approximation orders and shape preserving properties of the multiquadric trigonometric b spline quasi interpolant the purpose of the paper is to derive some properties of the multiquadric trigonometric b spline quasi interpolant firstly the paper captures its approximation orders for high order derivatives based on the error estimate one can choose the shape parameter properly such that the quasi interpolant gives optimal approximations to high order derivatives moreover the approximation orders also show that from the theoretical point of view the considered quasi interpolant can be applied when the approximation of high order derivatives is needed i e numerical solution of some pdes construction of lyapunov function etc secondly the paper derives some shape preserving properties of the quasi interpolant these properties suggest that the quasi interpolant may be used in the geometric modeling cad cam for instance that requires shape preservation finally to illustrate the validity of the results some numerical examples are presented both theoretical and numerical results demonstrate that the quasi interpolant cannot only provide excellent approximations to high order derivatives but also preserve the shapes well

properties of symmetric matrices abstract we find the extreme points and the smooth points of the unit ball of the banach space n of all real symmetric n n matrices

curvature characteristics and congruence of the thumb carpometacarpal joint differences between female and male joints abstract three dimensional geometric models of the articular surfaces of the thumb carpometacarpal cmc joint were constructed using precise data obtained from stereophotogrammetry spg it was demonstrated that by using a least squares surface fitting technique the spg data on the surface can accurately be described by a single parametric biquintic spline function from this mathematical description curvature maps of the surfaces were calculated for 13 cmc joints eight females average 64 yr old five males average 70 yr old the surface geometry of each joint was analyzed comparisons were made between trapezial and metacarpal surfaces of the joint and differences determined between males and females with regard to joint surface areas the female trapezium is significantly smaller than that of the metacarpal the shape of the female trapezial surface is also fundamentally different from of males no gender related difference exists regarding the shape of the metacarpal surface congruence of the two opposing articular surfaces was defined by their relative principal curvatures from these definitions congruence in the radioulnar and dorsovolar anatomic directions as well as the global congruence of the joint were calculated most cmc joints were found to be more congruent along the radioulnar direction than the dorsovolar direction and globally female joints were found to be less congruent than male joints the concept of joint congruence has played a central role in a number of hypotheses relating to the etiology of cmc joint osteoarthritis oa although conflicting hypotheses do exist the precise quantitative findings of this study may lead to an improved understanding of cmc joint oa and perhaps explain its prevalence in the female population over 55

semidefinite extreme points of the unit ball in a polynomial space abstract let be the triangle in r 2 bounded by the lines x 0 y 0 x y 1 the standard simplex in r 2 denote by 2 the set of all real bivariate algebraic polynomials of total degree at most two let b be the unit ball of the space 2 endowed with the supremum norm on we give a full description of the semidefinite extreme points of b the present paper completes the description of the set e of all extreme points of b started in milev and naidenov 2008 13 and milev and naidenov 2011 14 we study as an application the path connectedness of e the conclusion is that e 1 consists of two path connected components

on the real polynomial bohnenblust hille inequality abstract it was recently proved by f bayart and the fourth and fifth authors that the complex polynomial bohnenblust hille inequality is subexponential here we show that for real scalars this no longer holds moreover we show among other results that if d r m stands for the real bohnenblust hille constant for m homogeneous polynomials then lim sup m d r m 1 m 2 a quite surprising result having in mind that the exact value of the bohnenblust hille constants is still a mystery

