an interpretive method for moving force identification dynamic load data have been valuable for bridge and pavement design traditional ways to acquire truck axle and gross weight information are expensive and subject to bias and this has led to the development of weigh in motion wim techniques most of the existing wim systems have been developed to measure only the static axle loads this paper aims to introduce a method to identify moving dynamic loads on bridges using the bridge responses caused by such loads a closed form solution can be obtained to identify moving constant loads while numerical methods must be used to identify the time varying moving loads the set of equations that leads to the solution is based on euler s equation of beams a two axle vehicle model is developed to generate the theoretical responses and the corresponding interactive moving forces studies were carried out to check whether the proposed method could recover the original interactive moving forces and the method was found to be feasible

limiting distributions for l sb 1 regression estimators under general conditions it is well known that l 1 estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0 in this paper we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0

free vibration analysis of a uniform multi span beam carrying multiple spring mass systems abstract the literature regarding the free vibration analysis of single span beams carrying a number of spring mass systems is plenty but that of multi span beams carrying multiple spring mass systems is fewer thus this paper aims at determining the exact solutions for the natural frequencies and mode shapes of a uniform multi span beam carrying multiple spring mass systems firstly the coefficient matrices for an intermediate pinned support an intermediate spring mass system left end support and right end support of a uniform beam are derived next the numerical assembly technique for the conventional finite element method is used to establish the overall coefficient matrix for the whole vibrating system finally equating the last overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes in this paper the natural frequencies and associated mode shapes of the vibrating system are obtained directly from the differential equation of motion of the continuous beam and no other assumptions are made thus the last solutions are the exact ones the effects of attached spring mass systems on the free vibration characteristics of the 1 4 span beams are studied

estimation of extreme conditional quantiles through power transformation the estimation of extreme conditional quantiles is an important issue in numerous disciplines quantile regression qr provides a natural way to capture the covariate effects at different tails of the response distribution however without any distributional assumptions estimation from conventional qr is often unstable at the tails especially for heavy tailed distributions due to data sparsity in this article we develop a new three stage estimation procedure that integrates qr and extreme value theory by estimating intermediate conditional quantiles using qr and extrapolating these estimates to tails based on extreme value theory using the power transformed qr the proposed method allows more flexibility than existing methods that rely on the linearity of quantiles on the original scale while extending the applicability of parametric models to borrow information across covariates without resorting to nonparametric smoothing in addition we propose a test procedure to assess the commonality of ext

nonparametric estimates of regression quantiles and their local bahadur representation let x y be a random vector such that x is d dimensional y is real valued and y theta x varepsilon where x and varepsilon are independent and the alpha th quantile of varepsilon is 0 alpha is fixed such that 0 0 and set r p m 2p d where m is a nonnegative integer smaller than p let t theta denote a derivative of theta of order m it is proved that there exists a pointwise estimate hat t n of t theta based on a set of i i d observations x 1 y 1 cdots s n y n that achieves the optimal nonparametric rate of convergence n r under appropriate regularity conditions further a local bahadur type representation is shown to hold for the estimate hat t n and this is used to obtain some useful asymptotic results

geometric bounds on the growth rate of null controllability cost for the heat equation in small time given a control region omega on a compact riemannian manifold m we consider the heat equation with a source term g localized in omega it is known that any initial data in l 2 m can be steered to 0 in an arbitrarily small time t by applying a suitable control g in l 2 0 t times omega and as t tends to 0 the norm of g grows like exp c t times the norm of the data we investigate how c depends on the geometry of omega 72 words we prove c geq d 2 4 where d is the largest distance of a point in m from omega when m is a segment of length l controlled at one end we prove c leq alpha l 2 for some alpha 2 moreover this bound implies c leq alpha l omega 2 where l omega is the length of the longest generalized geodesic in m which does not intersect omega the em control transmutation method used in proving this last result is of a broader interest

boundary controllability of parabolic coupled equations abstract this paper is concerned with the boundary controllability of non scalar linear parabolic systems more precisely two coupled one dimensional parabolic equations are considered we show that in this framework boundary controllability is not equivalent and is more complex than distributed controllability in our main result we provide necessary and sufficient conditions for the null controllability

local likelihood smoothing of sample extremes trends in sample extremes are of interest in many contexts an example being environmental statistics parametric models are often used to model trends in such data but they may not be suitable for exploratory data analysis this paper outlines a semiparametric approach to smoothing sample extremes based on local polynomial fitting of the generalized extreme value distribution and related models the uncertainty of fits is assessed by using resampling methods the methods are applied to data on extreme temperatures and on record times for the women s 3000 m race

