a nonlocal supercritical neumann problem abstract we establish existence of positive non decreasing radial solutions for a nonlocal nonlinear neumann problem both in the ball and in the annulus the nonlinearity that we consider is rather general allowing for supercritical growth in the sense of sobolev embedding the consequent lack of compactness can be overcome by working in the cone of non negative and non decreasing radial functions within this cone we establish some a priori estimates which allow via a truncation argument to use variational methods for proving existence of solutions as a side result we prove a strong maximum principle for nonlocal neumann problems which is of independent interest

the sensitivity of muscle force predictions to changes in physiologic cross sectional area abstract the mechanical effects of a muscle are related in part to the size of the muscle and to its location relative to the joint it crosses for more than a century researchers have expressed muscle size by its physiological cross sectional area pcsa researchers mathematically calculating muscle and joint forces typically use some expression of a muscle s pcsa to constrain the solution to one which is reasonable i e a solution in which small muscles may not have large forces and large muscles have large forces when expected or when there is significant electromyographic activity it is obvious that muscle mass and therefore any expression of pcsa varies significantly from person to person even in individuals of similar weight and height since it is not practical to predict the pcsa of each muscle in a living subject s limb or trunk it is important to generally understand the sensitivity of muscle force solutions to possible variations in pcsa we used nonlinear optimization techniques to predict 47 muscle forces and hip contact forces in a living subject the pcsa volume muscle fiber length of each of 47 lower limb muscle elements from two cadaver specimens and the 47 pcsa s reported by pierrynowski were input into an optimization algorithm to create three solution sets the three solutions were qualitatively similar but at times a predicted muscle force could vary as much as two to eight times in contrast the joint force solutions were within 11 of each other and therefore much less variable when using optimization techniques to predict muscle forces it must be recognized that the solution is sensitive to many assumptions and variables such as pcsa the muscle force solutions are therefore best used to determine relative values i e trends in parametric studies on the other hand the joint force solutions are less sensitive to such variations and the absolute values are more reliable

sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors we assessed and compared sensitivities of dynamic simulations to musculotendon mt parameters for gait and dynamometer experiments our aim with this comparison was to investigate whether dynamometer experiments could provide information about mt parameters that are important to reliably study mt function during gait this would mean that dynamometer experiments could be used to estimate these parameters muscle contribution to the joint torque mt torque rather than relative mt force primarily affects the resulting gait pattern and torque measured by the dynamometer in contrast to recent studies therefore we assessed the sensitivity of the mt torque rather than the sensitivity of the relative mt force based on sensitivity of the mt torque to a parameter perturbation mt parameters of the knee flexors and extensors were classified in three categories low medium and high for gait classification was based on the average sensitivity during a gait cycle for isometric and isokinetic dynamometer experiments classification was based on the highest sensitivity found in the experiments the calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of mt parameters of the knee flexors and extensors suggesting that not all mt parameters need to be estimated in general the highest sensitivity was found for tendon slack length however for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium the classification of the individual mt parameters for gait and dynamometer experiments was largely similar we therefore conclude that dynamometer experiments provide information about mt parameters important to reliably study mt function during gait so that subject specific estimates of mt parameters could be made based on dynamometer experiments

solvability conditions and general solution for mixed sylvester equations in this paper we give some necessary and sufficient solvability conditions for the mixed sylvester matrix equations and parameterize general solution when it is solvable moreover we investigate the maximal and minimal ranks of the general solution and maximal and minimal ranks and inertias of hermitian part of solution respectively

technical communique complete parametric approach for eigenstructure assignment in a class of second order linear systems this note deals with eigenstructure assignment in the second order linear system email protected email protected cq bu using the proportional plus derivative feedback controller u k 0q k email protected under the controllability condition of the matrix pair ab very simple general and complete parametric expressions in direct closed forms for both the closed loop eigenvector matrix and the feedback gains are established in terms of the closed loop eigenvalues and a group of parameter vectors the main computations are two sets of elementary matrix transformations which can be replaced by a series of singular value decompositions when the closed loop eigenvalues are chosen a priori the approach utilizes directly the original system data a b and c and involves manipulations on only n dimensional matrices an example illustrates the effect of the proposed approach