a new model to predict in vivo human knee kinematics under physiological like muscle activation although a number of approaches have attempted to model knee kinematics rarely have they been validated against in vivo data in a larger subject cohort here we assess the feasibility of four bar linkage mechanisms in addressing knee kinematics and propose a new approach that is capable of accounting for lengthening characteristics of the ligaments including possible laxity as well as the internal external rotation of the joint mr scans of the knee joints of 12 healthy volunteers were taken at flexion angles of 0 degrees 30 degrees and 90 degrees under both passive and active muscle conditions by reconstructing the surfaces at each position the accuracy of the four bar linkage mechanism was assessed for every possible combination of points within each cruciate ligament attachment area the specific set of parameters that minimized the deviation between the predictions and the in vivo pose was derived producing a mean error of 1 8 and 2 5 on the medial and 1 7 and 2 4mm on the lateral side at 30 degrees and 90 degrees flexion respectively for passive motion significantly improving on the models that did not consider internal external rotation for active flexion mean medial errors were 3 3 and 4 7 mm and lateral errors 3 4 and 4 8 mm using this best parameter set a generic predictive model was created and assessed against the known in vivo positions producing a maximum average error of 4 9 mm at 90 degrees flexion the accuracy achieved shows that kinematics may be accurately reconstructed for subject specific musculoskeletal models to allow a better understanding of the load distribution within the knee

on the polynomial numerical index of the real spaces c0 l1 and l abstract we give a lower bound for the polynomial numerical index of order k for real lush spaces we use this bound to compute the polynomial numerical index of order 2 of the real spaces c 0 l 1 and l finally we present an example of a real banach space x whose polynomial numerical indices are positive while the ones of its bidual are zero

a generalization of multiple wright convex functions via randomization abstract in the paper we define and study classes w n m j of non negative real functions associated with the classes m j of j times monotone functions these classes are generalizations of n wright convex functions introduced in gilanyi and pales 2008 2 and studied by maksa and pales 2009 6 we prove that each function from w n m j can be represented as a series of functions generated by a function from m j we give an integral representation of these functions in the case when a random variable has an exponential or a discrete arithmetic distribution as a consequence we show that for an arithmetic discrete n 1 w n m j m and that when the is exponential we have equality in the above formula

effects of variation on extensor elements and operative procedures in patellofemoral disorders the influence of both insertion and strength elasticity of each extensor in patellofemoral disorders was fully investigated through a two dimensional mathematical model analysis in a horizontal plane in combination with experimental design theory for analyzing mutually correlated influences in the model patellofemoral joint profiles projected on a horizontal plane have been expressed as spline functions each muscle of the quadriceps has been represented as a string pulled by the respective force fascias and tendons have been represented by springs nonlinear equations have been constructed to represent the forces involved and then solved by numerical iteration an analysis of variance was performed on the data derived from a series of simulations obtaining the following results the strength of most extensors has been shown to have an influence on the increase in lateral contact force but not patellar translation the tibial tubercle position has significant influence on both patellar translation and lateral contact force the quadriceps insertion on the femur has no influence on patellar translation the insertion of each extensor on the patella has been shown to have a strong effect on patellar translation but not on contact force

geometry of 2 homogeneous polynomials on lp spaces 1 p abstract we characterise extreme 2 homogeneous polynomials of diagonal form on l p with p 2 and give a class of examples of smooth points we describe the unit ball of p 2 l p 2 for both the cases p 2 and p we apply the results thus found to study the geometry of the predual of p 2 l p 2 and to show that for p 2 an extreme 2 homogeneous polynomial on l p 2 remains extreme when regarded as a polynomial on l p

the accuracy of joint surface models constructed from data obtained with an electromagnetic tracking device electromagnetic tracking devices are widely used in biomechanics in this article a method is evaluated to construct models of articular surfaces using an electromagnetic tracking device first the accuracy of the space tracker was examined and optimised then from several joint surfaces random points were measured and eighth degree polynomials were fitted to these measurements to check if the fit converged well plots of cross sections of the model with corresponding data points were examined the accuracy of the models was determined by comparing them with computed tomography data and by reproducibility tests all the fits converged well to the data the root mean square rms error of the models varied from 0 07 to 0 18mm and was proportional to the size and complexity of the surface this was mainly due to systematic errors made by the space tracker which were also proportional to the size and complexity of the surface

strongly convex functions of higher order abstract the notion of strongly n convex functions with modulus c 0 is introduced and investigated relationships between such functions and n convex functions in the sense of popoviciu as well as generalized convex functions in the sense of beckenbach are given characterizations by derivatives are presented some results on strongly jensen n convex functions are also given

