a new class of gaussian quadrature formulas based on birkhoff type data we shall show that quadrature formulas of double precision also using evaluation functionals of derivatives of the function instead of evaluation functionals of the function only exist if the order of the derivatives is prescribed in the form of a certain pyramidal display this type of gaussian formulas is derived through an extremal property of certain polynomials extending the extremal property of the classical gaussian formulas the results generalize to the multiple node case

a new family of extended gauss quadratures with an interior interval constraint starting from two sequences ga c n and gd b n of ordinary gauss quadrature formulae with an orthogonality measure d on the open intervals a c and d b respectively we construct a new sequence ga b e n of extended gaussian quadrature formulae for d on a b which is based on some preassigned points the nodes of ga c n gd b n and the e n zeros contained in c d of a nonclassical orthogonal polynomial on a b with respect to a linear functional the principal result gives explicit formulae relating these polynomials and shows how their recurrence coefficients in the three term recurrence formulae are related thus a new class of gaussian quadratures having some nodes contained in a given interior interval can be computed directly by standard software for ordinary gauss quadrature formulae

existence and concentration of positive solutions for a system of coupled saturable schrodinger equations abstract it is considered a saturable system of coupled schrodinger equations with asymptotically linear nonlinearities the bound states solutions with finite energy are proved to exist and have a concentration behavior under hypotheses involving the coupling and saturation parameters the proof is based on variational methods

some perspectives on the eigenvalue problem this expository paper explores the relationships among a number of algorithms for solving eigenvalue problems including the power method subspace iteration the qr algorithm and the arnoldi and symmetric lanczos algorithms the symmetric lanczos algorithm is shown to be identical to the three term recursion stieltjes procedure for computing orthogonal polynomials with respect to a measure on the real line the connection between measures on the line and symmetric tridiagonal jacobi matrices is investigated if such a matrix is transformed by a step of the qr algorithm there is a corresponding transformation in the measure the tridiagonal matrices are also exploited for the construction of gaussian quadrature formulas for measures on the line the developments on the real line are replicated with suitable modifications on the unit circle via lanczos like procedures for unitary operators the best known procedure of this type is the recursion of szego for computing orthogonal polynomials on the

a well conditioned collocation method using a pseudospectral integration matrix in this paper a well conditioned collocation method is constructed for solving general p th order linear differential equations with various types of boundary conditions based on a suitable birkhoff interpolation we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features the condition number of the linear system is independent of the number of collocation points and the underlying boundary conditions are imposed exactly moreover the new basis leads to an exact inverse of the pseudospectral differentiation matrix of the highest derivative at interior collocation points which is therefore called the pseudospectral integration matrix psim we show that psim produces the optimal integration preconditioner and stable collocation solutions with even thousands of points

apparent mass of the human body in the vertical direction inter subject variability abstract the biodynamic responses of the seated human body to whole body vibration vary considerably between people but the reasons for the variability are not well understood this study was designed to determine how the physical characteristics of people affect their apparent mass and whether inter subject variability is influenced by the magnitude of vibration and the support of a seat backrest the vertical apparent masses of 80 seated adults 41 males and 39 females aged 18 65 were measured at frequencies between 0 6 and 20 hz with four backrest conditions no backrest upright rigid backrest reclined rigid backrest reclined foam backrest and with three magnitudes of random vibration 0 5 1 0 and 1 5 m s 2 rms relationships between subject physical characteristics age gender weight and anthropometry and subject apparent mass were investigated with multiple regression models the strongest predictor of the modulus of the vertical apparent mass at 0 6 hz at resonance and at 12 hz was body weight with other factors having only a marginal effect after correction for other variables the principal resonance frequency was most consistently associated with age and body mass index as age increased from 18 to 65 years the resonance frequency increased by up to 1 7 hz and when the body mass index was increased from 18 to 34 kg m 2 the resonance frequency decreased by up to 1 7 hz these changes were greater than the 0 9 hz increase in resonance frequency between sitting without a backrest and sitting with a reclined rigid backrest and greater than the 1 0 hz reduction in resonance frequency when the magnitude of vibration increased from 0 5 to 1 5 m s 2 rms it is concluded that the effects of age body mass index posture vibration magnitude and weight should be taken into account when defining the vertical apparent mass of the seated human body