muscle activities of the lower limb during level and uphill running this study aimed to compare the muscle activities of the lower limb during overground level running lr and uphill running ur by using a musculoskeletal model six male distance runners ran at three running speeds slow 3 3 m s medium 4 2 m s and high 5 0 m s on a level runway and a slope of 9 1 grade in which force platforms were mounted a musculoskeletal leg model and optimization were used to estimate the muscle activation and muscle torque from the joint torque of the lower limb calculated by the inverse dynamics approach at high speed the activation and muscle torque of the muscle groups surrounding the hip joints such as the hamstrings and iliopsoas during the recovery phase were significantly greater during ur than during lr at all the running speeds the knee extension torque by the vasti during the support phase was significantly smaller during ur further the hip flexion and knee extension torques by the rectus femoris during ur were significantly greater than those during lr at all the speeds this would play a role in compensating for the decrease in the knee extension torque by the vasti and in maintaining the trunk in a forward leaning position these results revealed that the activation and muscle torque of the hip extensors and flexors were augmented during ur at the high speed

an emg driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo this paper examined if an electromyography emg driven musculoskeletal model of the human knee could be used to predict knee moments calculated using inverse dynamics across a varied range of dynamic contractile conditions muscle tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three dimensional anatomical model of the lower limb muscle activation was determined using a second order discrete non linear model using rectified and lowpass filtered emg as input a modified hill type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs the model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion extension fe muscle moment with those measured by inverse dynamics the model was calibrated for each subject using 5 different tasks including passive and active fe in an isokinetic dynamometer running and cutting manoeuvres recorded using three dimensional motion analysis once calibrated the model was used to predict the fe moments estimated via inverse dynamics from over 200 isokinetic dynamometer running and sidestepping tasks the inverse dynamics joint moments were predicted with an average r 2 of 0 91 and mean residual error of b12 nm a re calibration of only the emg to activation parameters revealed fe moments prediction across weeks of similar accuracy changing the muscle model to one that is more physiologically correct produced better predictions the modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks r 2003 elsevier science ltd all rights reserved

integration by parts formula for regional fractional laplacian we obtain the integration by parts formula for the regional fractional laplacian which are generators of symmetric stable processes on a subset of mathbb r n 0 2 in this formula a local operator appears on the boundary connected with the regional fractional laplacian on domain hence this formula can be understood as the green formula for the regional fractional laplacian the similar integration by parts formula is also given for more general nonlocal operators the reflected stable like processes are studied

effects of hip center location on the moment generating capacity of the muscles we have developed a three dimensional biomechanical model of the human lower extremity to study how the location of the hip center affects the moment generating capacity of four muscle groups the hip abductors adductors flexors and extensors the model computes the maximum isometric force and the resulting joint moments that each of 25 muscle tendon complexes develops at any body position abduction adduction flexion and extension moments calculated with the model correspond closely with isometric joint moments measured during maximum voluntary contractions we used the model to determine 1 the hip center locations that maximize and minimize the moment generating capacity of each muscle group and 2 the effects of superior inferior anterior posterior and medial lateral displacement of the hip center on the moment arms maximum isometric muscle forces and maximum isometric moments generated by each muscle group we found that superior inferior displacement of the hip center has the greatest effect on the force and moment generating capacity of the muscles a 2 cm superior displacement decreases abduction force 44 moment arm 12 and moment 49 while a 2 cm inferior displacement increases abduction force 20 moment arm 7 and moment 26 similarly a 2 cm superior displacement decreases flexion force 27 moment arm 6 and moment 22 while inferior displacement increases all three variables anterior posterior displacement alters the moment generating capacity of the flexors and extensors considerably primarily due to moment arm changes medial lateral displacement has a large effect on the moment generating capacity of the adductors only a 2 cm medial displacement decreases adduction moment arm 20 force 26 and moment 40 these results demonstrate that the force and moment generating capacities of the muscles are sensitive to the location of the hip center