norm or numerical radius attaining polynomials on c k abstract let c k c be the banach space of all complex valued continuous functions on a compact hausdorff space k we study when the following statement holds every norm attaining n homogeneous complex polynomial on c k c attains its norm at extreme points we prove that this property is true whenever k is a compact hausdorff space of dimension less than or equal to one in the case of a compact metric space a characterization is obtained as a consequence we show that for a scattered compact hausdorff space k every continuous n homogeneous complex polynomial on c k c can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the unit ball of c k c is a norming set for every continuous complex polynomial similar results can be obtained if norm is replaced by numerical radius

knee model sensitivity to cruciate ligaments parameters a stability simulation study for a living subject abstract if the biomechanic function of the different anatomical sub structures of the knee joint was needed in physiological conditions the only possible way is a modelling approach subject specific geometries and kinematic data acquired from the same living subject were the foundations of the 3d quasi static knee model developed each cruciate ligament was modelled by means of 25 elastic springs paying attention to the anatomical twisting of the fibres the sensitivity of the model to the cross sectional area was performed during the anterior posterior tibial translations the sensitivity to all the cruciate ligaments parameters was performed during the internal external rotations the model reproduced very well the mechanical behaviour reported in literature during anterior posterior translations in particular considering 30 of the mean insertional area during the internal external tibial rotations similar behaviour of the axial torques was obtained in the three sensitivity analyses the overlapping of the ligaments was assessed at about 25 of internal axial rotation the presented model featured a good level of accuracy in combination with a low computational weight and it could provide an in vivo estimation of the role of the cruciate ligaments during the execution of daily living activities

geometry of three homogeneous polynomials on real hilbert spaces let h be a two dimensional real hilbert space we give a characterisation of the extreme and the smooth points of the unit ball of the space of three homogeneous polynomials on h in terms of the coefficients of the polynomial we also determine the smooth points of the unit ball of the predual of the space of three homogeneous polynomials

support type properties of convex functions of higher order and hadamard type inequalities abstract it is well known that every convex function f i r where i r is an interval admits an affine support at every interior point of i i e for any x 0 int i there exists an affine function a i r such that a x 0 f x 0 and a f on i convex functions of higher order precisely of an odd order have a similar property they are supported by the polynomials of degree no greater than the order of convexity in this paper the attaching method is developed it is applied to obtain the general result theorem 2 from which the mentioned above support theorem and some related properties of convex functions of higher both odd and even order are derived they are applied to obtain some known and new hadamard type inequalities between the quadrature operators and the integral approximated by them it is also shown that the error bounds of quadrature rules follow by inequalities of this kind

a stereophotogrammetric method for measurements of ligament structure a stereophotogrammetric method is presented to reconstruct the course of a curve in the three dimensional space this method is exclusively suitable as a non destructive tool to determine the surface fiber structure of ligaments tendons and other organised collagenous structures in addition it is a convenient tool to measure the geometry of articular surfaces and other complicated surface shapes

the bishop phelps bollobas theorem fails for bilinear forms on l1 l1 abstract in this paper we show that the bishop phelps bollobas theorem fails for bilinear forms on l 1 l 1 while it holds for linear operators from l 1 to l

inverses depending holomorphically on a parameter in a banach space abstract we show that the existence of a right inverse at each point for a holomorphic mapping from a pseudo convex domain in a banach space with an unconditional basis into a unital banach algebra implies the existence of a holomorphic right inverse variations of this result are given

geometry of banach spaces of trinomials abstract for each pair of numbers m n n with m n we consider the norm on r 3 given by a b c m n sup a x m b x n c x 1 1 for every a b c r 3 we investigate some geometrical properties of these norms we provide an explicit formula for m n a full description of the extreme points of the corresponding unit balls and a parametrization and a plot of their unit spheres

