nonlinear panel flutter by finite element method les equations non lineaires sont calculees a partir de considerations energetiques et la force d etirement non lineaire est formulee en termes de deplacement transversal seul

basically full ideals in local rings abstract let a be a finitely generated module over a noetherian local ring r m we say that a nonzero submodule b of a is basically full in a if no minimal basis for b can be extended to a minimal basis of any submodule of a properly containing b we prove that a basically full submodule of a is m primary and that the following properties of a nonzero m primary submodule b of a are equivalent a b is basically full in a b b mb a m c mb is the irredundant intersection of b irreducible ideals d c b for each cover c of b moreover if b is an m primary submodule of a then b mb a m is the smallest basically full submodule of a containing b and b b is a semiprime operation on the set of nonzero m primary submodules b of a we prove that all nonzero m primary ideals are closed with respect to this operation if and only if m is principal in relation to the closure operation b b we define and study the bf reductions of an m primary submodule d of a that is the m primary submodules c of d such that c d c if g m denotes the form ring of r with respect to m and g m its maximal homogeneous ideal we prove that m n m n for all resp for all large positive integers n if and only if grade g m 0 resp grade m 0 for a regular local ring r m we consider the m primary monomial ideals with respect to a fixed regular system of parameters and determine necessary and sufficient conditions for such an ideal to be basically full

a finite element method for non linear forced vibrations of beams geometric non linearities for large amplitude free and forced vibrations of beam are investigated longitudinal displacement and inertia are included in the formulation the finite element method is used the harmonic force matrix is introduced and derived various out of plane and inplane boundary conditions are considered results showing the dependence of the amplitude on the frequency ratio and on the strain are presented for different boundary conditions and loads it is concluded that the effects of longitudinal deformation and inertia are to reduce the non linearity

integral closedness of complete intersection ideals the aim of this paper is to give some structure theorem of certain integrally closed ideals in noetherian rings let a be a noetherian ring and i an ideal of a then an element x of a is said to be integral over z if x satisfies an equation x c x c 0 in a with ci e i the integral closure i of z is by definition the set of elements in a which are integral over z and the ideal z is called integrally closed if f i let ua z resp ht i denote the smallest number of elements in systems of generators for z resp the height of i let min a z be the set of minimal prime divisors of i in this paper we shall study the problem when the ideals z of a such that ua z ht z are integrally closed and our result is stated as follows

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

normalization of modules we introduce techniques to derive estimates for the degrees of the generators of the integral closure of several classes of rees algebras of modules and to bound the length of normalization processes in the case of regular base rings the bounds are expressed in terms of buchsbaum rim multiplicities and a module version of briancon skoda numbers

bifurcations and internal resonances in space curved rods abstract the paper discusses a geometrically non linear model of space curved beams the timoshenko type model is used which includes the shear effects and rotatory inertia the motion of the system is described by a non linear matrix equation which accounts for non linearities up to the second order to solve the non linear problem discretization methods based on the galerkin method are used and the resulting non linear eigenvalue problem is then solved by the continuation methods the analysis of the discretized problem allows the study of the bifurcations of solutions the post bifurcation analysis is used to explain the phenomenon of internal resonance which is of much importance in the prediction of the dynamic response of the analyzed systems the approach is illustrated by numerical examples which consider the free vibration of beams and circular arches with different boundary conditions

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

monoidal extensions of a locally quasi unmixed ufd abstract let r be a locally quasi unmixed domain a b 1 b n an asymptotic sequence in r i a b 1 b n r and s r b 1 a b n a r i a the monoidal transform of r with respect to i it is shown that s is a locally quasi unmixed domain a b 1 a b n a is an asymptotic sequence in s and there is a one to one correspondence between the asymptotic primes a i of i and the asymptotic primes a a s of a s i s moreover if a b 1 b n is an r sequence this extends to a one to one correspondence between ass r r i and ass s s a s in the case that r is a unique factorization domain the height one prime ideals of s are examined to determine how far s is from being a ufd a complete description is given of which height one prime ideals p of s are principal or have a principal primary ideal in the case that p r has height 1 if the prime divisors of a satisfy a mild condition a similar description is given in the case that p r has height 1 these are applied to give similar results for the rees ring r 1 t i t where t is an indeterminate