a non invasive protocol to determine the personalized moment arms of knee and ankle muscles one difficulty that comes with predicting muscular forces is the accuracy of experimental data particularly the assessment of muscle moment arms with respect to each joint rotation axis this paper presents a non invasive experimental protocol to obtain the personalized muscle moment arms with respect to the ankle and knee joints a specific pointer is used by a specialist of lower limb anatomy in order to define the local portion of the line of action of the different muscles closed to the joint on the standing subject s lower limb with this pointer the three dimensional coordinates of several points representing the line of action of 12 ankle and knee muscles are collected by a motion analysis system the collection is done five times by the same operator and one time by two different operators from this data the intra and inter operator repeatabilities are tested relative icc and absolute sem reliabilities are determined in order to evaluate the intra operator repeatability of this non invasive protocol the icc values obtained are higher than 0 91 for 10 among 12 muscles the intra operator repeatability is thus confirmed from the records realized by the two operators the differences are negligible thus the inter operator repeatability is also confirmed the moments arms obtained using this non invasive experimental protocol are compared with those calculated from origin and insertion points reported in the literature according to the work of whites pierrynowskis and kepples respectively the estimations obtained using the non invasive experimental protocol are found for some muscles more realistic than those calculated using the literature data and are always coherent with the role of the muscles described in anatomical books

fractional hardy sobolev inequalities on half spaces abstract we investigate the existence of extremals for hardy sobolev inequalities involving the dirichlet fractional laplacian s of order s 0 1 on half spaces

a hopf s lemma and a strong minimum principle for the fractional p laplacian abstract our propose here is to provide a hopf lemma and a strong minimum principle for weak supersolutions of p s u c x u p 2 u in where is an open set of r n s 0 1 p 1 c c and p s is the fractional p laplacian

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

solution to the second order sylvester matrix equation mvf sup 2 dvf kv bw this note provides a complete general parametric solution v w to the generalized second order sylvester matrix equation mvf sup 2 dvf kv bw with f being an arbitrary square matrix the primary feature of this solution is that the matrix f does not need to be in any canonical form or may be even unknown a priori the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems involving second order dynamical systems

whole body reaching movements formulated by minimum muscle tension change criterion it is well known that planar reaching movements of the human shoulder and elbow joints have invariant features roughly straight hand paths and bell shaped velocity profiles the optimal control models with the criteria of smoothness or precision which determine a unique movement pattern predict such features of hand trajectories in this letter on expanding the research on simple arm reaching movements we examine whether the smoothness criteria can be applied to whole body reaching movements with many degrees of freedom determining a suitable joint trajectory in the whole body reaching movement corresponds to the optimization problem with constraints since body balance must be maintained during a motion task first we measured human joint trajectories and ground reaction forces during whole body reaching movements and confirmed that subjects formed similar movements with common characteristics in the trajectories of the hand position and body center of mass second we calculated the optimal trajectories according to the criteria of torque and muscle tension smoothness while the minimum torque change trajectories were not consistent with the experimental data the minimum muscle tension change model was able to predict the stereotyped features of the measured trajectories to explore the dominant effects of the extension from the torque change to the muscle tension change we introduced a weighted torque change cost function considering the maximum voluntary contraction mvc force of the muscle as the weighting factor of each joint torque we formulated the weighted torque change cost as a simplified version of the minimum muscle tension change cost the trajectories owing to the minimum weighted torque change criterion also showed qualitative agreement with the common features of the measured data proper estimation of the mvc forces in the body joints is essential to reproduce human whole body movements according to the minimum muscle tension change criterion

asymptotic analysis of the dirichlet fractional laplacian in domains becoming unbounded abstract in this paper we analyze the asymptotic behaviour of the dirichlet fractional laplacian r n k s with s 0 1 on bounded domains in r n k that become unbounded in the last k directions a dimension reduction phenomenon is observed and described via convergence

green function estimate for censored stable processes sharp two sided estimates for green functions of censored stable process y in a bounded c 1 1 open set d are obtained where 1 2 it is shown that the martin boundary and minimal martin boundary of y can all be identified with the euclidean boundary of d sharp two sided estimates for the martin kernel of y are also derived