a new approach for surface fitting method of articular joint surfaces the application of joint contact mechanics requires a precise configuration of the joint surfaces b spline and nurbs have been widely used to model joint surfaces but because these formulations use a structured data set provided by a rectangular net first then a grid there is a limit to the accuracy of the models they can produce however new imaging systems such as 3d laser scanners can provide more realistic unstructured data sets what is needed is a method to manipulate the unstructured data we created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces we applied our polynomial model to unstructured data sets from an artificial joint and confirmed that our polynomial produced a smoother and more accurate model than the conventional b spline method next we applied it to a diarthrodial joint surface containing many ripples and found that our function s noise filtering characteristics smoothed out existing ripples since no formulation was found to be optimal for all applications we used two formulations to model surfaces with ripples first we used our polynomial to describe the global shape of the objective surface minute undulations were then specifically approximated with a fourier series function finally both approximated surfaces were superimposed to reproduce the original surface in a complete fashion

a lindenstrauss theorem for some classes of multilinear mappings abstract under some natural hypotheses we show that if a multilinear mapping belongs to some banach multilinear ideal then it can be approximated by multilinear mappings belonging to the same ideal all whose arens extensions attain their norms at the same point we prove a similar result for the class of symmetric multilinear mappings we see that the quantitative bollobas type version of these results fails in every multilinear ideal

on the classes of higher order jensen convex functions and wright convex functions ii abstract the classes of n wright convex functions and n jensen convex functions are compared with each other it is shown that for any odd natural number n the first one is the proper subclass of the second one to reach this aim new tools connected with measure theory are developed

on algebras of holomorphic functions of a given type we show that several spaces of holomorphic functions on a riemann domain over a banach space including the nuclear and hilbert schmidt bounded type are locally m convex frechet algebras we prove that the spectrum of these algebras has a natural analytic structure which we use to characterize the envelope of holomorphy we also show a cartan thullen type theorem

multilinear forms subsymmetric polynomials and spreading models on banach spaces abstract some applications of ramsey theory to the study of multilinear forms and polynomials on banach spaces are given related to the existence of lower l q estimates of sequences we give an explicit representation of subsymmetric polynomials in banach spaces with subsymmetric basis finally we apply our results to get approximation of polynomials by subsymmetric polynomials and to the problem of stabilization of a certain chain of algebras generated by polynomials

simultaneously continuous retraction and bishop phelps bollobas type theorem abstract the dual space x of a banach space x is said to admit a uniformly simultaneously continuous retraction if there is a retraction r from x onto its unit ball b x which is uniformly continuous in norm topology and continuous in weak topology we prove that if a banach space resp complex banach space x has a normalized unconditional schauder basis with unconditional basis constant 1 and if x is uniformly monotone resp uniformly complex convex then x admits a uniformly simultaneously continuous retraction it is also shown that x admits such a retraction if x x i c 0 or x x i l 1 where x i is a family of separable banach spaces whose duals are uniformly convex with moduli of convexity i e with inf i i e 0 for all 0 e 1 let k be a locally compact hausdorff space and let c 0 k be the real banach space consisting of all real valued continuous functions vanishing at infinity as an application of simultaneously continuous retractions we show that a pair x c 0 k has the bishop phelps bollobas property for operators if x admits a uniformly simultaneously continuous retraction as a corollary c 0 s c 0 k has the bishop phelps bollobas property for operators for every locally compact metric space s

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

the finite helical axis of the knee joint a non invasive in vivo study using fast pc mri an understanding of the in vivo knee joint kinematics is critical for the further improvement and validation of knee joint models and for the development of better surgical and rehabilitative protocols unfortunately most studies exploring the finite helical axis fha tend to produce excellent qualitative results but quantitative results are often lacking thus the purpose of this study was to non invasively and in vivo quantify the tibiofemoral fha in a relatively large normal population during volitional knee extension using fast pc mri to report the data relative to consistent coordinate systems making it available for modeling input experimental comparison and for device design to determine the variability of the fha to investigate the screw home mechanism and to test the hypothesis that knee joint kinematics are independent of gender intra and inter subject repeatability was excellent the intra inter subject repeatability of the fha orientation in the frontal and axial planes was 1 8 3 3 and 3 7 6 0 of the average value respectively at the beginning of extension the fha was directed laterally and slightly superiorly and at the end of extension it was directed in the lateral inferior direction indicative of the screw home mechanism the fha location was not fixed during extension there was small but significant differences in all fha parameters between genders and normalizing positional data relative to epicondylar width helped to reduce this difference the data obtained in the current study forms an excellent base for future knee joint modeling and clinical studies