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

symmetric and arbitrarily high order birkhoff hermite time integrators and their long time behaviour for solving nonlinear klein gordon equations abstract the klein gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering its computation represents a major challenge the main theme of this paper is the construction of symmetric and arbitrarily high order time integrators for the nonlinear klein gordon equation by integrating birkhoff hermite interpolation polynomials to this end under the assumption of periodic boundary conditions we begin with the formulation of the nonlinear klein gordon equation as an abstract second order ordinary differential equation ode and its operator variation of constants formula we then derive a symmetric and arbitrarily high order birkhoff hermite time integration formula for the nonlinear abstract ode accordingly the stability convergence and long time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi definite matrix subject to suitable temporal and spatial smoothness a remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for pdes in the literature numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches

calculation of gauss quadratures with multiple free and fixed knots algorithms are derived for the evaluation of gauss knots in the presence of fixed knots by modification of the jacobi matrix for the weight function of the integral simple gauss knots are obtained as eigenvalues of symmetric tridiagonal matrices and a rapidly converging simple iterative process based on the merging of free and fixed knots of quadratic convergence is presented for multiple gauss knots the procedures also allow for the evaluation of the weights of the quadrature corresponding to the simple gauss knots a new characterization of simple gauss knots as a solution of a partial inverse eigenvalue problem is derived

existence and concentration of ground states for saturable nonlinear schrodinger equations with intensity functions in r2 abstract in this paper we study the existence and concentration behavior of semiclassical ground states for a class of saturable nonlinear schrodinger equations with intensity functions in r 2 0 1 e 2 v i x v 2 1 i x v 2 v v for x r 2 we show that for sufficiently negatively large coupling constant and sufficiently small e there exists a family of normalized ground states i e with the l 2 constraint of the problem we prove that the family of solutions concentrate around the maxima of the intensity function as e 0 our method is variational and depends upon a convexity technique together with the concentration compactness method

theoretical foundation methods and criteria for calibrating human vibration models using frequency response functions while simulations of the measured biodynamic responses of the whole human body or body segments to vibration are conventionally interpreted as summaries of biodynamic measurements and the resulting models are considered quantitative this study looked at these simulations from a different angle model calibration the specific aims of this study are to review and clarify the theoretical basis for model calibration to help formulate the criteria for calibration validation and to help appropriately select and apply calibration methods in addition to established vibration theory a novel theorem of mechanical vibration is also used to enhance the understanding of the mathematical and physical principles of the calibration based on this enhanced understanding a set of criteria was proposed and used to systematically examine the calibration methods besides theoretical analyses a numerical testing method is also used in the examination this study identified the basic requirements for each calibration method to obtain a unique calibration solution this study also confirmed that the solution becomes more robust if more than sufficient calibration references are provided practically however as more references are used more inconsistencies can arise among the measured data for representing the biodynamic properties to help account for the relative reliabilities of the references a baseline weighting scheme is proposed the analyses suggest that the best choice of calibration method depends on the modeling purpose the model structure and the availability and reliability of representative reference data

definition of a range of idealized values to characterize seated body biodynamic response under vertical vibration while a considerable quantity of data has been published on driving point mechanical impedance apparent mass and seat to head transmissibility magnitude and phase characteristics of seated subjects under vertical whole body vibration significant variation is known to exist between various data sets such variations may be partly attributed to differences associated with the methodology experimental conditions or subject population used by various investigators to determine the biodynamic response characteristics as part of this study various published data sets on driving point mechanical impedance apparent mass and seat to head transmissibility are identified for which the experimental conditions are reported to fall within a prescribed range of conditions for subjects maintaining an erect seated posture without backrest support while the feet are supported on a vibrating platform only those data sets are considered for which the magnitude of vertical sine and or random excitation is reported to have been maintained below 5 m s 2 a further screening of the data sets defining the magnitude and phase responses of each function is performed by eliminating all data representing outliers in the 0 5 20 hz frequency range on that basis mean and envelopes of the magnitude and phase responses associated with each function are derived in the 0 5 20 hz frequency range representing the most probable values likely applicable under the predefined range of conditions the resulting range of idealized values on the magnitude and phase responses are based on 8 and 7 data sets respectively for driving point mechanical impedance and apparent mass while only 4 and 3 data sets respectively were left to define the seat to head transmissibility magnitude and phase

singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities abstract we consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities the dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect we investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function necessary conditions to locate the possible concentration points are also given

