on barnes multiple zeta and gamma functions abstract we show how various known results concerning the barnes multiple zeta and gamma functions can be obtained as specializations of simple features shared by a quite extensive class of functions the pertinent functions involve laplace transforms and their asymptotics is obtained by exploiting this we also demonstrate how barnes multiple zeta and gamma functions fit into a recently developed theory of minimal solutions to first order analytic difference equations both of these new approaches to the barnes functions give rise to novel integral representations

weak uniqueness for the heat equation with noise the uniqueness in law for the equation x t t 1 2 x t x t w is established for 1 2 1 the proof uses a duality technique and requires the construction of an approximating sequence of dual processes

a weighted occupation time for a class of measured valued branching processes a weighted occupation time is defined for measure valued processes and a representation for it is obtained for a class of measure valued branching random motions on rd considered as a process in its own right the first and second order asymptotics are found as time t specifically the finiteness of the total weighted occupation time is determined as a function of the dimension d and when infinite a central limit type renormalization is considered yielding gaussian or asymmetric stable generalized random fields in the limit in one gaussian case the results are contrasted in high versus low dimensions

intermittency for stochastic partial differential equations driven by strongly inhomogeneous space time white noises abstract in this paper the main topic is to investigate the intermittent property of the one dimensional stochastic heat equation driven by an inhomogeneous brownian sheet which is a noise deduced from the study of the catalytic super brownian motion under some proper conditions on the catalytic measure of the inhomogeneous brownian sheet we show that the solution is weakly full intermittent based on the estimates of moments of the solution in particular it is proved that the second moment of the solution grows at the exponential rate the novelty is that the catalytic measure relative to the inhomogeneous noise is not required to be absolutely continuous with respect to the lebesgue measure on r

singularity of super brownian local time at a point catalyst in a one dimensional single point catalytic continuous super brownian motion studied by dawson and fleischmann the occupation density measure c at the catalyst s position c is shown to be a singular diffuse random measure the source of this qualitative new effect is the irregularity of the varying medium c describing the point catalyst the proof is based on a probabilistic characterization of the law of the palm canonical clusters x appearing in the levy khintchine representation of c in a historical process setting and the fact that these x have infinite left upper density with respect to lebesgue measure at the palm time point

finite time extinction of superprocesses with catalysts consider a catalytic super brownian motion x x with finite variance branching here catalytic means that branching of the reactant x is only possible in the presence of some catalyst our intrinsic example of a catalyst is a stable random measure on r of index 0 y 1 consequently here the catalyst is located in a countable dense subset of r starting with a finite reactant mass x 0 supported by a compact set x is shown to die in finite time we also deal with two other cases with a power low catalyst and with a super random walk on z d with an i i d catalyst our probabilistic argument uses the idea of good and bad historical paths of reactant particles during time periods t n t n 1 good paths have a significant collision local time with the catalyst and extinction can be shown by individual time change according to the collision local time and a comparison with feller s branching diffusion on the other hand the remaining bad paths are shown to have a small expected mass at time t n 1 which can be controlled by the hitting probability of point catalysts and the collision local time spent on them

complete characterizations of the gamma function abstract in this paper we obtain the complete monotonicities regarding both the functions x and x defined by x 1 2 x x e x e x 12 x 2 x x e x 1 x as direct consequences x is strictly increasing and strictly concave on 0 and x is strictly decreasing and strictly convex on 0 furthermore we show that x consists the properties lim x 0 x 0 and lim x x 1 as well as x holds the properties lim x 0 x and lim x x 0