extreme polynomials and multilinear forms onl1 abstract given a 2 homogeneous polynomialp x y ax2 by2 cxywith real coefficients let p rand p cdenote the norms ofpon the real and complex banach spacel21 respectively we show p r p c and obtain a sufficient and necessary condition on the coefficientsa b andcforpto have norm 1 applying these results we characterize extreme points of the unit ball of p 2l1 for the real banach spacel21and examine them for the complex banach spacel21 we apply them to find extreme points and strongly extreme points of the unit ball of p 2l1 and get an extremal 2 homogeneous polynomial onl1that is not an extreme point we also characterize extreme points and strongly extreme points of the unit ball of l ml1 or l ml1 0 1

three dimensional mathematical model analysis of the patellofemoral joint this paper is concerned with a mathematical model analysis of the patellofemoral joint in the human knee taking into account the articular surface geometry and mechanical properties of the ligament it was made by the application of a computer aided design theory previously studied and it was possible to express the articular surface geometries in a mathematical formulation and hence elucidate the joint movement mechanics this method was then applied to a three dimensional geometrical model of the patellofemoral joint for the modelling of tendofemoral contact at large angles of knee flexion the geodestic line theory was adopted applying the newton raphson method and the runge kutta gil method to the model variables such as patellar attitudes patellofemoral contact force and tensile force of the patellar ligament for various knee flexion angles were computed applying the hertzian elastic theory contact stress was also computed these results showed good agreement with the previously reported experimental results as an application for the model some parameter analyses were performed in terms of the contact stress variations and compared with those of the normal knee the simulation results indicated that both the q angle increase and decrease increased contact stress the patella alta showed undulating variations of stress while the patella infera showed little change of stress and the tibial tuberositas elevation showed 20 30 reduction of stress

on the polynomial lindenstrauss theorem abstract under certain hypotheses on the banach space x we show that the set of n homogeneous polynomials from x to any dual space whose aron berner extensions are norm attaining is dense in the space of all continuous n homogeneous polynomials to this end we prove an integral formula for the duality between tensor products and polynomials we also exhibit examples of lorentz sequence spaces for which there is no polynomial bishop phelps theorem but our results apply finally we address quantitative versions in the sense of bollobas of these results

holomorphic mappings on we describe the holomorphic mappings of bounded type and the arbitrary holomorphic mappings from the complex banach space 11 into a complex banach space x it is shown that these mappings have monomial expansions and the growth of the norms of the coefficients is characterized in each case this characterization is used to give new descriptions of the compact open topology and the nachbin ported topology on the space a 11 x of holomorphic mappings and to prove a lifting property for holomorphic mappings on 11 we also show that the monomials form an equicontinuous unconditional schauder basis for the space 11 so of holomorphic functions on 11 with the topology of uniform convergence on compact sets

symmetric multilinear forms on hilbert spaces where do they attain their norm abstract we characterize the sets of norm one vectors x 1 x k in a hilbert space h such that there exists a k linear symmetric form attaining its norm at x 1 x k we prove that in the bilinear case any two vectors satisfy this property however for k 3 only collinear vectors satisfy this property in the complex case while in the real case this is equivalent to x 1 x k spanning a subspace of dimension at most 2 we use these results to obtain some applications to symmetric multilinear forms symmetric tensor products and the exposed points of the unit ball of l s h k

the unit ball of the complex mathcal p 3h let h be a two dimensional complex hilbert space and mathcal p 3h the space of 3 homogeneous polynomials on h we give a characterization of the extreme points of its unit ball mathsf b mathcal p 3h from which we deduce that the unit sphere of mathcal p 3h is the disjoint union of the sets of its extreme and smooth points we also show that an extreme point of mathsf b mathcal p 3h remains extreme as considered as an element of mathsf b mathcal l 3h finally we make a few remarks about the geometry of the unit ball of the predual of mathcal p 3h and give a characterization of its smooth points