seated occupant apparent mass characteristics under automotive postures and vertical vibration abstract the biodynamic apparent mass response characteristics of 24 human subjects 12 males and 12 females seated under representative automotive postures with hands in lap passengers and hands on steering wheel drivers are reported the measurements were carried out under white noise vertical excitations of 0 25 0 5 and 1 0m s2r m s acceleration magnitudes in the 0 5 40hz frequency range and a track measured input 1 07m s2 the measured data have been analyzed to study the effects of hands position body mass magnitude and type of vibration excitation and feet position on the biodynamic response expressed in terms of apparent mass a comparison of the measured response of subjects assuming typical automotive postures involving inclined cushion inclined backrest and full use of backrest support with data determined under different postural conditions and excitation levels revealed considerable differences the biodynamic response of automobile occupants seated with hands in lap peaks in the 6 5 8 6hz frequency range which is considerably higher than the reported range of fundamental frequencies 4 5 5hz in most other studies involving different experimental conditions the peak magnitude tends to decrease considerably for the driving posture with hands on steering wheel while a second peak in the 8 12 hz range becomes more apparent for this posture the results suggest that biodynamic response of occupants seated in automotive seats and subject to vertical vibration need to be characterized as a minimum by two distinct functions for passenger and driving postures a higher body mass in general yields higher peak magnitude response and lower corresponding frequency for both postures the strong dependence of the response on the body mass is further demonstrated by grouping the measured data into four different mass ranges less than 60 kg between 60 5 and 70 kg between 70 5 and 80 kg and above 80 kg from the results it is concluded that hands position and body mass have the most significant influence on the apparent mass response under automotive posture and vibration

a characterization of positive quadrature formulae a positive quadrature formula with n nodes which is exact for polynomials of degree in r 1 0 r is based on the zeros of certain quasi orthogonal polynomials of degree n we show that the quasi orthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal entries as a consequence for a fixed n every positive quadrature formula is a gaussian quadrature formula for some nonnegative measure

quasi orthogonal polynomials quadrature and interpolation abstract we investigate the quasi orthogonal polynomials by expressing them as characteristic polynomials of symmetric matrices many properties of zeros of quasi orthogonal polynomials are derived from this formulation we derive new formulae for quadrature and interpolation based on the zeros of quasi orthogonal polynomials and prove the mean convergence of lagrange interpolation

gauss radau and gauss labatto quadratures with double end points abstract we develop explicit formulae for generalized gauss radau and gauss lobatto quadrature rules having end points of multiplicity 2 and containing chebyshev weight functions of any of the four kinds

continuity of the birkhoff interpolation the birkhoff interpolation polynomial p x t 0 leqq t leqq 1 of a given function depends upon the knots of interpolation x 0 leqq x 1 x 2 cdots x m leqq 1 there is a natural extension of p x t to the case when some of the knots coincide this extension is proved to be continuous the method of proof is by decoalescence

apparent mass of seated man first determination with a soft seat and dynamic seat pressure distributions abstract data of the impedance and or the apparent mass of the sitting human body during the exposure to whole body vibration in z direction using rigid seats were standardized in the iso 5982 these data are available as target functions for model developments models developed on this data basis should also apply to driver seats with a soft seat and backrest cushion although the qualitative different contact conditions were neglected due to insufficient technical prerequisites the determination of forces at the interface between subject and soft seat was impossible until very recently results of studies during static conditions showed clear differences in the pressure distributions between the rigid and the soft contact areas in this experimental study pressure distributions on a seat cushion were measured during whole body vibration in z direction random signal in the frequency range between 0 3 and 20 hz vibration magnitudes 0 25 0 8 and 1 6 m s 2 unweighted root mean square measured at the seat base with a sampling rate of 32 m s the apparent masses were calculated by the forces derived from the pressure distributions and accelerations measured at one point of the seat cushion near the buttocks the moduli of the apparent masses derived for the soft seat were clearly lower than those determined for a rigid seat these apparent masses showed a similar dependence on the vibration magnitude as the apparent mass functions derived in the usual way for rigid seats factors that could explain differences between the apparent mass functions derived for the soft and rigid seat were discussed and evaluated the data of this study indicate the possibility and necessity to consider the contact conditions at the interface when deriving target functions for the model development recommendations for technical improvements and further experimental studies with driver seats were derived