structural damage detection by a new iterative regularization method and an improved sensitivity function abstract a new sensitivity based damage detection method is proposed to identify and estimate the location and severity of structural damage using incomplete noisy modal data for these purposes an improved sensitivity function of modal strain energy mse based on lagrange optimization problem is derived to adapt the initial sensitivity formulation of mse to damage detection problem with the aid of new mathematical approaches in the presence of incomplete noisy modal data the sensitivity matrix is sparse rectangular and ill conditioned which leads to an ill posed damage equation to overcome this issue a new regularization method named as regularized least squares minimal residual rlsmr is proposed to solve the ill posed damage equation this method relies on krylov subspace and exploits bidiagonalization and iterative algorithms to solve linear mathematical systems for the majority of krylov subspace methods conventional direct methods for the determination of an optimal regularization parameter may not be proper to cope with this limitation a hybrid technique is introduced that depends on the residual of rlsmr method the number of iterations and the bidiagonalization algorithm the accuracy and performance of the improved and proposed methods are numerically examined by a planner truss by incorporating incomplete noisy modal parameters and finite element modeling errors a comparative study on the initial and improved sensitivity functions is conduced to investigate damage detectability of these sensitivity formulations furthermore the accuracy and robustness of rlsmr method in detecting damage are compared with the well known tikhonov regularization method results show that the improved sensitivity of mse is an efficient tool for using in the damage detection problem due to a high sensitivity to damage and reliable damage detectability in comparison with the initial sensitivity function additionally it is observed that the rlsmr method with the aid of the hybrid technique successfully solves the ill posed damage equation and provides better damage detection results compared with the tikhonov regularization technique

system identification method by using inverse solution of equations of motion in time domain and noisy condition abstract in direct system identification dsi method inverse solution of the equations of motion is applied to obtain physical parameters of a linear system structural mass damping and stiffness matrices with the small error in measurement caused by sensor drift or signal noise these physical parameters are identified with a significant drift in this paper a new simple post processing method is proposed for error reduction in dsi in the time domain in a manner that structural properties are identified without applying the optimization process in noisy condition baseline correction is applied through a nonic curve fitting approach the modified signals are partitioned into a number of sub signals and their mean is applied for system identification the number of sub signals is optimized so that the root mean square rms of off diagonal components of the mass matrix becomes near zero seeking more precision the residual force in every time step at all degrees of freedom dofs is minimized the validity of the proposed method is tested on a multistory structure subjected to a random force at the foundation level in terms of incomplete measurement and 5 noise identified parameters including mass stiffness and damping matrices have satisfying mean errors of 0 094 0 545 and 4 42 with the coefficient of variations of 0 35 1 38 and 6 98 respectively the sensitivity of the proposed method to the noise level is also investigated it is observed that the baseline slop of velocity and displacement signals are sharply increased when the noise level goes beyond 3

mathieu series and associated sums involving the zeta functions almost twelve decades ago mathieu investigated an interesting series s r in the study of elasticity of solid bodies since then many authors have studied various problems arising from the mathieu series s r in various diverse ways in this paper we present a relationship between the mathieu series s r and certain series involving the zeta functions by means of this relationship we then express the mathieu series s r in terms of the trigamma function j z or equivalently the hurwitz or generalized zeta function z s a accordingly various interesting properties of s r can be obtained from those of j z and z s a among other results certain integral representations of s r are deduced here by using the aforementioned relationships among s r j z and z s a

detecting structural damage using frequency response functions these techniques need a large number of sensors to locate damage and the structural response characteristics vary with small changes in boundary conditions and the environment in this condensed paper optimization of frequency response functions is investigated as a means to diagnose damage using a minimum number of sensors

absolute continuity results for superprocesses with some applications let x1 and x2 be instances of a measure valued dawsonwatanabe 4 super process where the underlying spatial motions are given by a borel right process x and where the branching mechanism has finite variance a necessary and sufficient condition on x0 and x2 is found for the law of xi 2 to be absolutely continuous with respect to the law of x2 the conditions are the natural absolute continuity conditions on s but some care must be taken with the set of times s t being considered the result is used to study the closed support of super brownian motion and give sufficient conditions for the existence of a nontrivial collision measure for a pair of independent superlevy processes or more generally for a super levy process and a fixed measure the collision measure gauges the extent of overlap of the two measures as a final application we give an elementary proof of the instantaneous propagation of a super levy process to all points to which the underlying levy process can jump this result is then extended to a much larger class of superprocesses using different techniques