vibration analysis of non linear beams subjected to a moving load using the finite element method this paper is concerned with the non linear vibration of immovably supported variable beams in which the geometric non linearity due to the axial force generated by stretching the middle surface is taken into account when the beam is subjected to a moving load the dynamic deflections of the beam are computed by using a galerkin finite element formulation and the time differential terms are integrated by using the implicit direct integration method three types of approximations for solving the non linear problem are considered in the first of which both the longitudinal deflections and inertia are considered with only the longitudinal deflections being considered and in the second neither the longitudinal deflections nor inertia in the third the results obtained by using these non linear models are numerically compared with that obtained by the linear model

natural frequency changes of a cracked timoshenko beam by modified fourier series a new method is presented in this paper for computing the natural frequencies of a timoshenko beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is developed particularly for a timoshenko beam having an arbitrary number of transverse open cracks unlike the conventional fourier series the modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked timoshenko beam in the usual way and thus reduces the problem to a simple one by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form that renders the task of computer coding quite straightforward

minimal time for the null controllability of parabolic systems the effect of the condensation index of complex sequences let a d a be a diagonalizable generator of a c0 semigroup of contractions on a complex hilbert space x b l c y y being some suitable extrapolation space of x and u l2 0 t c under some assumptions on the sequence of eigenvalues k k 1 c of a d a we prove the existence of a minimal time t0 0 depending on bernstein s condensation index of and on b such that y ay bu is null controllable at any time t t0 and not null controllable for t t0 as a consequence we solve controllability problems of various systems of coupled parabolic equations in particular new results on the boundary controllability of one dimensional parabolic systems are derived these seem to be difficult to achieve using other classical tools

exact solution of free vibration of a uniform tensioned beam combined with both lateral and rotational linear sub systems abstract a general exact solution of free vibration of a uniform tensioned beam with any number of both lateral and rotational sub systems is addressed this study is completed in complex domain because of the presence of the non proportional damping caused by the dampers utilized in sub systems the sub systems constructed herein could degenerate to the conventional supports and sub systems and be arbitrarily placed accordingly the solution is also suitable for multi span beams the argument principle method apm which does not need initial values and iteration is employed to solve the characteristic equation in complex domain nevertheless the presence of multi valued square root functions due to the axial loading renders the function non analytic in complex domain a variable substitution method in which the main branch of logarithmic function is chosen is proposed to solve this problem the results obtained are compared with those in literature furthermore several typical case studies were completed and the root loci of the frequency parameters attained are compared with those obtained by the finite element method fem a good agreement is observed which confirms the validity of the presented methodologies in this paper

nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load this paper focuses on the geometrically nonlinear dynamic analysis of an eccentrically prestressed simply supported damped beam subjected to a concentrated moving harmonic load the nonlinear dynamic deflections of the beam are obtained by polynomial functions the kelvin voigt model for the material of the beam is used two coupled nonlinear systems of equations of motion are derived using lagrange s equations under the assumptions of the euler bernoulli beam theory with the von karman s nonlinear strain displacement relationships the rotary inertia axial displacement and axial inertia are included in the formulation the nonlinear equations of motion are solved by using the implicit time integration method of newmark in conjunction with the newton raphson iteration method in this study the effects of large deflections the internal damping of the beam the velocity of the moving harmonic load the prestress load the eccentricity of the prestress load and the excitation frequency on the dynamic response of the beam are discussed the obtained results are compared with the results based on the linear beam theory convergence studies are performed numerical results show that the above mentioned effects play a very important role in the deflections of the beam

a sturdy reduced bias extreme quantile var estimator please see the supplementary material for an important correction the main objective of statistics of extremes lies in the estimation of quantities related to extreme events in many areas of application such as statistical quality control insurance and finance a typical requirement is to estimate a high quantile that is the value at risk at a level p varp high enough so that the chance of an exceedance of that value is equal to p small in this article we deal with the semiparametric estimation of varp for heavy tails the classical semiparametric estimators of parameters characterizing the tail behavior of the underlying model f usually exhibit a high bias for low thresholds that is for large values of k the number of top order statistics used for the estimation we shall here deal with bias reduction techniques for heavy tails trying to improve the performance of the classical high quantile estimators through the use of an adequate bias corrected tail index estimator the new high quantil