a body mass dependent mechanical impedance model for applications in vibration seat testing abstract a three degree of freedom model is proposed to predict the biodynamic responses of the seated human body of different masses a baseline model is initially derived to satisfy both the mean apparent mass and seat to head transmissibility responses proposed in iso dis 5982 2000 applicable for mean body mass of 75 kg the validity of the resultant generic mass dependent model is verified by comparing the apparent mass and driving point mechanical impedance responses computed for total body masses of 55 75 and 90 kg with the range of idealized values proposed for body masses within the 49 93 kg range considering the lack of data that could be found to define the apparent mass mechanical impedance of subjects with different body masses when applying the experimental conditions defined in iso dis 5982 2000 an attempt is made to adapt the parameters of the base model to fit the measured apparent mass data applicable to groups of automobile occupants within different mass ranges this is achieved through constrained parametric optimization which consists of minimizing the sum of squared errors between the computed response and the mean apparent mass data measured for automobile occupants within four mass groups less than 60 kg 60 5 70 5 kg 70 5 80 kg and above 80 kg the results show a reasonably good agreement between the model responses and the measured apparent mass data particularly at frequencies below 10 hz the results suggest that the proposed mass dependent model can effectively predict the apparent mass responses of automobile occupants over a wide range of body masses and for two different postures passenger hands in lap and driver hands on steering wheel postures

positive quadrature formulas iii asymptotics of weights first we discuss briefly our former characterization theorem for positive interpolation quadrature formulas abbreviated qf provide an equivalent characterization in terms of jacobi matrices and give links and applications to other qf in particular to gauss kronrod quadratures and recent rediscoveries then for any polynomial t n which generates a positive qf a weight function depending on n is given with respect to which t n is orthogonal to p n 1 with the help of this result an asymptotic representation of the quadrature weights is derived in general the asymptotic behaviour is different from that of the gaussian weights only under additional conditions do the quadrature weights satisfy the so called circle law corresponding results are obtained for positive qf of radau and lobatto type

on the bivariate shepard lidstone operators we propose a new combination of the bivariate shepard operators coman and trimbitas 2001 2 by the three point lidstone polynomials introduced in costabile and dell accio 2005 7 the new combination inherits both degree of exactness and lidstone interpolation conditions at each node which characterize the interpolation polynomial these new operators find application to the scattered data interpolation problem when supplementary second order derivative data are given kraaijpoel and van leeuwen 2010 13 numerical comparison with other well known combinations is presented

orbital stability and energy estimate of ground states of saturable nonlinear schrodinger equations with intensity functions in r2 abstract conventionally the existence and orbital stability of ground states of nonlinear schrodinger nls equations with power law nonlinearity subcritical case can be proved by an argument using strict subadditivity of the ground state energy and the concentration compactness method of cazenave and lions 4 however for saturable nonlinearity such an argument is not applicable because strict subadditivity of the ground state energy fails in this case here we use a convexity argument to prove the existence and orbital stability of ground states of nls equations with saturable nonlinearity and intensity functions in r 2 besides we derive the energy estimate of ground states of saturable nls equations with intensity functions using the eigenvalue estimate of saturable nls equations without intensity function

uniqueness of gauss birkhoff quadrature formulas we show that the gauss birkhoff quadrature formulas introduced in 4 are uniquely determined this will be verified using techniques of continuous deformation the methods of proof also yield an interlacing condition for the knots as the number of them increases

erratum standing waves for nonlinear schrodinger equations with a general nonlinearity erratum arch rational mech anal doi 10 1007 s00205 006 0019 3through answering to some questions from joao marcos bezzerra do oon the paper above we found some mistakes in the paper we thank him forhis interest and careful reading here we correct these mistakes first at the beginning of the proof of proposition 4 14 17 line on page193 the correct version is by compactness of s

standing waves for nonlinear schrodinger equations with a general nonlinearity for elliptic equations e2 u v x u f u 0 x rn n 3 we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component of positive local minimum points of v as e 0 under conditions on f which we believe to be almost optimal

a fast algorithm for gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations after studying gaussian type quadrature formulae with mixed boundary conditions we suggest a fast algorithm for computing their nodes and weights it is shown that the latter are computed in the same manner as in the theory of the classical gauss quadrature formulae in fact all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix hence we can adapt existing procedures for generating such quadrature formulae comparative results with various methods now in use are given in the second part of this paper new algorithms for spectral approximations for second order elliptic problems are derived the key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix hence our algorithms can be used to introduce explicit resolutions for the time dependent problems this is the so called lumped mass method the performance of the approach is illustrated with several numerical examples in one and two space dimensions