one dimensional stochastic partial differential equations and the branching measure diffusion an existence theorem in the spirit of keisler ke is proved for the simple one dimensional diffusion equation driven by white noise modulated by a non linear function of the solution this is used to obtain a density and a stochastic partial differential equation in one dimension for the critical branching diffusion studied by dawson et al

asymptotic formulas for the triple gamma function γ3 by means of its integral representation abstract there is an abundant literature on inequalities for the gamma function and its various related functions as well as their approximations only very recently several authors began to investigate various inequalities for the double gamma function 2 and its approximation here in this sequel to some of these recent works we aim at presenting an integral representation of the triple gamma function 3 which is then used to derive an asymptotic formula for 3 as a by product of the results presented here integral representations and asymptotic formulas for the gamma function and the double gamma function 2 are also given the methods and techniques used in this paper can easily be extended to derive the corresponding integral representations and asymptotic formulas for the multiple gamma functions n n 4

sample path large deviations for super brownian motion we derive two large deviation principles of freidlin wentzell type for rescaled super brownian motion for one of the appearing rate functions an integral representation is given and interpreted as kakutani hellinger energy as a tool we develop estimates for the laplace functionals of historical super brownian motion and certain maximal inequalities also it is shown that the holder norm of index 1 2 of the processt f x t possesses some finite exponential moments provided the functionf is smooth

large time behavior of interface solutions to the heat equation with fisher wright white noise the one dimensional heat equation driven by fisher wright white noise is studied from initial conditions with compact support solutions retain this compact support and die out in finite time there exist interface solutions which change from the value 1 to the value 0 in a finite region the motion of the interface location is shown to approach that of a brownian motion under rescaling solutions with a finite number of interfaces are approximated by a system of annihilating brownian motions

an integral equation for changes in the structural dynamics characteristics of damaged structures this paper presents a relationship between the structural dynamic characteristics of damaged and intact structures such a relationship is derived in the form of an integral equation and is used to develop a method of flaw identification the resulting flaw identification procedure uses the experimental data and relates the flaw to the observed structural dynamic response the algorithm enables one to detect the damage locations and the corresponding damage magnitude simultaneously numerical simulations and experiments are conducted to validate the theory

using transfer function parameter changes for damage detection of structures a novel approach is presented for damage detection of large flexible structures by using the parameter change of the transfer function first an interval modeling technique which represents the system uncertainty under the environmental change via the intervals of transfer function parameters is used to distinguish the structural damage from the environmental change in this paper a coherence approach is developed for locating the damage position when the structural damage is observed only a few sensors are required in using the proposed coherence approach for damage detection this has the advantage of using the proposed algorithm for practical applications also this approach has the flexibility of using the multi input and multi output system a nine bay truss example is used to demonstrate and verify the approach developed nomenclature a b denominator and numerator parameters of transfer function c coherence of the tested system to damage g interval model g transfer function k number of modes m number of outputs n number of tests for environmental change p parameter vector of transfer function r magnitude ratio of the tested system to damage r jr magnitude ratio bounds w weight of parameter change wa w weights of intervals for interval model x y unit vectors of cartesian coordinate system ap parameter change vector superscripts

an experimentally validated damage detection theory in smart structures abstract a method for the non destructive detection and location of damage using parameterized partial differential equations and galerkin approximation techniques is presented damages in a structure cause changes in the physical coefficients of mass density elastic modulus and damping coefficients this paper examines the use of beam like structure with piezoceramic sensors and actuators to perform identification of those physical parameters and hence to detect the damage the method casts the inverse problem as an optimization problem the iterative method is based on enhanced least square error minimization experimental results are presented from tests on cantilevered aluminum beams damaged at different locations and with damage of different dimensions it is demonstrated that the method can sense the presence of damage and locate and characterize the damage to a satisfactory precision