validation of a three dimensional model of the knee three dimensional mathematical models of the tibio femoral joint require input of the geometry of articulating surfaces and ligament insertions and the mechanical properties of cartilage and ligaments this paper describes a validation of a knee model through a direct specimen related comparison between the knee model and the kinematics of four knee joint specimens from which the geometry data were used as input of the model the knee model is quasi static and is based on equilibrium of forces and moments the stiffness properties of the ligaments and articular cartilage were estimated on the basis of data reported in the literature the so called reference strains in the ligament bundles for the joint in extension were determined by using an optimization procedure minimizing the difference between the kinematics of the model and the kinematics of experimentally obtained flexion motions with an internally or an externally rotated tibia f 3 nm load a reasonable to good agreement between the model and the experimental kinematics could be obtained for internal external rotation laxity and the coupled translations and varu valgus rotation the disparity between model and experiment varied from knee to knee average deviations ranging from close to zero to 8 internal rotation deviation and from 5 mm posterior to 3 mm anterior position deviation the average anterior posterior laxities at both 20 and 90 flexion were within the variations reported in the literature although for each individual joint with some underestimation or overestimation it was concluded that the optimization procedure compensated for the lack of menisci and capsular structures by higher prestrains thereby overestimating the ligament forces despite the gross simplifica tions relative to the complex anatomy of the knee the present knee model can realistically simulate the passive motion characteristics of the human knee joint copyright 0 1996 elsevier science ltd

new integral representations of nth order convex functions in this paper we give an integral representation of an n convex function f in general case without additional assumptions on function f we prove that any n convex function can be represented as a sum of two n 1 times monotone functions and a polynomial of degree at most n we obtain a decomposition of n wright convex functions which generalizes and complements results of maksa and pales 2009 13 we define and study relative n convexity of n convex functions we introduce a measure of n convexity of f we give a characterization of relative n convexity in terms of this measure as well as in terms of nth order distributional derivatives and radon nikodym derivatives we define study and give a characterization of strong n convexity of an n convex function f in terms of its derivative f n 1 x which exists a e without additional assumptions on differentiability of f we prove that for any two n convex functions f and g such that f is n convex with respect to g the function g is the support for the function f in the sense introduced by w sowicz 2007 29 up to polynomial of degree at most n

the hermite hadamard inequality in beckenbach s setting abstract the classical hermite hadamard inequality gives a lower and an upper estimations for the integral average of convex functions defined on compact intervals involving the midpoint and the endpoints of the domain the aim of the present paper is to extend this inequality and to give analogous results when the convexity notion is induced by beckenbach families the key tool of the investigations is based on some general support theorems that are obtained via the pure geometric properties of beckenbach families and can be considered as generalizations of classical support and chord properties of ordinary convex functions the markov krein type representation of beckenbach families is also investigated

fitting parametrized polynomials with scattered surface data currently used joint surface models require the measurements to be structured according to a grid with the currently available tracking devices a large quantity of unstructured surface points can be measured in a relatively short time in this paper a method is presented to fit polynomial functions to three dimensional unstructured data points to test the method spherical cylindrical parabolic hyperbolic exponential logarithmic and sellar surfaces with different undulations were used the resulting polynomials were compared with the original shapes the results show that even complex joint surfaces can be modelled with polynomial functions in addition the influence of noise and the number of data points was also analyzed from a surface diam 20 mm which is measured with a precision of 0 2 mm a model can be constructed with a precision of 0 02 mm

on the bishop phelps bollobas theorem for multilinear mappings abstract we study the bishop phelps bollobas property and the bishop phelps bollobas property for numerical radius our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases we characterize the pair l 1 x y to have the bpbp for bilinear forms and prove that on l 1 the numerical radius and the norm of a multilinear mapping are the same we also show that l 1 fails the bpbp nu for multilinear mappings although l 1 satisfies it in the operator case for every measure

