic knee extensor and flexor torque data were measured simultaneously with agonist and antagonist emg during concentric and eccentric contractions at joint velocities of 30 degrees s and 60 degrees s age gender height body mass agonist emg antagonist emg joint position and joint velocity were entered as predictive variables of net torque a three layer ann model was developed and trained using an adjusted back propagation algorithm accuracy results were compared against those of forward stepwise regression models stepwise regression models included body mass body height and joint position as the most influential predictors followed by agonist emg for concentric and eccentric contractions estimation of eccentric torque included antagonist emg following the agonist activation ann models resulted in more accurate torque estimation r 0 96 compared to the stepwise regression models r 0 71 ann model accuracy increased greatly when the number of hidden units increased from 5 to 10 continuing to increase gradually with additional hidden units the average number of training epochs necessary for solution convergence and the relative accuracy of the model indicate a strong ability for the ann model to generalize these estimations to a broader sample the ann model appears to be a feasible technique for estimating joint torque in the knee

emg to force processing iii estimation of model parameters for the human triceps surae muscle and assessment of the accuracy by means of a torque plate the parameters of the active state and the series elastic component of the hill muscle model were estimated for the human calf muscles by means of a torque plate on seven normal subjects together with the results of the calfergometer experiments part ii this yields the complete set of parameters for the emg to force processor based on the hill model part i the accuracy of the processor was assessed by means of a set of severe test contractions in which the subjects tilted on one foot at various velocities slow to as fast as possible the mechanical work m dt and the integrated torque m dt were calculated for these contractions m being the torque calculated by the emg processor and the measured angular velocity these values of the work and the integrated torque were compared to those obtained with the measured torque mm instead of m the relative error for positive work negative work and integrated torque was 6 2 14 means s d data on the peak values of m mm are also given

joint moments and muscle activity in the lower extremities and lower back in lifting and lowering tasks the mechanical loading on the body during the act of lifting has been estimated frequently the opposite act of lowering has received much less attention the aim of the present study was to compare the mechanical loading of the musculoskeletal system in lifting and lowering eight subjects repetitively lifted and lowered a load using two different techniques a leg and a back technique the ankle knee hip and lumbosacral joint moments were estimated and the myoelectrical emg activity of seven leg and back muscles was recorded the differences between the lifting and lowering phase for the leg technique were similar to those observed when the back technique was applied the joint moment curves in lifting showed a high level of agreement with the time reversed moment curves in lowering peak moments in lowering were only slightly lower than in lifting peak lumbar moments were 5 4 lower these small differences were related to different acceleration profiles at the centre of gravity of the body load complex the emg activity was considerably lower in lowering than in lifting the mean emg in lowering average for seven muscles was only about 69 of the emg in lifting this was attributed to the different types of muscle actions involved in lifting mainly concentric and lowering mainly eccentric furthermore the emg results suggest that similar inter muscular coordination is involved in lowering and lifting the results give rise to the assumption that in lifting and lowering similar muscle forces are produced to meet the nearly equal joint moments but in lowering these forces are distributed over a smaller cross sectional area of active muscle which might imply a higher risk of injury

coordination of the leg muscles in backlift and leglift abstract net joint moments are often used to quantify the loading of structures e g the intervertebral disc at l5s1 during lifting this quantification method is also used to evaluate the loading of the knee for instance to determine the effect of backlifting as opposed to leglifting however the true loading of the joint as derived from net joint moments can be obscured by a possible co contraction of antagonists to unravel the mechanisms that determine the net joint moments in the knee the leglift was compared to the backlift although a completely different net knee moment curve was found when comparing the two lifting techniques it appeared to be closely related to the ground reaction force vector and its orientation with respect to the joint centre of rotation r 0 995 this close relation was established by co contraction of both flexors and extensors of the knee furthermore a close relation appeared to exist between the joint moment difference between hip and knee and the activity difference between rectus femoris muscle and hamstring r 0 72 and 0 83 in leglift and backlift respectively the knee ankle joint moment difference and the activity of the gastrocnemius showed a close relation as well r 0 89 and 0 96 in leglift and backlift respectively these relations can be interpreted as a mechanism to distribute net moments across joints it is concluded that during lifting tasks the intermuscular coordination is aimed at coupling of joint moments such that the ground reaction force points in a direction that provides balance during the movement the use of net joint moments as direct indicators for joint loading e g knee seems therefore questionable