branching particle systems and superprocesses we start from a model of a branching particle system with immigration and with death rate and branching mechanism depending on time and location then we consider a limit case when the mass of particles and their life times are small and their density is high this way we construct a measure valued process x t which we call a superprocess replacing the underlying markov process xi t by the corresponding historical process xi leq t we construct a measure valued process m t in functional spaces which we call a historical superprocess the moment functions for superprocesses are evaluated linear positive additive functionals are studied they are used to construct a continuous analog of a random tree obtained by stopping every particle at a time depending on its path say at the first exit time from a domain a related special markov property for superprocesses is proved which is useful for applications to certain nonlinear partial differential equations the concluding section is devoted to a survey of the literature and the terminology on markov processes used in the paper is explained in the appendix

a new iterative model updating method using incomplete frequency response function data abstract a new iterative model updating method is proposed for reduced model using incomplete frequency response function frf data it uses a modified difference vector between the analytical and experimental frf data to construct a linear sensitivity updating equation system to improve the convergence performance of the proposed algorithm a concept of pseudo master degree of freedom dof is put forward and the finite element fe model is reduced to the measured and user selected pseudo dofs the frfs at pseudo master dofs are estimated using the impedance matrix of iteratively modified analytical model and the measured frfs at master dofs they are only used to improve the sensitivity matrix and difference calculation between the analytical and experimental frf data without introducing additional difference equation at the end a 25 truss structure is used to evaluate the performance of the proposed method

polygamma functions of negative order liouville s fractional integration is used to define polygamma functions z for negative integer n it is shown that such k n z can be represented in a closed form by means of the first derivatives of the hurwitz zeta function relations to the barnes g function and generalized glaisher s constants are also discussed 1998 elsevier science b v all rights reserved

on the construction and support properties of measure valued diffusions on d subseteq mathbb r d with spatially dependent branching in this paper we construct a measure valued diffusion on d r d whose underlying motion is a diffusion process with absorption at the boundary corresponding to an elliptic operator l 1 2 a b on d r d and whose spatially dependent branching term is of the form x z x z 2 x d where satisfies a very general condition and 0 in the case that and are bounded from above we show that the measure valued process can also be obtained as a limit of approximating branching particle systems we give criteria for extinction survival recurrence transience of the support compactness of the support compactness of the range and local extinction for the measure valued diffusion we also present a number of examples which reveal that the behavior of the measure valued diffusion may be dramatically different from that of the approximating particle systems

the hausdorff measure of the support of two dimensional super brownian motion we show that two dimensional super brownian motion is a multiple of the h hausdorff measure on its closed support where h r r 2 log 1 r log log log 1 r this complements known results in dimensions greater than 2

structural model updating using frequency response function and quasi linear sensitivity equation a method is presented for structural mass and stiffness estimation including damping effects and using vibration data it uses the frequency response function frf and natural frequencies data for finite element model updating the frf data are compiled using the measured displacement velocity or acceleration of the damaged structure a least square algorithm method with appropriate normalization is used for solving the over determined system of equations with noise polluted data sensitivity equation normalization and proper selection of measured frequency points improved the accuracy and convergence in finite element model updating using simulated measurements shows that this method can detect locate and quantify the severity of damage within structures

extremal values of multiple gamma and sine functions abstract we study the extremal values of multiple gamma and sine functions in the fundamental intervals we show the number and locations of the extremal points and prove that all the local maximum and minimum values are greater and less than one respectively

the support of measure valued branching processes in a random environment we consider the one dimensional catalytic branching process introduced by dawson and fleischmann which is a modification of the super brownian motion the catalysts are given by a nonnegative infinitely divisible random measure with independent increments we give sufficient conditions for the global support of the process to be compact and sufficient conditions for noncompact global support since the catalytic process is related to the heat equation compact support may be surprising on the other hand the super brownian motion has compact global support we find that all nonnegative stable random measures lead to compact global support and we give an example of a very rarified levy process which leads to noncompact global support