on the controllability of parabolic systems with a nonlinear term involving the state and the gradient we present some results concerning the controllability of a quasi linear parabolic equation with linear principal part in a bounded domain of mathbb r n with dirichlet boundary conditions we analyze the controllability problem with distributed controls supported on a small open subset and boundary controls supported on a small part of the boundary we prove that the system is null and approximately controllable at any time if the nonlinear term f y nabla y grows slower than y log 3 2 1 y nabla y nabla y log 1 2 1 y nabla y at infinity generally in this case in the absence of control blow up occurs the proofs use global carleman estimates parabolic regularity and the fixed point method

vibration of multi span non uniform beams under moving loads by using modified beam vibration functions based on hamilton s principle the vibration of a multi span non uniform beam subjected to a moving load is analysed by using modified beam vibration functions as the assumed modes the modified beam vibration functions satisfy the zero deflection conditions at all the intermediate point supports as well as the boundary conditions at the two ends of the beam numerical results are presented for both uniform and non uniform beams under moving loads of various velocities examples show that this method converges very quickly and good results are obtained

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

modified ode solver for vibration of tube in tube structures abstract for some complex boundary value problems such as ordinary differential equations odes with eigenvalue problems finding a closed form of solution is usually very difficult sometimes even impossible the main purpose of this paper is to present a numerical solution of eigenvalues for free vibration of tube in tube tall buildings by using ode solver modified in the paper in order that an existing ode solver may be compatible with solving the eigenvalue problem a solution strategy for the ode solver is modified that is the strategy organically puts the following techniques together standard transform for non linear problem inverse iteration orthogonalization and eigenvalue shift etc in comparison to the results calculated by other analytical methods and the finite element method shows that the present ode solver can be conveniently taken for accurate and reliable solutions of the eigenvalue problem of the vibration

free vibration analysis of a uniform cantilever beam with point masses by an analytical and numerical combined method abstract the natural frequencies and mode shapes of a uniform cantilever beam carrying any number of concentrated masses were determined by using an analytical and numerical combined method anc method the eigenvalue equation was first derived analytically by using the expansion theorem and then the eigenvalues and eigenvectors were calculated numerically in comparison with the general finite element method fem the anc method has the advantage that there is no necessity to derive the property matrices of each beam element and then to develop the overall ones of the entire beam in comparison with the transfer matrix method tmm the anc method requires no tedious matrix multiplication so that some computer time may be saved the anc method is also better than the pure analytical closed form method since instead of a few special cases a uniform beam carrying any number of point masses of various magnitudes or distributions along the beam length can be easily solved besides by using the anc method there is no difficulty in taking more modes in the mode superposition equation and hence more higher mode natural frequencies of better accuracy may be obtained

a lack of fit test for quantile regression we propose an omnibus lack of fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector the test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error in addition the test is suitable for detecting the local alternatives of any order arbitrarily close to n 1 2 from the null hypothesis the limiting distribution of the proposed test statistic is non gaussian but can be characterized by a gaussian process we propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for

vibration and stability of cracked hollow sectional beams this paper presents simple tools for the vibration and stability analysis of cracked hollow sectional beams it comprises two parts in the first the influences of sectional cracks are expressed in terms of flexibility induced each crack is assigned with a local flexibility coefficient which is derived by virtue of theories of fracture mechanics the flexibility coefficient is a function of the depth of a crack the general formulae are derived and expressed in integral form it is then transformed to explicit form through 128 point gauss quadrature according to the depth of the crack the formulae are derived under two scenarios the first is for shallow cracks of which the penetration depth is contained within the top solid sectional region the second is for deeper penetration in which the crack goes into the middle hollow sectional region the explicit formulae are best fitted equations generated by the least squares method the best fitted curves are presented from the curves the flexibility coefficients can be read out easily while the explicit expressions facilitate easy implementation in computer analysis in the second part the flexibility coefficients are employed in the vibration and stability analysis of hollow sectional beams the cracked beam is treated as an assembly of sub segments linked up by rotational springs division of segments are made coincident with the location of cracks or any abrupt change of sectional property the crack s flexibility coefficient then serves as that of the rotational spring application of the hamilton s principle leads to the governing equations which are subsequently solved through employment of a simple technique it is a kind of modified fourier series which is able to represent any order of continuity of the vibration buckling modes illustrative numerical examples are included

on the eigenfrequencies for mass loaded beams under classical boundary conditions a frequency analysis of loaded beams is performed for ten classical beams involving guided fixed free an or pinned ends the explicit frequency equations are obtained by satisfying the differential equation of the eignvalue problem the boundary and comptatibility conditions a solution set of the transcendental expression will be compared with the experimental results and also with those obtained by using rayleigh s method

