a distribution is completely determined by its translated moments suppose the random variable x has finite p th moment if p is not an even integer then the distribution of x is completely determined by the sequence of translated moments e x a p a

single layer plate theories applied to the flexural vibration of completely free thick laminates two different refined single layer plate theories are used to analyze the flexural vibration of thick symmetrically laminated rectangular plates with all edges free both theories account for parabolic distribution of the transverse shear strains through the thickness of the plate the first theory includes the transverse normal effect and employs a three dimensional constitutive law whereas the second neglects this effect and employs plane stress reduced stiffnesses numerical results are obtained by using the ritz method characteristic orthogonal polynomials are used in the series representing the displacement functions convergence studies are shown to verify the accuracy of the approximate method the accuracy of the results is further assessed by comparison with results from three dimensional finite element analyses numerical results are presented for various plates including cross ply and angle ply laminated plates the effect of transverse shear and normal deformation on the plate natural frequencies is illustrated by comparing the frequencies of the two higher order theories and the classical plate theory for decreasing length to thickness ratio

free vibration of laminated composite and sandwich plates using global local higher order theory abstract in this paper the global local higher order theory is used to study the free vibration of laminated composite and sandwich plates this global local theory can satisfy the free surface conditions and the geometric and stress continuity conditions at interfaces and the number of unknowns is independent of the layer numbers of the laminate based on the higher order theory a refined three noded triangular element satisfying c1 weak continuity conditions is presented for general laminated composite plates results obtained from present global local higher order theory have been found in good agreement with those obtained from three dimensional elasticity theories moreover this theory is still suitable for analysis of laminated plates with arbitrary layouts and soft core sandwich plates whereas numerical results show that the global higher order and first order theory overestimate natural frequency for these special structures this theory cannot only calculate the natural frequencies but can accurately predict the modal stress distributions in the thickness direction without any smooth techniques

limiting average criteria for nonstationary markov decision processes this paper deals with the so called limiting average criteria for nonstationary markov decision processes with possibly unbounded rewards and borel state space a new set of conditions is provided under which the existence of both a solution to the optimality equations and the limiting average epsilon geq 0 optimal markov policies is derived also a rolling horizon algorithm for computing limiting average epsilon 0 optimal markov policies is developed furthermore the results in this paper are illustrated by several examples such as the water regulation problem

optimal average value convergence in nonhomogeneous markov decision processes abstract we address the undiscounted nonhomogeneous markov decision process with average reward criterion and prove two structural results first we establish equivalence of this problem to a discounted markov decision process by means of an ergodic coefficient embedded in the original problem second we prove for the original problem that the optimal finite horizon average values converge to the infinite horizon optimal average value under an ergodic condition

solving the vibration of thick symmetric laminates by reissner mindlin plate theory and thep ritz method abstract a global p ritz method is employed for vibration analysis of thick rectangular laminates with various combinations of boundary conditions in the method a set of boundary beam characteristic orthogonal polynomials is used as admissible functions in the ritz minimization procedures to incorporate the effects of transverse shear deformation and rotary inertia first order reissner mindlin plate theory is employed several example problems are presented for symmetric laminates of different boundary conditions numerical results are carefully established through convergence studies comparisons are made with the known published values to verify the accuracy of the p ritz method finally results in terms of non dimensional frequency parameters for various boundary conditions aspect ratios and relative thickness ratios are presented

optimization of average rewards of time nonhomogeneous markov chains we study the optimization of average rewards of discrete time nonhomogeneous markov chains in which the state spaces transition probabilities and reward functions depend on time the analysis encounters a few major difficulties 1 notions crucial to homogeneous markov chains such as ergodicity stationarity periodicity and connectivity no longer apply 2 the average reward criterion is under selective i e it does not depend on the decisions in any finite period and thus dynamic programming is not amenable and 3 because of the under selectivity an optimal average reward policy may not be the best in any finite period

nonhomogeneous markov decision processes with borel state space the average criterion with nonuniformly bounded rewards this paper deals with nonhomogeneous markov decision processes with borel state space and nonuniformly bounded rewards under the average criterion first under the minorant type assumption we prove the existence of an appropriate solution to the optimality equations second from the optimality equations we also establish the existence of e 0 optimal markov policies under the additional conditions third some sufficient conditions for the validity of the assumptions in this paper and several examples such as inventory production systems are provided finally as an application of the optimality equations a rolling horizon algorithm is given