temporal monotonicity of the solutions of some semilinear parabolic equations with fractional diffusion abstract suppose that the functions g and are nonnegative and satisfy suitable regularity conditions then we prove in this work that the parabolic semilinear problem t u t x u t x g x f u t x x t 0 x r n u 0 x x x r n has a unique positive and time monotone solution here is the fractional laplacian with 0 2 and the source term f is a convex function with f 0 0 moreover using the temporal monotonicity we show that the elliptic equation v x g x f v x x x r d with boundary condition lim x v x 0 has a positive solution we provide also sufficient conditions for the integrability of both solutions

certain classes of series involving the zeta function the authors apply the theory of the double gamma function which was recently revived in the study of determinants of laplacians to evaluate some families of series involving the riemann zeta function introducing a presumably new mathematical constant in the theory of the double gamma function they also systematically evaluate a definite integral of the double gamma function and various classes of series associated with zeta functions some of these definite integrals are expressed in terms of quotients of double gamma functions

some completely monotonic functions involving polygamma functions and an application by using the first binet s formula the strictly completely monotonic properties of functions involving the psi and polygamma functions are obtained as direct consequences two inequalities are proved as an application the best lower and upper bounds of the nth harmonic number are established

sums of certain series of the riemann zeta function abstract the object of the present paper is to investigate systematically several interesting families of summation formulas involving infinite series of the riemann zeta function many of the various results which are unified and generalized here in a remarkably simple manner have received considerable attention in recent years we also present a brief account of a number of analogous results associated with the hurwitz s generalized zeta function

identification of joint properties of a structure using frf data abstract the connections between structural components i e joints are extremely difficult to model accurately by using a pure analytical approach alternatively joint properties can be extracted from experimental data a method for identifying extracting joint properties from the measured frequency response function frf data is presented in this paper one of the major difficulties in accurate identification of joint properties is that the identification results can be significantly affected by various errors in the measured data even if errors in the measured data are at an insignificantly low level say 5 in frfs their effects on the identification can be severe enough so that in some cases the predicted joint properties can be completely irrelevant to the true properties of joints apart from the accuracy of the data used for the identification the accuracy of the identification also significantly depends upon the mathematical formulae used for the identification even with the same experimental data the accuracies of the identification by different methods can be significantly different therefore developing methods that are insensitive to measurement errors is of utmost importance for the identification of joint properties from experimental data in this paper techniques for improving the accuracy of joint identification are discussed it is demonstrated that by using all available information effectively the accuracy of the identification can be much improved both numerical and experimental examples are presented

inequalities involving γ x and γ 1 x we prove that the double inequality 1 x 1 x x x 1 x 1 2 0 with the best possible constants 0 and 3 2 the right hand side refines 1 x 1 1 x 2 x 0 which was proved in 1974 by w gautschi moreover we present sharp inequalities for the product the sum the difference and the ratio of x and 1 x

certain classes of series associated with the zeta function and multiple gamma functions abstract the authors apply the theory of multiple gamma functions which was recently revived in the study of the determinants of the laplacians in order to evaluate some families of series involving the riemann zeta function by introducing a certain mathematical constant they also systematically evaluate this constant and some definite integrals of the triple gamma function various classes of series associated with the zeta function are expressed in closed forms many of these results are also used here to compute the determinant of the laplacian on the four dimensional unit sphere s 4 explicitly

completely monotonic functions of positive order and asymptotic expansions of the logarithm of barnes double gamma function and euler s gamma function abstract we introduce completely monotonic functions of order r 0 and show that the remainders in asymptotic expansions of the logarithm of barnes double gamma function and euler s gamma function give rise to completely monotonic functions of any positive integer order

critical branching in a highly fluctuating random medium a model of one dimensional critical branching superprocess is constructed in a random medium fluctuating both in time and space the medium describes a moving system of point catalysts and branching occurs only in the presence of these catalysts although the medium has an infinite overall density the clumping features of the branching model can be exhibited by rescaling time space and mass by an exactly calculated scaling power which is stronger than in the constant medium case the main technique used is the asymptotic analysis of a generalized diffusion reaction equation in the space time random medium which given the medium prescribes the evolution of the laplace transition functional of the markov branching process