reinhardt domains of holomorphy in banach spaces abstract it is known that in c 0 the holomorphic functions representable by multiple power series the series of monomials are those of nuclear type in this article we show that in a banach space with unconditional schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and in fact the domain of convergence of such a series

factorization of holomorphic mappings in infinite dimensions this note is concerned with a generalization of the first identity to the non linear setting of holomorphic i e complex analytic functions on e in fact our interest in this generalization arose from a study made by the second author 15 of a suitable generalization of the second identity to the holomorphic setting however our results and methods have little in common with 15 in somewhat simplistic terms our results provide further evidence that in many situations one is justified in regarding the space h e of holomorphic functions on e as the holomorphic dual of e which shares many properties with the standard linear dual of e see for example 6 a brief outline of this paper follows after which we recall some basic results about holomorphic mappings between infinite dimensional locally convex spaces in section 2 we investigate when a holomorphic function f u c on a balanced open subset u of e admits a factorization through u a characterization of factorizable functions is given in terms of the derivative o f f our basic technique is

the effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions although variability in connective tissue parameters is widely reported and recognized systematic examination of the effect of such parametric uncertainties on predictions derived from a full anatomical joint model is lacking as such a sensitivity analysis was performed to consider the behavior of a three dimensional non linear finite element knee model with connective tissue material parameters that varied within a given interval the model included the coupled mechanics of the tibio femoral and patello femoral degrees of freedom seven primary connective tissues modeled as non linear continua articular cartilages described by a linear elastic model and menisci modeled as transverse isotropic elastic materials were included in this study a multi factorial global sensitivity analysis is proposed which can detect the contribution of influential material parameters while maintaining the potential effect of parametric interactions to illustrate the effect of material uncertainties on model predictions exemplar loading conditions reported in a number of isolated experimental paradigms were used our findings illustrated that the inclusion of material uncertainties in a coupled tibio femoral and patello femoral model reveals biomechanical interactions that otherwise would remain unknown for example our analysis revealed that the effect of anterior cruciate ligament parameter variations on the patello femoral kinematic and kinetic response sensitivities was significantly larger over a range of flexion angles when compared to variations associated with material parameters of tissues intrinsic to the patello femoral joint we argue that the systematic sensitivity framework presented herein will help identify key material uncertainties that merit further research and provide insight on those uncertainties that may not be as relative to a given response

the dolbeault complex in infinite dimensions i infinite dimensional complex analysis was a popular subject in the sixties and seventies but in the last fifteen years enjoyed much less attention oddly enough this very same period began to see the emergence of examples of infinite dimensional complex manifolds in mathematical physics representation theory and geometry thus it appears to be a worthwhile undertaking to revisit infinite dimensional complex analysis and in particular to clarify fundamental properties of infinite dimensional complex manifolds the most fundamental questions at this point seem to be related to the solvability of the inhomogeneous cauchy riemann or 0 equations and more generally to the study of the dolbeault complex as an example in le3 we use a result on the a equation to describe the virasoro group as an infinite dimensional complex manifold up to now precious little has been known about the solvability of the infinite dimensional equation the available results pertain to solving the equation in domains in or over locally convex topological vector spaces and almost exclusively on the level of 0 1 forms postponing the precise definitions to sections 1 2 below we discuss those results that are of immediate relevance to this paper see d2 for more in li ligocka observes that h6rmander s proof of ehrenpreis theorem see e hor can be extended to infinite dimensions to solve the equation

use of distraction loading to estimate subject specific knee ligament slack lengths abstract knee ligaments guide and restrain joint motion and their properties influence joint mechanics inverse modeling schemes have been used to estimate specimen specific ligament properties where external joint forces are assumed to balance with internal ligament and contact forces this study simplifies this assumption by adjusting experimental loads to remove internal contact forces the purpose of this study was to use novel experimental loading in an inverse modeling scheme to estimate ligament slack lengths perform validation using additional loading scenarios and evaluate sensitivity to the applied loading joint kinematics and kinetics were experimentally measured for a set of load cases an optimization scheme used a specimen specific forward kinematics model to estimate ligament slack lengths by minimizing the residual between model and experimentally measured kinetics the calibrated model was used for a form of validation by evaluating non optimized load cases additionally uncertainty analysis related kinetic errors to previously reported kinematic errors the six dof tibial reactions realized rms errors less than 23 n and 0 75 nm for optimized load cases and 33 n and 2 25 nm for the non optimized load cases the uncertainty analysis which was performed using the optimized load cases showed average kinetic rms errors less than 26 n and 0 45 nm the model s recruitment patterns were similar to those found in clinical and cadaveric studies this study demonstrated that experimental distraction loading can be used in an inverse modeling scheme to estimate ligament slack lengths with a forward kinematics model