refined nine parameter triangular thin plate bending element by using refined direct stiffness method based on a new generalized variational principle a refined direct stiffness method rdsm which can be directly used to improve non conforming elements is proposed the formulation is similar to that of the direct stiffness method dsm but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured the well known bciz nine parameter triangular thin plate bending element is refined by the rdsm to yield a new nine parameter thin plate bending element rt 9 numerical examples are presented to show that the present model passes the patch test and possesses high accuracy

vibration and stability of laminated plates based on a local high order plate theory abstract a local high order deformation theory is used to determine the natural frequencies and buckling loads of laminated composite plates the modal shear and normal stresses are also evaluated the displacement fields in this theory are assumed to be piece wise continuous high order polynomial series layer by layer or sublaminate by sublaminate in the thickness direction this theory accounts for the effects of transverse shear and normal deformation the equations of motion based on this theory are obtained by using hamilton s principle the present analytical solutions for the natural frequencies and buckling loads of rectangular cross ply laminates with fully simple supports are determined by applying the fourier series expansion method the present analytical solutions are compared with the three dimensional elasticity solutions and with analytical solutions obtained from other analyses by global first order and high order lamination theories the effects of aspect side to thickness and elastic modulus to shear modulus ratios on the natural frequencies and buckling loads are also studied

state classification of time nonhomogeneous markov chains and average reward optimization of multi chains in a discrete time nonhomogeneous markov chain tnhmc the states spaces transition probabilities and reward functions at different times may be different in this paper with the confluencity previously introduced we show that the states of a tnhmc can be classified into the branching states and a number of classes of confluent states versus the transient and recurrent states in the time homogeneous case the optimization of average reward in tnhmc s consisting of a single confluent class uni chain have been addressed in a previous paper by the author in this paper we show that with confluencity and the state classification and under some bound conditions we can obtain the necessary and sufficient conditions for optimal policies of the average reward of tnhmcs consisting of multiple confluent classes multi chains just like in the uni chain tnhmc case the sufficient condition does not need to hold in any zero frequently visited time sequence this under selectivity makes the problem not amenable to dynamic programming a direct comparison based approach is used to prove the results the results enhance our understanding of state classification and performance optimization with the notion of confluencity

existence and discovery of average optimal solutions in deterministic infinite horizon optimization we consider the problem of making a sequence of decisions each chosen from a finite action set over an infinite horizon so as to minimize its associated average cost both the feasibility and cost of a decision are allowed to depend upon all of the decisions made prior to that decision moreover time varying costs and constraints are allowed a feasible solution is said to be efficient if it reaches each of the states through which it passes at minimum cost we show that efficient solutions exist and that under a state reachability condition efficient solutions are also average optimal exploiting the characterization of efficiency via a solution s short run as opposed to long run behavior a forward algorithm is constructed which recursively discovers the first second and subsequent decisions of an efficient and hence average optimal infinite horizon solution

optimality conditions for long run average rewards with underselectivity and nonsmooth features we study three existing issues associated with optimization of long run average rewards of time nonhomogeneous markov processes in continuous time with continuous state spaces 1 the underselectivity i e the optimal policies do not depend on their actions in any finite time period 2 its related issue the bias optimality i e policies that optimize both long run average and transient total rewards and 3 the effects of a nonsmooth point of a value function on performance optimization these issues require considerations of the performance in the entire period with an infinite horizon and therefore are not easily solvable by dynamic programming which works backwards in time and takes a local view at a particular time instant in this paper we take a different approach called the relative optimization theory which is based on a direct comparison of the performance measures of any two policies we derive tight necessary and sufficient optimality conditions that take the underselectivity into consideration we derive bias optimality conditions for both long run average and transient rewards and we show that the effect of a wide class of nonsmooth points called semismooth points of a value function on the long run average performance is zero and can be ignored

completeness of location families translated moments and uniqueness of charges a sufficient condition for statistical completeness of location families generated by a probability density in euclidean space is given as an application completeness of families generated by a symmetric stable law is proved our criterion complementing a classical result of wiener and recent work of isenbeck and ruschendorf is in terms of regularity of the generating density and zerofreeness of its characteristic function its proof rests on a local version of the convolution theorem for fourier transforms of tempered distributions a more general version of the criterion is applicable to apparently different problems as is illustrated by giving a simultaneous proof of a theorem on translated moments by p hall and a uniqueness result of m riesz in potential theory