series involving the zeta function and multiple gamma functions the theory of multiple gamma functions which was recently revived in the study of the determinants of the laplacians was applied in several earlier works in order to evaluate some families of series involving the riemann zeta function as well as to compute the determinants of the laplacians here in the present paper the authors address the converse problem and apply various known or new formulas for series associated with the zeta and related functions with a view to developing the corresponding theory of multiple gamma functions and then using these series to compute the determinants of the laplacians on the n dimensional unit sphere s n n 5 6 7 explicitly

spectral functions special functions and the selberg zeta function the functional determinant of an eigenvalue sequence as defined by zeta regularization can be simply evaluated by quadratures we apply this procedure to the selberg trace formula for a compact riemann surface to find a factorization of the selberg zeta function into two functional determinants respectively related to the laplacian on the compact surface itself and on the sphere we also apply our formalism to various explicit eigenvalue sequences reproducing in a simpler way classical results about the gamma function and the barnesg function concerning the latter our method explains its connection to the selberg zeta function and evaluates the related glaisher kinkelin constanta

large deviations for the three dimensional super brownian motion let t dx denote a three dimensional super brownian motion with deterministic initial state 0 dx dx the lebesgue measure let v r 3 r be holder continuous with compact support not identically zero and such that r 3v x dx 0 we show that log p 0 t r 3v x s dx ds bt 3 4 is of order t 1 2 as t for b 0 this should be compared with the known result for the case r 3v x dx 0 in that case the normalization bt 3 4 b 0 must be replaced by bt b r 3v x dx in order that the same statement hold true while this result only captures the logarithmic order the method of proof enables us to obtain complete results for the corresponding moderate deviations and central limit theorems

occupation time large deviations for critical branching brownian motion super brownian motion and related processes we derive a large deviation principle for the occupation time functional acting on functions with zero lebesgue integral for both super brownian motion and critical branching brownian motion in three dimensions our technique based on a moment formula of dynkin allows us to compute the exact rate functions which differ for the two processes obtaining the exact rate function for the super brownian motion solves a conjecture of lee and remillard we also show the corresponding clt and obtain similar results for the superprocesses and critical branching process built over the symmetric stable process of index in r d with d 2 2 d

some two sided inequalities for multiple gamma functions and related results there is an abundant literature on inequalities for the euler s gamma function c and its various related functions yet only very recently several authors began to study inequalities for the barnes double gamma function c 2 here in this paper we aim at presenting several two sided inequalities for the multiple gamma functions c n n 2 3 4 5 in our investigation of these two sided inequalities for the multiple gamma functions c n n 2 3 4 5 we employ and extend a method based upon taylor s formula and express email protected n 1 x as series involving the zeta functions we also give a more convenient explicit form of the multiple gamma functions c n email protected n n being the set of positive integers the main two sided inequalities for the multiple gamma functions c n n 2 3 4 5 which we have presented in this paper are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple gamma functions c n when email protected 6

regularity and irregularity of bolds 1 beta stable super brownian motion this paper establishes the continuity of the density of 1 stable super brownian motion 0 1 for fixed times in d 1 and local unboundedness of the density in all higher dimensions where it exists we also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists and local unboundedness of the occupation density the local time in the spatial parameter for dimensions d 2 where the local time exists

structural damage detection using measured frf data abstract the underlying principle behind structural damage detection techniques is that vibration signature e g modal properties or frequency response function frf data is a sensitive indicator of structural physical integrity and thus can be used to detect damage since indirectly measured modal data contain accumulative errors incurred in modal parameter extraction and provide much less information than frf data it is more reasonable and reliable to use directly measured frf data for structural damage detection in this paper a new damage detection algorithm is formulated to utilize an original analytical model and frf data measured prior and posterior to damage for structural damage detection based on nonlinear perturbation equations of frf data an algorithm has been derived which can be used to determine a damage vector indicating both location and magnitude of damage from perturbation equations of frf data an additional development with respect to the proposed technique is an effective technique introduced for weighting perturbation equations of frf data at selected locations and frequencies so as to reduce influence of measurement errors on accuracy of damage detection to the minimum for extension of the proposed algorithm to cases of incomplete measurement in terms of coordinates an iterative version of the proposed algorithm has been introduced the validity and applicability of the proposed damage detection algorithm have been demonstrated through numerical and experimental studies on a practical plane 3 bay frame structure respectively