dynamic response of a rotating flexible arm carrying a moving mass abstract a clamped free flexible arm rotating in a horizontal plane and carrying a moving mass is studied in this paper the arm is modelled by the euler bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored the assumed mode method in conjunction with hamilton s principle is used to derive the equation of motion of the system which takes into account the effect of centrifugal stiffening due to the rotation of the beam the eigenfunctions of a cantilever beam which satisfy the prescribed geometric boundary conditions are used as basis functions in the assumed mode method the equation of motion is expressed in non dimensional matrix form pre designed transformed cosine profiles are used as trajectory inputs for the hub angle and the moving mass the equation of motion is solved numerically using the fourth order runge kutta method graphical results are presented to show the influence of centrifugal stiffening effect moving mass values mass travelling time hub angle and mass trajectory profile on the deflection of the beam

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

estimation of the retransformed conditional mean in health care cost studies summary we propose a new approach for analyzing skewed and heteroscedastic health care cost data through regression of the conditional quantiles of the transformed cost using the appealing equivariance property of quantiles to monotone transformations we propose a distribution free estimator of the conditional mean cost on the original scale the proposed method is extended to a two part heteroscedastic model to account for zero costs commonly seen in health care cost studies simulation studies indicate that the proposed estimator has competitive and more robust performance than existing estimators in various heteroscedastic models

a note on the vibrations of restrained beams and rods with point masses abstract this paper is concerned with the approximate determination of the fundamental frequency and first mode shape of a beam or rod to which springs and point masses are attached after formulating the general eigenvalue problem which forms the basis of the analysis the theory is applied to three examples and it is shown that the results are quite satisfactory

dynamic analysis of a multi span uniform beam carrying a number of various concentrated elements abstract this paper employs the numerical assembly method nam to determine the exact frequency response amplitudes of a multiple span beam carrying a number of various concentrated elements and subjected to a harmonic force and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force first the coefficient matrices for the intermediate concentrated elements pinned support applied force left end support and right end support of a beam are derived next the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method fem finally the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix the graph of dynamic response amplitudes versus various exciting frequencies gives the frequency response curve for any point of a multiple span beam carrying a number of various concentrated elements for the case of zero harmonic force the above mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained

motion of a moving elastic beam carrying a moving mass analysis and experimental verification abstract in this paper vibrational motion of an elastic beam fixed on a moving cart and carrying a moving mass is investigated the equations of motion of the beam mass cart system are derived and the coupled dynamic equations are solved by the unconstrained modal analysis in modal analysis the exact normal mode solutions corresponding to the eigenfrequencies for each position of the moving mass and the ratios of the weight of the beam mass cart system are used proper transformation of time solutions between the normal modes for a position and those for the next position of the moving mass is also considered numerical simulations are carried out to obtain open loop responses of the system in tracking pre designed paths of the moving mass the simulation results show that the model predicts the dynamic behavior of the beam mass cart system well experiments are carried out to show the validity of the proposed analytical method

maximizing the natural frequency of a beam with an intermediate elastic support the minimum stiffness of a simple or point support that raises a natural frequency of a beam to its upper limit is investigated for different boundary conditions the approach produces the closed form solution for the minimum stiffness based on the derivative of a natural frequency with respect to the support position it is seen that when an intermediate elastic support is positioned properly the effect is similar to a rigid support the solution process also provides insight into the dynamics of a beam with an intermediate support for more general boundary conditions the resulting solutions can be used to guide the practical design of a support

natural frequencies and ope loop responses of an elastic beam fixed on a moving cart and carrying an intermediate lumped mass abstract in this paper the motion of a bernoulli euler cantilever beam clamped on a moving cart and carrying an intermediate lumped mass is considered the equations of motion of the beam mass cart system are analyzed through unconstrained modal analysis and a unified characteristic equation for calculating the natural frequencies of the system is established the changes of natural frequencies and the corresponding mode shapes with respect to the changes in the ratios between the beam mass the lumped mass and the cart mass and to the concentrated position of the lumped mass are investigated with the frequency equation which can be generally applied to this kind of system the exact and assumed mode solutions including the dynamics of the base cart are obtained and the open loop responses of the system by arbitrarily designed forcing functions are given by numerical simulations the results match well with physical phenomena even in the extreme cases where the mass is attached to the bottom and to the top of the beam