design optimization of a total knee replacement for improved constraint and flexion kinematics total knee replacement tkr constraint and flexion range of motion can be limiting factors in terms of kinematics performance and cause for revision these characteristics are closely related to the shape of the implant components no previous studies have used a rigorous and systematic design optimization method to determine the optimal shape of tkr components previous studies have failed to define a quantifiable objective function for optimization have not used any optimization algorithms and have only considered a limited design space 4 or less design variables this study addresses these limitations and determines the optimum shape of the femoral component and ultra high molecular weight polyethylene uhmwpe insert in terms of kinematics the constraint characteristics with respect to those of the natural knee the importance of the posterior cruciate ligament and the flexion range of motion were all considered the kinematics optimized design featured small femoral radii of curvature in the frontal and sagittal planes but asymmetric with slightly larger radii of curvature for the lateral condyle this condyle was also less conforming than the medial side compared to a commercially available tkr design the kinematics performance based on constraint and flexion range of motion was improved by 81 with constraint characteristics generally closer to those of the natural knee and a 12 6 increase in the flexion range of motion up to 143 the results yielded a new tkr design while demonstrating the feasibility of design optimization in tkr design

the bishop phelps bollobas theorem for operators on l1 μ in this paper we show that the bishop phelps bollobas theorem holds for l l1 l1 for all measures and and also holds for l l1 l for every arbitrary measure and every localizable measure finally we show that the bishop phelps bollobas theorem holds for two classes of bounded linear operators from a real l1 into a real c k if is a finite measure and k is a compact hausdorff space in particular one of the classes includes all bochner representable operators and all weakly compact operators

complemented subspaces of spaces of multilinear forms and tensor products abstract among other things we show that l q is isomorphic to a complemented subspace of the space of multilinear forms on l p 1 l p n where q 1 is given by 1 p 1 1 p n 1 q 1 the proof strongly depends on the l module structure of the spaces l p

support type properties of generalized convex functions chebyshev systems induce in a natural way a concept of convexity the functions convex in this sense behave in many aspects similarly to ordinary convex functions in this paper support type properties are investigated using osculatory interpolation the existence of support like functions is established for functions convex with respect to chebyshev systems unique supports are determined a characterization of the generalized convexity via support properties is presented

bishop phelps bollobas property for bilinear forms on spaces of continuous functions it is shown that the bishop phelps bollobas theorem holds for bilinear forms on the complex c 0 l 1 times c 0 l 2 for arbitrary locally compact topological hausdorff spaces l 1 and l 2

norm attaining bilinear forms onl1 0 1 abstract we show that the set of norm attaining bilinear forms onl1 0 1 is not dense in the space of all continuous bilinear forms

decomposition of higher order wright convex functions in this paper we consider higher order wright convex functions and prove that they are representable as the sum of a continuous higher order convex function and a polynomial function

equivalent norms in polynomial spaces and applications abstract in this paper equivalence constants between various polynomial norms are calculated as an application we also obtain sharp values of the hardy littlewood constants for 2 homogeneous polynomials on l p 2 spaces 2 p we also provide lower estimates for the hardy littlewood constants for polynomials of higher degrees

bases in spaces of multilinear forms over banach spaces fil dimant veronica universidad de san andres departamento de matematica y ciencias argentina

a multilinear lindenstrauss theorem abstract we show that the set of n linear mappings on a product of n banach spaces such that all their arens extensions attain their norms at the same element is norm dense in the space of all bounded n linear mappings