sensitivity of predicted muscle forces to parameters of the optimization based human leg model revealed by analytical and numerical analyses there are different opinions in the literature on whether the cost functions the sum of muscle stresses squared and the sum of muscle stresses cubed can reasonably predict muscle forces in humans one potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization based models in this study the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees of freedom dof model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function analytical results revealed that generally the non zero optimal force of each muscle depends in a very complex non linear way on moments at all three joints and moment arms and physiological cross sectional areas pcsas of all muscles deviations of the model parameters moment arms and pcsas from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria but also the number of non zero forces in the optimal solution and the combination of muscles with non zero predicted forces muscle force magnitudes calculated by both criteria were similar they could change several times as model parameters changed whereas patterns of muscle forces were typically not as sensitive it is concluded that different opinions in the literature about the behavior of optimization based models can be potentially explained by differences in employed model parameters

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

solution to matrix equation av bw evf and eigenstructure assignment for descriptor systems a simple complete analytical restriction free parametric solution with complete and explicit freedom of matrix equation av bw evf is presented based on the presented solution of this equation an approach for eigenstructure assignment for continuous descriptor system ex ax bu via descriptor variable feedback u kx is proposed parametric forms of the gain matrix and the eigenvectors associated with the assigned finite closed loop eigenvalues are given the approach is shown to be better than that of fahmy and o reilly 1989 int j contr 49 129 143 in the sense that it not only possesses the functions of the approach of fahmy and o reilly 1989 int j contr 49 129 143 but also has the following three advantages 1 it eliminates the requirements on the assigned finite closed loop poles 2 it provides more design parameters and 3 it needs less computational work

a physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

solutions to a family of matrix equations by using the kronecker matrix polynomials closed form solutions to a family of generalized sylvester matrix equation in form of i 0 fa ixf email protected i 0 jb kyf email protected j 0 fe jrf j are given by using the so called kronecker matrix polynomials it is found that the structure of the solutions is independent of the orders f j and f this type of uniform closed form solutions includes our early results as special cases the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in linear systems

about weight factors in the non linear objective functions used for solving indeterminate problems in biomechanics a lot of non linear objective criteria are applied for solving the indeterminate problems formulated for di erent biomechanical models most of them can be covered by the expression c i dfo i dn it might be noted however that most of the suggested criteria are not applicable if considerable antagonistic co contractions exist this could be an e ect of treating the agonistic muscles and their respective antagonists in one and the same manner in the objective function using a completely inverse approach the muscle forces are supposed to be known quantities and a simple 1dof model actuated by three agonistic muscles and one corresponding antagonist it has been shown which values of the weight factors c i may predict di erent levels of muscle forces from the two antagonistic groups three hypothetical border variants for magnitudes of the muscle forces are considered exor muscles are only active extensor muscles are only active considerable co contraction of exors and extensors exists the main conclusions are the signs of c i at agonistic muscles have to be opposite to the c i signs at their antagonists the signs of the weight factors depend on the direction of the net external joint moment the closer c i to zero the bigger force will be predicted in the ith muscle 1999 elsevier science ltd all rights reserved

biomechanical modeling and optimal control of human posture the present work describes the biomechanical modeling of human postural mechanics in the saggital plane and the use of optimal control to generate open loop raising up movements from a squatting position the biomechanical model comprises 10 equivalent musculotendon actuators based on a 40 muscles model and three links shank thigh and hat head arms and trunk optimal control solutions are achieved through algorithms based on the consistent approximations theory schwartz and polak 1996 where the continuous non linear dynamics is represented in a discrete space by means of a runge kutta integration and the control signals in a spline coefficient functional space this leads to non linear programming problems solved by a sequential quadratic programming sqp method due to the highly non linear and unstable nature of the posture dynamics numerical convergence is difficult and specific strategies must be implemented in order to allow convergence results for control muscular excitations and angular trajectories are shown using two final simulation times as well as specific control strategies are discussed