a bahri lions theorem revisited abstract in 1988 a bahri and p l lions a bahri p l lions morse index of some min max critical points i application to multiplicity results comm pure appl math 41 1988 1027 1037 studied the following elliptic problem u u p 2 u f x u u h 0 1 where is a bounded smooth domain of r n 2 p 2 n 2 n 2 and f x u is not assumed to be odd in u they proved the existence of infinitely many solutions under an appropriate growth restriction on f in the present paper we improve this result by showing that under the same growth assumption on f the problem admits in fact infinitely many sign changing solutions in addition we derive an estimate on the number of their nodal domains we also deal with the corresponding fourth order equation 2 u u p 2 u f x u with both dirichlet and navier boundary conditions as well as with strongly coupled elliptic systems

emg to force processing ii estimation of parameters of the hill muscle model for the human triceps surae by means of a calfergometer on a calfergometer isotonic contractions were performed by the calf muscles of human subjects the measured torque mm was compared to the torque m processed from the emg and the joint angle by means of an electronic processor based on the hill muscle model by means of these experiments the model parameters were determined for the torque angle relation the torque angular velocity relation and the parallel elastic component pec experiments were done a for the soleus only 4 subjects and b for the combination of soleus and gastrocnemius 8 subjects it turned out that the torque angle parameters varied among subjects the torque angular velocity parameters for soleus only varied also among subjects for the combined calf muscle group the interindividual differences in the torque angular velocity parameters could be neglected one of the parameters of the pec was the same for all subjects while the other was variable among the subjects the obtained parameter values are discussed and compared with available literature data values for the r m s and the peak error in the isotonic phases of the contraction are given and compared with values predicted from the stochastic properties of the emg signal

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

a liouville type result for quasi linear elliptic equations on complete riemannian manifolds we extend a liouville type result of d g aronson and h f weinberger and e n dancer and y du concerning solutions to the equation pu b x f u to the case of a class of singular elliptic operators on riemannian manifolds which include the laplacian and are the natural generalization to manifolds of the operators studied by j serrin and collaborators in euclidean setting in the process we obtain an a priori lower bound for positive solutions of the equation in consideration which complements an upper bound previously obtained by the authors in the same context

positive solutions of yamabe type equations on complete manifolds and applications we study the semilinear equation u a x u b x u 1 on a complete riemannian manifold we determine conditions on the coefficients that guarantee existence and nonexistence of positive solutions a very general uniqueness result is also established our main results are valid without explicit curvature assumptions and appear to be new even in rm

identification of dynamic myoelectric signal to force models during isometric lumbar muscle contractions a 14 muscle myoelectric signal mes driven muscle force prediction model of the l3 l4 cross section is developed which includes a dynamic mes force relationship and allows for cocontraction model parameters are estimated from mes and moments data recorded during rapid exertions in trunk flexion extension lateral bending and axial twist nine young healthy males participated in the experimental testing the model used in the parameter estimation is of the output error type consistent and physically feasible parameter estimates were obtained by normalizing the rms mes to maximum exertion levels and using nonlinear constrained optimization to minimize a cost function consisting of the trace of the output error covariance matrix model performance was evaluated by comparing measured and mes predicted moments over a series of slow and rapid exertions moment prediction errors were on the order of 25 30 and 40 during attempted trunk flexion extensions lateral bends and axial twists respectively the model and parameter estimation methods developed provide a means to estimate lumbar muscle and spine loads as well as to empirically investigate the use and effects of cocontraction during physical task performances