smooth quantile ratio estimation in a study of health care expenditures attributable to smoking we seek to compare the distribution of medical costs for persons with lung cancer or chronic obstructive pulmonary disease cases to those without controls using a national survey which includes hundreds of cases and thousands of controls the distribution of costs is highly skewed toward larger values making estimates of the mean from the smaller sample dependent on a small fraction of the biggest values one approach to deal with the smaller sample is to rely on a simple parametric model such as the log normal but this makes the undesirable assumption that the distribution of the log expenditures is symmetric we propose a novel approach to estimate the mean difierence of two highly skewed distributions which we call smooth quantile ratio estimation square square is obtained by smoothing over percentiles the ratio of the cost quantiles of the cases and controls square deflnes a large class of estimators of including 1 the sample mean difference 2 the maximum likelihood estimate under log normal samples and 3 l estimates we detail asymptotic properties of square such as consistency and asymptotic normality and also provide a closed form expression for the asymptotic variance through a simulation study we show that square has lower mean squared error than several competitors including the sample mean difierence and log normal parametric estimates in several realistic situations we apply square to the 1987 national medicare expenditure survey to estimate the difierence in medical expenditures between persons sufiering from the smoking attributable diseases lung cancer and chronic obstructive pulmonary disease and persons without these diseases software in r ihaka and gentleman 1996 for the implementation of square and of all its special cases and the cost data used in this paper are available at http biostat jhsph edu fdominic square html

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

dynamic response of a beam with intermediate point constraints subject to a moving load abstract the transverse vibration of a beam with intermediate point constraints subject to a moving load is analyzed by using the euler beam theory and the assumed mode method the point constraints in the form of supports are assumed to be linear springs of large stiffness results of numerical simulations are presented for various combinations of constant axial velocity of the moving load and number of point constraints

on the numerical convergence of discretization methods for the free vibrations of beams with attached inertia elements abstract this paper is concerned with a numerical convergence study of three discretization methods rayleigh ritz galerkin and finite element as applied to the analysis of free bending linear vibrations of a uniform bernoulli euler beam carrying inertia elements at intermediate points a cantilever beam carrying a lumped mass with rotary inertia at an arbitrary intermediate point and another at the beam tip is used as a case study the first five frequency parameters of this beam obtained by using the rayleigh ritz method in conjunction with broadly admissible base beam eigenfunctions galerkin s method in conjunction with strictly admissible base beam eigenfunctions and the classical finite element method are compared with the exact ones over a wide range of values of the system parameters conclusions are drawn regarding the effects of the various system parameters on the accuracy and convergence characteristics of the above three discrete methods and on the mode shapes and the first five frequency parameters of the beam system

free vibration analysis for tube in tube tall buildings an approximate solution procedure is formulated for free vibration analysis of tube in tube tall buildings in this paper the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients on the assumption that the transverse displacement is a harmonic vibration a power series solution which represents the mode shape function of tube in tube tall buildings is derived applying the boundary conditions yields the boundary value problem from which the frequency equation is established and solved through a numerical process to determine the natural frequencies two numerical examples are performed and compared with results available in the published literature to show the accuracy of the proposed method care has been exercised to retain sufficient terms in power series in evaluating natural frequencies of accepted accuracy the influences of the factors including flexural rigidity mass per unit length and building height to the natural frequency are discussed the method proposed herein enables one to calculate as an alternative the natural frequency of tube in tube tall buildings with good accuracy associated by calculators and hand prior to use of the complicated computer programs

natural frequencies of a non uniform beam with multiple cracks via modified fourier series abstract a new method is presented in this paper for computing the natural frequencies of a non uniform beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is specially developed for a beam with transverse open cracks unlike conventional fourier series modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked beam in the most usual way and thus reduce the problem to a simple one the beam can be of non uniform cross section and the number of cracks can be arbitrary by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form which renders the programming quite straightforward

sturm liouville equation for free vibration of a tube in tube tall building the equation for free vibration of a tube in tube tall building which is obtained by considering an influence coefficient due to the shear lag effect and using the equivalent closed tube method is proved strictly to be the fourth order sturm liouville differential equation and a formulation for calculating natural frequencies of the structure is obtained directly in comparison with other numerical and experimental results the frequencies found from the proposed method are quite satisfactory for practical use and are simple to calculate

vibration of multi span timoshenko beams to a moving force abstract a method of modal analysis is proposed in this paper to investigate the forced vibration of multi span timoshenko beams the ratio of the radius of gyration of the cross section to one span length is defined as a parameterr the effect ofron the first modal frequency of a beam is studied a concentrated force traversing on the beam is used as an example the effects of span number rotary inertia and shear deformation on the maximum moment the maximum deflection and the critical velocity of a beam are examined the results are compared with those of a multi span bernoulli euler beam