frequency maximization of laminated sandwich plates under general boundary conditions using layerwise optimization method with refined zigzag theory abstract the present paper extends the layerwise optimization lo procedure to the maximization problem of the fundamental frequencies of sandwich plates with fibrous composites and low stiffness core layers frequencies are calculated by the ritz method based on a refined zigzag theory rzt polynomial functions which satisfy at least geometrical boundary conditions with boundary indexes are employed as displacement functions and they enable satisfying arbitrary sets of boundary conditions for rectangular plates results of the experimental modal analysis validate the accuracy of the present calculations and a comparison with results of the classical laminated theory clpt and the first order share deformation theory fsdt supports the effectiveness of the present method optimized results are compared with other typical sets of lay up configurations and this shows the lo method as suitable means to the optimization problem for sandwich plates

identification of additive and polynomial models of mismeasured regressors without instruments abstract we show nonparametric point identification of a measurement error model with covariates that can be interpreted as invalid instruments our main contribution is to replace standard exclusion restrictions with the weaker assumption of additivity in the covariates measurement errors are ubiquitous and additive models are popular so our results combining the two should have widespread potential application we also identify a model that replaces the nonparametric function of the mismeasured regressor with a polynomial in that regressor and other covariates this allows for rich interactions between the variables at the expense of introducing a parametric restriction our identification proofs are constructive and so can be used to form estimators we establish root n asymptotic normality for one of our estimators

a study of transverse normal stress effect on vibration of multilayered plates and shells this paper evaluates transverse normal stress zzeffect on vibration of multilayered structures to this purpose a mixed plate model initially introduced by toledano and murakami has been extended to dynamics analysis of double curved shells these models allow both continuous interlaminar transverse shear and normal stresses as well as the zigzag form of the displacement distribution in the shell thickness directions to be modelled governing equations have been derived by employing a reissner s mixed theorem classical models on the basis of standard displacement formulations have been considered for comparison purposes the evaluations of transverse stress effects have been conducted by comparing constant linear and higher order distributions of transverse displacement components in the plate thickness directions free vibrational response of layered simply supported plates cylindrical and spherical shells made of isotropic as well as orthotropic layers has been analyzed the numerical investigation carried out and comparison with earlier results has concluded that 1 the possibility of describing interlaminar continuous transverse normal stress makes the mixed theories more attractive with respect to other available modelling 2 any refinements of classical models are meaningless unless the effects of interlaminar continuous transverse shear and normal stresses are both taken into account in a multilayered shell theory

free vibrations of laminated rectangular plates analyzed by higher order individual layer theory abstract a higher order plate theory is used in each individual layer to determine the natural frequencies and the relative stress and deflection distributions through the thickness of simply supported rectangular plates this theory approximates the in plane and normal displacements by third and second order functions of the thickness co ordinate respectively the theory satisfies the displacement compatibility and stress equilibrium conditions along the interfaces between adjacent layers numerical results are calculated for the cases of isotropic and orthotropic homogeneous plates and for symmetric and non symmetric cross ply laminates the present theory predicts more modes of free vibration than other approximate theories also the relative stress and deflection distributions obtained by the present higher order theory are in very good agreement with results by three dimensional elasticity theory

rolling horizon procedures in nonhomogeneous markov decision processes by far the most common planning procedure found in practice is to approximate the solution to an infinite horizon problem by a series of rolling finite horizon solutions although many empirical studies have been done this so called rolling horizon procedure has been the subject of few analytic studies we provide a cost error bound for a general rolling horizon algorithm when applied to infinite horizon nonhomogeneous markov decision processes both in the discounted and average cost cases we show that a doeblin coefficient of ergodicity acts much like a discount factor to reduce this error in particular we show that the error goes to zero for any fixed rolling horizon as this doeblin measure of control over the future decreases the theory is illustrated through an application to vehicle deployment

vibration frequencies of simply supported polygonal sandwich plates via kirchhoff solutions this study is concerned with the free vibration of general polygonal sandwich plates based on the reissner mindlin shear deformation plate theory the polygonal plate considered is simply supported on all its straight edges it will be shown herein that the vibration frequencies of such sandwich plates may be computed from their well known kirchhoff plate counterparts via an exact relationship this exact relationship should be useful for the development of approximate vibration formulae for sandwich plates of other shapes boundary and loading conditions and may also serve in checking vibration frequencies computed from shear deformable plate analysis software

complete and symmetrically complete families of distributions on utilise la polarisation pour unifier et etendre les resultats classiques concernant la completude des statistiques d ordre generalisees avec des distributions dominees et non dominees