reflected symmetric α stable processes and regional fractional laplacian in this paper we investigate the reflected symmetric stable processes and their generators we show that the generators are regional fractional laplacians on the closed region in the case of 1 2 their existence requires that open image in new window on the boundary among other things we obtain the integration by parts formula of the regional fractional laplacian and the semi martingale decomposition of the reflected symmetric stable processes

an open source lower limb model hip joint validation musculoskeletal lower limb models have been shown to be able to predict hip contact forces hcfs that are comparable to in vivo measurements obtained from instrumented prostheses however the muscle recruitment predicted by these models does not necessarily compare well to measured electromyographic emg signals in order to verify if it is possible to accurately estimate hcfs from muscle force patterns consistent with emg measurements a lower limb model based on a published anatomical dataset klein horsman et al 2007 clinical biomechanics 22 239 247 has been implemented in the open source software opensim a cycle to cycle hip joint validation was conducted against hcfs recorded during gait and stair climbing trials of four arthroplasty patients bergmann et al 2001 journal of biomechanics 34 859 871 hip joint muscle tensions were estimated by minimizing a polynomial function of the muscle forces the resulting muscle activation patterns obtained by assessing multiple powers of the objective function were compared against emg profiles from the literature calculated hcfs denoted a tendency to monotonically increase their magnitude when raising the power of the objective function the best estimation obtained from muscle forces consistent with experimental emg profiles was found when a quadratic objective function was minimized average overestimation at experimental peak frame 10 1 for walking 7 8 for stair climbing the lower limb model can produce appropriate balanced sets of muscle forces and joint contact forces that can be used in a range of applications requiring accurate quantification of both the developed model is available at the website https simtk org home low limb london

strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions we present some comparison results for solutions to certain non local elliptic and parabolic problems that involve the fractional laplacian operator and mixed boundary conditions given by a zero dirichlet datum on part of the complementary of the domain and zero neumann data on the rest these results represent a non local generalization of a hopf s lemma for elliptic and parabolic problems with mixed conditions in particular we prove the non local version of the results obtained by davila and davila and dupaigne for the classical case s 1 in 23 24 respectively

strong maximum principles for fractional laplacians we give a unified approach to strong maximum principles for a large class of nonlocal operators of order s 0 1 that includes the dirichlet the neumann restricted or regional and the neumann semirestricted laplacians

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

a complete analytical solution to the equation ta ft lc and its applications in this note a complete analytical and restriction free solution with complete and explicit freedom of the matrix equation ta ft lc is proposed here a c is given and is observable and f is in the jordan form with arbitrary given eigenvalues this solution appears to be new because it can be applied directly to obtain significantly better solutions to the following three basic design problems 1 2 d system eigenvalue assignment 2 function observer design and 3 state feedback eigenstructure design as shown in this note

weighted least squares solutions to general coupled sylvester matrix equations this paper is concerned with weighted least squares solutions to general coupled sylvester matrix equations gradient based iterative algorithms are proposed to solve this problem this type of iterative algorithm includes a wide class of iterative algorithms and two special cases of them are studied in detail in this paper necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented sufficient conditions that are easy to compute are also given the optimal step sizes such that the convergence rates of the algorithms which are properly defined in this paper are maximized and established several special cases of the weighted least squares problem such as a least squares solution to the coupled sylvester matrix equations problem solutions to the general coupled sylvester matrix equations problem and a weighted least squares solution to the linear matrix equation problem are simultaneously solved several numerical examples are given to illustrate the effectiveness of the proposed algorithms

moment distribution among human elbow extensor muscles during isometric and submaximal extension to understand better how the central nervous system cns distributes a joint moment among muscles moment distribution among the three heads of the triceps and the anconeus muscles during isometric elbow extension was quantified in vivo and noninvasively electrical stimulation was used to activate an individual muscle selectively at various contraction levels and the relationship between the peak m wave amplitude and peak elbow extension moment was established across various contraction levels for each muscle the relationship was then used to calibrate the corresponding emg signal and determine moment distribution among the muscles during voluntary isometric elbow extension results showed that moment distribution among muscles was not proportional to the muscles physiological cross sectional areas pcsa and the cns favored uniarticular muscles for the isometric task performed the uniarticular lateral and medial heads of the triceps were dominant contributing approximately 70 90 of the total elbow extension moment and the anconeus contributed significantly especially at the lower levels of elbow extension moment up to approximately 15 of the extension moment in contrast the two joint long head of the triceps contributed significantly less than the uniarticular heads of the triceps while the absolute contributions of all the muscles increased with the total elbow extension moment the relative contributions of the muscles may increase or decrease with the elbow extension moment cross validation using fresh data not used in determining the moment distribution showed close match between the measured and predicted elbow extension moment except for trials in which fatigue became significant