an exact modal analysis approach to vibration analysis of structures with mass spring subsystems and rotational joints abstract a novel exact modal analysis approach is presented for vibration analysis of plane continuous structures which are coupled with discrete mass spring subsystems and include elastic rotational joints modelling local flexibility using the theory of generalised functions to handle the discontinuities of the response variables every continuous member with any number of mass spring subsystems and joints is treated as a two node element for which a 6 6 exact dynamic stiffness matrix is obtained in closed form as a result the global dynamic stiffness matrix is built by a standard finite element assembling procedure with size depending only on the number of nonzero nodal degrees of freedom of member to member nodes upon deriving pertinent orthogonality conditions for the modes the system response under arbitrary loads is obtained by modal impulse and modal frequency response functions under the assumption of proportional damping the solutions are exact and can be used as benchmark for classical finite element solutions the approach is formulated for various mass spring subsystems acting in transverse and axial directions relative to every member

vibration frequencies of a rotating flexible arm carrying a moving mass abstract a clamped free flexible beam rotating in a horizontal plane and carrying a moving mass is modelled by the euler bernoulli beam theory the equation of motion is derived by hamilton s principle including the effects of centrifugal stiffening arising from the rotation of the beam the motion of the moving mass and the beam is coupled the equation of motion is a coupled non linear partial differential equation where the coupling terms have to be evaluated at the position of the moving mass in order to obtain the mode shapes which account for the motion of the moving mass the solution is discretized into space and time functions and the beam is divided into two separate regions with respect to the moving mass this results in two non homogeneous linear mode shape ordinary differential equations with four boundary one discontinuity and three continuity conditions the power series method is used to solve for the mode shape differential equations a frequency equation is derived giving the relationship between the non dimensional modal frequencies and the four non dimensional parameters i e the moving mass position the moving mass the beam angular velocity and the total moment of inertia about the hub the numerical bisection method is used to solve for the vibration frequencies under different parameters results are presented for the first three modes of vibration

bayesian empirical likelihood for quantile regression bayesian inference provides a flexible way of combining data with prior information however quantile regression is not equipped with a parametric likelihood and therefore bayesian inference for quantile regression demands careful investigation this paper considers the bayesian empirical likelihood approach to quantile regression taking the empirical likelihood into a bayesian framework we show that the resultant posterior from any fixed prior is asymptotically normal its mean shrinks toward the true parameter values and its variance approaches that of the maximum empirical likelihood estimator a more interesting case can be made for the bayesian empirical likelihood when informative priors are used to explore commonality across quantiles regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas e g high or low percentile levels through empirical likelihood the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains by using an mcmc algorithm in the computation we avoid the daunting task of directly maximizing empirical likelihood the finite sample performance of the proposed method is investigated empirically where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels a theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method

estimation of high conditional quantiles for heavy tailed distributions estimation of conditional quantiles at very high or low tails is of interest in numerous applications quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution however high tails are often associated with data sparsity so quantile regression estimation can suffer from high variability at tails especially for heavy tailed distributions in this article we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors we establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates in a real application involving statistical downscaling of daily precipitation in

new phenomena for the null controllability of parabolic systems minimal time and geometrical dependence abstract we consider the null controllability problem for two coupled parabolic equations with a space depending coupling term we analyze both boundary and distributed null controllability in each case we exhibit a minimal time of control that is to say a time t 0 0 such that the corresponding system is null controllable at any time t t 0 and is not if t t 0 in the distributed case this minimal time depends on the relative position of the control interval and the support of the coupling term we also prove that for a fixed control interval and a time 0 0 there exist coupling terms such that the associated minimal time is 0

on the eigenfrequencies of a cantilever beam with attached tip mass and a spring mass system this paper deals with the derivation of the frequency equation of a special combined dynamic system it consists of a clamped free bernoulli euler beam with a tip mass where a spring mass system is attached to it the derivation of the frequency equation is essentially carried out by means of the lagrange multipliers method frequency equations of some simpler systems are also obtained from the general expression by using limiting processes these equations are then numerically solved for various combinations of physical parameters the comparison with the results from the solution of the corresponding bernoulli euler frequency equations shows that the frequency equations established are very accurate

tail index regression in extreme value statistics the tail index is an important measure to gauge the heavy tailed behavior of a distribution under pareto type distributions we employ the logarithmic function to link the tail index to the linear predictor induced by covariates which constitutes the tail index regression model we then propose an approximate log likelihood function to obtain regression parameter estimators and subsequently show the asymptotic normality of those estimators numerical studies are presented to illustrate theoretical findings