a comparison of three muscle pennation assumptions and their effect on isometric and isotonic force abstract three different pennation angle assumptions are compared to experimental data from huijing and woittiez neth j zool 34 21 32 1984 that relate fibre length to angle of pennation changes the assumptions tested are 1 neglecting pennation 2 assuming a fixed pennation and 3 assuming a constant muscle volume and thickness resulting in pennation angle being dependent on fibre length each assumption is compared by transforming fibre force length and force velocity characteristics to muscle properties in general the fixed pennation assumption provides the worst estimate of muscle force output with a peak error of 0 31 f o during isometric contractions at small muscle lengths a better estimate of muscle force output was provided by neglecting pennation entirely the assumption that the pennation angle changed with fibre length maintained an error of less than 0 05 f o for most lengths and velocities tested and provided the best estimate of muscle force output

on the existence of many solutions for a class of superlinear elliptic systems abstract we seek multiple solutions to systems of semilinear elliptic equations of the type u x h x u x x u x 0 x where r n n 1 is a bounded regular domain and u u1 u2 r 2 for a class of potentials where the variables are strongly coupled as in the model h x u1 u2 u1 1 u2 2 with i 1 we provide the existence of nine nontrivial solutions characterized by sign properties of each component

lumbar muscle force estimation using a subject invariant 5 parameter emg based model the use of electromyographic measures in concert with modeled or empirical representations of muscle physiology is a common approach for estimation of muscle force existing models of the lumbar musculature have allowed model parameters to vary for an individual subject while this approach improves apparent predictive ability it loses some degree of construct validity since parameter variability may not be physiologically justifiable an emg based five parameter model adapted and generalized from earlier reports is presented here inherent in the model is the requirement of subject invariant modeling parameters as a practical analysis tool was desired the model relies on relatively few calibration constants whose determination is described empirical evaluation was undertaken using a database of 398 experimental trials involving lifting and transferring objects of moderate mass model performance evaluated by comparison of measured and predicted lumbar moments was comparable to earlier models with r2 mean s d values of 0 76 0 15 for sagittal plane moments and rms mean s d errors of 14 1 7 4 9 7 5 3 and 8 6 3 6 nm in the sagittal frontal and horizontal planes respectively these empirical results and the argument of physiological veracity support the use of a subject invariant model

predictions of knee and ankle moments of force in walking from emg and kinematic data abstract a deterministic model was developed and validated to calculate instantaneous ankle and knee moments during walking using processed emg from representative muscles instantaneous joint angle as a correlate of muscle length and angular velocity as a correlate of muscle velocity and having available total instantaneous joint moments for derivation of certain model parameters a linear regression of the moment on specifically processed emg recorded while each subject performed cycled isometric calibration contractions yielded the constants for a basic moment emg relationship using the resultant moment for optimization the predicted moment was proportionally augmented for longer muscle lengths and reduced for shorter lengths similarly the predicted moment was reduced for shortening velocities and increased if the muscle was lengthening the plots of moments predicted using the full model and those calculated from link segment mechanics followed each other quite closely the range of root mean square errors were 3 2 9 5 nm for the ankle and 4 7 13 0 nm for the knee

simulation of quadrupedal locomotion using a rigid body model locomotion of the horse is simulated using a mathematical model based on rigid body dynamics a general method to generate the equations of motion for a two dimensional rigid body model with an arbitrary number of hinge joints is presented and a numerical solution method restricted to tree structured models is described joint movements originating from muscular forces or moments are simulated but the method also allows that parts of the model follow strictly the pattern of kinematic data moment generators with first order linear feedback were used as a rotational muscle equivalent ground hoof interaction forces are approximated by a viscoelastic model and pseudo coulomb friction in vertical and horizontal directions respectively results of model simulations are compared to experimentally recorded data subsequently adjustments are made to improve the agreement between simulation and experimental results