extension of a state of the art optimization criterion to predict co contraction most studies concerned with the prediction of muscle forces have tried to predict a physiologically reasonable synergistic muscle behavior in addition to the load sharing of synergistic muscles co contraction of antagonistic muscles also occurs an extension to a standard quadratic criterion for the calculation of muscle forces is presented in this study this extension however is not limited to quadratic optimization the extension is applied to a planar one degree of freedom model of the human knee for this model an analytical solution is presented with the extended criterion it was possible to predict and control the amount of co contraction for the knee model the enforced antagonistic muscle activity led to higher agonistic muscle activity in the absence of an external load flexor and extensor muscles were activated as a consequence the knee joint was preloaded this might indicate that antagonistic muscle activity is generated to maintain or improve joint stability in conclusion this study presents a novel approach to predict co contraction when using optimization techniques to determine muscle forces by introducing a shift parameter for the optimization criterion

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

numerical computation of a coprime factorization of a transfer function matrix abstract a new algorithm is presented for computing a coprime factorization of a transfer function matrix the method is based on reformulating the problem as a problem of constructing a minimal basis of the right nullspace of a matrix pencil b a due to the special structure and rank properties of the pencil obtained after transforming b a to generalized schur form the original problem can be easily solved in a numerically reliable way

individual specific muscle maximum force estimation using ultrasound for ankle joint torque prediction using an emg driven hill type model abstract emg driven models can be used to estimate muscle force in biomechanical systems collected and processed emg readings are used as the input of a dynamic system which is integrated numerically this approach requires the definition of a reasonably large set of parameters some of these vary widely among subjects and slight inaccuracies in such parameters can lead to large model output errors one of these parameters is the maximum voluntary contraction force f om this paper proposes an approach to find f om by estimating muscle physiological cross sectional area pcsa using ultrasound us which is multiplied by a realistic value of maximum muscle specific tension ultrasound is used to measure muscle thickness which allows for the determination of muscle volume through regression equations soleus gastrocnemius medialis and gastrocnemius lateralis pcsas are estimated using published volume proportions among leg muscles which also requires measurements of muscle fiber length and pennation angle by us f om obtained by this approach and from data widely cited in the literature was used to comparatively test a hill type emg driven model of the ankle joint the model uses 3 emgs soleus gastrocnemius medialis and gastrocnemius lateralis as inputs with joint torque as the output the emg signals were obtained in a series of experiments carried out with 8 adult male subjects who performed an isometric contraction protocol consisting of 10 s step contractions at 20 and 60 of the maximum voluntary contraction level isometric torque was simultaneously collected using a dynamometer a statistically significant reduction in the root mean square error was observed when us obtained f om was used as compared to f om from the literature

censored stable processes we present several constructions of a censored stable process in an open set d rn i e a symmetric stable process which is not allowed to jump outside d we address the question of whether the process will approach the boundary of d in a finite time we give sharp conditions for such approach in terms of the stability index and the thickness of the boundary as a corollary new results are obtained concerning besov spaces on non smooth domains including the critical exponent case we also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary we derive a boundary harnack principle in c1 1 open sets

on the generalized sylvester mapping and matrix equations general parametric solution to a family of generalized sylvester matrix equations arising in linear system theory is presented by using the so called generalized sylvester mapping which has some elegant properties the solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution the results provide great convenience to the computation and analysis of the solutions to this family of equations and can perform important functions in many analysis and design problems in linear system theory it is also expected that this so called generalized sylvester mapping tool may have some other applications in control system theory