sharp estimates of the one dimensional boundary control cost for parabolic systems and application to the n dimensional boundary null controllability in cylindrical domains in this paper we consider the boundary null controllability of a system of n parabolic equations on domains of the form omega 0 pi times omega 2 with omega 2 a smooth domain of mathbb r n 1 n 1 when the control is exerted on 0 times omega 2 with omega 2 subset omega 2 we obtain a necessary and sufficient condition that completely characterizes the null controllability this result is obtained through the lebeau robbiano strategy and requires an upper bound of the cost of the one dimensional boundary null control on 0 pi the latter is obtained using the moment method and it is shown to be bounded by ce c t when t goes to 0

non linear vibration of timoshenko beam due to a moving force and the weight of beam the large deflection theory is employed to derive the equations of motion of the timoshenko beam due to the coupling effect of an external force with the weight of the beam galerkin s method is employed to obtain the dynamic responses of the beam a set of two discrete moving forces is taken as an example to investigate the characteristics of these responses results show that the effect of weight of the beam decreases the fundamental period of the structure further both the dynamic deflection and the dynamic moment of the beam predicated by the theory including the effect of weight of the beam are less than those of the beam predicated either by the small deflection theory or by the large deflection theory without including the effect of weight of the beam

power transformed linear quantile regression with censored data we propose a class of power transformed linear quantile regression models for survival data subject to random censoring the estimation procedure follows two sequential steps first for a given transformation parameter we can easily obtain the estimates for the regression coefficients by minimizing a well defined convex objective function second we can estimate the transformation parameter based on a model discrepancy measure by constructing cumulative sum processes we show that both the regression and transformation parameter estimates are strongly consistent and asymptotically normal the variance covariance matrix depends on the unknown density function of the error term so we estimate the variance by the usual bootstrap approach we examine the performance of the proposed method for finite sample sizes through simulation studies and illustrate it with a real data example

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

decay rate estimates for the quasi linear timoshenko system with nonlinear control and damping terms in this work we consider a class of quasi linear timoshenko systems with nonlinear control and damping terms we investigate the stabilization of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on control and damping terms

vibration of multi span non uniform bridges under moving vehicles and trains by using modified beam vibration functions abstract based on the lagrangian approach the vibration of a multi span non uniform bridge subjected to a moving vehicle is analyzed by using modified beam vibration functions as the assumed modes the vehicle is modelled as a two degree of freedom system the method is extended to the action of a moving train by modelling it as a series of two degree of freedom systems all the derived formulae are expressed in matrix form and therefore programming is quite straightforward the total number of unknowns for this method is very small compared with that of the finite element method convergence is very quick and in almost all cases 12 16 terms are sufficient to give satisfactory results

on the frequency response function of a damped cantilever simply supported in span and carrying a tip mass abstract this paper deals with the determination of the frequency response function of a cantilevered bernoulli euler beam which is viscously damped by a single damper the beam is simply supported in span and carries a tip mass the frequency response function is obtained through a formula that was established for the receptance matrix of discrete linear systems subjected to linear constraint equations by considering the simple support as a linear constraint imposed on generalized co ordinates the comparison of the numerical results obtained via a boundary value problem formulation justifies the approach used here

extremal quantile regression quantile regression is an important tool for estimation of conditional quantiles of a response y given a vector of covariates x it can be used to measure the effect of covariates not only in the center of a distribution but also in the upper and lower tails this paper develops a theory of quantile regression in the tails specifically it obtains the large sample properties of extremal extreme order and intermediate order quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values this modeling setup combines restrictions of extreme value theory with leading homoscedastic and heteroscedastic linear specifications of regression analysis in large samples extreme order regression quantiles converge weakly to arg min functionals of stochastic integrals of poisson processes that depend on regressors while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design

moving forces identification on a multi span continuous bridge abstract a continuous bridge is modelled as a multi span continuous timoshenko beam with non uniform cross section the vibration behaviour of this beam subjected to moving loads is analyzed by hamilton s principle with the intermediate point constraints represented by very stiff linear springs a method based on the modal superposition and optimization technique is developed to identify the moving forces in the time domain the damped least squares method is used in the identification to provide bounds to the results the errors in the moving force identification are discussed in the paper both computation simulations and laboratory tests show that the method is effective for identifying the moving loads using different combinations of measured responses