a new approach to the single point catalytic super brownian motion a new approach is provided to the super brownian motionx with a single point catalyst c as branching rate we start from a superprocessu with constant branching rate and spatial motion given by the 1 2 stable subordinator we prove that the occupation density measure c ofx at the catalystc is distributed as the total occupation time measure ofu furthermore we show thatxt is determined from c by an explicit representation formula heuristically a mass c ds of particles leaves the catalyst at times and then evolves according to ito s brownian excursion measure as a consequence of our representation formula the density fieldx ofx satisfies the heat equation outside ofc with a noisy boundary condition atc given by the singularly continuous random measure c in particular x isc outside the catalyst we also provide a new derivation of the singularity of the measure c

inequalities for the double gamma function we establish various new upper and lower bounds in terms of the classical gamma and digamma functions for the double gamma function or barnes g function

damage detection in elastic structures using vibratory residual forces and weighted sensitivity a methodology is presented for detecting structural damage in elastic structures by nondestructiv e means measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and or stiffness variations where damage is characterized as a stiffness reduction the current approach is unique among other approaches in that it accounts for 1 variations in system mass system stiffness and mass center locations 2 perturbations of both the natural frequencies and modal vectors and 3 statistical confidence factors for the structural parameters and potential experimental instrumentation error moreover this procedure can be used with either full or reduced models a wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage lexible space structures launch vehicles and satellites are susceptible to structural damage over their operating lives from impact operating loads and fatigue undetected and uncorrected damage can lead to structural deterioration of their members and consequently jeopardize the flight safety of the structure thus numerous damage inspection methods and monitoring procedures have been developed examples include x ray ultrasonic testing magnetic resonance coin tap dye penetration and visual inspection these methods can be time consuming and are local assessments often requir ing the exposure of structural elements to the inspector and equipment for detecting damage as a monitoring system for detecting damage of spacecraft in orbit i e space station freedom none of these methods are appropriate an alterna tive approach which formed the basis for our current study is to recognize the fact that modal vibration test data struc tural natural frequencies and mode shapes characterize the state of the structure 1 therefore postflight and in flight e g monitoring data can be used to distinguish whether changes damage have occurred to the structure by comparing these data with a set of baseline data modal testing as a means of inspection has several advantages direct exposure of struc tural elements is not required and at the same time more of the complete structure can be inspected in one modal test by having appropriately placed sensors the consequences of this are a reduction in schedule and cost the use of vibration test data to locate structural damage has been attempted to evaluate the integrity of offshore oil and gas platforms 2 3 composite laminates 4 continuum struc tures 5 8 and recently large space structures 9 11 the early ana lytical and experimental approaches2 3 had limited success as a result of inadequate instrumentation and addressing only fre quency shifts associated with stiffness changes while ignoring changes in the modal vectors the continuum based meth ods5 8 provide valuable insight into the magnitude of fre quency shifts but their usefulness is severely limited to simple structures bars beams plates with unrealistic boundary con

a space time property of a class of measure valued branching diffusions si d on montre que la diffusion ramifiee d dimensionnelle d indice etudiee par dawson et d autres distribue sa masse sur un support aleatoire de facon uniforme relativement a la mesure de hausdorff

uniform asymptotic expansions for the barnes double gamma function we develop uniform asymptotic approximations for the barnes double gamma function for various parameter values this involves the use of the method of matched asymptotic expansions to solve the defining functional difference equation in various asymptotic regions the resulting solutions provide extremely accurate approximations to the double gamma function we also give applications of our results to functional difference equations that arise in the theory of moving contact lines and acoustic wave diffraction