controllability to the trajectories of phase field models by one control force in this article we study the controllability to the trajectories of 2 2 nonlinear parabolic systems for control forces acting on a single equation of the system this result which in particular applies to caginalp s phase field model actually extends those obtained for the semilinear heat equations the proof relies on kakutani s fixed point theorem and makes use of an observability estimate for the associated linearized system

study on different beam models in moving force identification abstract several methods have been developed recently to identify moving forces on a beam the results from all of them exhibit fluctuations at the beginning and end of the time history and they are natural outcomes of the ill conditioned inverse problem accuracy of the identified forces also depends on the parameters of the beam force system which have not been systematically studied this paper employs tikhonov regularization technique to provide bounds to the ill conditioned results in the identification problem the calculation of the optimal regularization parameter is discussed the improved algorithm is then used to study the effect of different parameters on the identification results through single force and multi forces identification both the timoshenko beam theory and the euler bernoulli beam theory are included in the study for a comparison laboratory results on two moving forces identification are also presented for illustration timoshenko beam model is found better than the euler bernoulli beam model in the identification and the limits of applications of the moving force identification method are also reported

a new approach for determining the natural frequencies and mode shapes of a uniform beam carrying any number of sprung masses abstract in theory one may obtain five equations from each attaching point of a spring mass system and two boundary equations from each end of the uniform beam hence for a uniform beam carrying n spring mass systems simultaneous equations of the form b c 0 will be obtained the solutions of b 0 where represents a determinant give the natural frequencies of the constrained beam and the substitution of each corresponding values of c j j 1 4 into the eigenfunction will define the associated mode shapes while the foregoing theory is simple the lengthy explicit mathematical expressions become impractical if the total number of spring mass systems is larger than two for this reason it was applied to do the free vibration analysis of a uniform beam carrying one spring mass system only in the existing literature the purpose of this paper is to present a numerical technique to apply the foregoing theory to obtain the exact solutions for the lowest several natural frequencies and mode shapes of a uniform beam carrying any number of spring mass systems with various boundary conditions to this end each integration constant c vi and each mode displacement z v v 1 n i 1 4 at the attaching point and the two ends of the beam are considered as nodal displacements of a finite beam element and are assigned an appropriate degree of freedom dof hence each associated coefficient matrix will be equivalent to the stiffness matrix of a beam element and the conventional numerical assembly technique for the finite element method fem may be used to determine the overall coefficient matrix b therefore the eigenvalue equation b c 0 is easily obtained

vibration frequencies for beams on variable one and two parameter elastic foundations abstract this work presents a method to find the exact vibration frequencies of beams resting on variable one and two parameter elastic foundations the proposed solution is based on a new method that enables one to find the dynamic stiffness matrix for the member including the effects of the variable foundation stiffness the natural frequencies of vibrations are found as the frequency that causes the determinant of the stiffness matrix to be equal to zero several examples are given and compared to published results to demonstrate the accuracy and flexibility of the method

on the natural frequencies and mode shapes of a multispan timoshenko beam carrying a number of various concentrated elements abstract the purpose of this paper is to utilize the numerical assembly method nam to determine the exact natural frequencies and mode shapes of the multispan timoshenko beam carrying a number of various concentrated elements including point masses rotary inertias linear springs rotational springs and spring mass systems first the coefficient matrices for an intermediate pinned support an intermediate concentrated element left and right end support of a timoshenko beam are derived next the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method finally the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions respectively the effects of distribution of in span pinned supports and various concentrated elements on the dynamic characteristics of the timoshenko beam are also studied

hierarchical spline models for conditional quantiles and the demand for electricity abstract methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of koenker and bassett spline parameterizations of the conditional quantile functions are used the methods are illustrated by estimating hierarchical models for household electricity demand using data from the chicago metropolitan area the empirical results show that lower quantiles of demand base load vary only slightly across residential households this variability is difficult to explain using household characteristics however upper quantiles of the demand distribution vary considerably and are systematically related to household characteristics and appliance ownership the implications of analyzing mean demand behavior rather than various quantiles of the distribution of demand are also discussed

empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset

boundary controllability of a one dimensional phase field system with one control force abstract in this paper we present some controllability results for linear and nonlinear phase field systems of caginalp type considered in a bounded interval of r when the scalar control force acts on the temperature equation of the system by means of the dirichlet condition on one of the endpoints of the interval in order to prove the linear result we use the moment method providing an estimate of the cost of fast controls using this estimate and following the methodology developed in 19 we prove a local exact boundary controllability result to constant trajectories of the nonlinear phase field system to the authors knowledge this is the first nonlinear boundary controllability result in the framework of non scalar parabolic systems framework in which some hyperbolic behaviors could arise