vibration analysis of a non linear beam subjected to moving loads by using the galerkin method abstract this paper presents the analysis of dynamic deflections of a beam including the effects of geometric non linearity subjected to moving vehicle loads the beam is assumed to be elastic and simply supported with immovable ends and the vehicles are assumed to be single degree of freedom spring mass damper with the vehicles moving on the beam from one end to the other the dynamic reflections of the beam and vehicles are computed by using the galerkin method thus the dynamic deflections are assumed to be a set of time functions multiplied by approximate functions respectively and the time functions are numerically computed by solving the non linear differential equations by the newmark method

vibration and buckling analysis of rectangular plates with nonlinear elastic end restraints against rotation abstract the fundamental natural frequencies and buckling loads of a rectangular plate with nonlinearly rotational restraints are obtained by using the finite element technique if the rotational springs are unsymmetric the iterative scheme must be employed to acquire the solutions of the nonlinear problem the values which describe the free vibration and stability behaviour of the plate will increase when either the parameters of rotational spring or the initial rotational angles increase incidentally it can be concluded that these results grown nonlinearly with respect to either the linear or nonlinear rotational spring constants finally both the frequency and stability parameters are evaluated for several boundary conditions which are quite useful in engineering analysis and design

sensor selection for estimation with correlated measurement noise in this paper we consider the problem of sensor selection for parameter estimation with correlated measurement noise we seek optimal sensor activations by formulating an optimization problem in which the estimation error given by the trace of the inverse of the bayesian fisher information matrix is minimized subject to energy constraints fisher information has been widely used as an effective sensor selection criterion however existing information based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics by contrast here we derive the closed form of the fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime and develop both a convex relaxation approach and a greedy algorithm to find near optimal solutions we further extend our framework of sensor selection to solve the problem of sensor scheduling where a greedy algorithm is proposed to determine non myopic multi time step ahead sensor schedules lastly numerical results are provided to illustrate the effectiveness of our approach and to reveal the effect of noise correlation on estimation performance

lagrange type formulation for finite element analysis of non linear beam vibrations abstract a lagrange type formulation for finite element analysis of non linear vibrations of immovably supported beams is presented two equations of motion coupled in axial and transverse displacements are derived by using lagrange s equations by neglecting the in plane inertial effects these equations are written in terms of the transverse displacement alone upon defining certain properties for the non linear oscillatory behaviour of the transverse displacement the governing equation is reduced to an equation in space alone from which the eigenvalue like quantity is computed the governing equation is solved in two ways a direct iteration technique is used in the first method to compute a numerically exact mode shape and the corresponding frequency a rayleigh quotient type of formulation similar to linear vibration analysis is used in the second approach to evaluate the frequency of vibration for a fundamental mode which is determined from a linear fem model and is maintained constant at all amplitudes numerical results are compared with available results and they corroborate the observations of earlier research workers

integrally closed modules over two dimensional regular local rings this paper is based on work of rees on integral closures of modules and initiates the study of integrally closed modules over two dimensional regular local rings in analogy with the classical theory of complete ideals of zariski the main results can be regarded as generalizations of zariski s product theorem they assert that the tensor product mod torsion of integrally closed modules is integrally closed that the symmetric algebra mod torsion of an integrally closed module is a normal domain and that the first fitting ideal of an integrally closed module is an integrally closed ideal a construction of indecomposable integrally closed modules is also given the primary technical tool is a study of the buchsbaum rim multiplicity

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

application of the ritz method to the analysis of non linear free vibrations of beams this paper presents an analytical solution for geometrically non linear free vibrations of beams with elastically supported ends in the horizontal direction the equation of motion is obtained by employing hamilton s principle and assuming that horizontal inertia forces can be neglected the ritz method with a continuum solution and an iterative procedure are used for determining the frequencies and non linear modes of vibrations the orthogonality conditions for these modes are also discussed numerical results for various beam boundary conditions are presented and compared with available results

on linear complete intersections or some of its localizations becomes a complete intersection is a major factor in section 1 we describe a jacobian formulation of serre s normality criterion for symmetric algebras it is used to provide several classes of examples of normal and non normal rees algebras of prime ideals in regular domains adding to the catalog of cohen macaulay domains that are symmetric algebras we examine almost complete intersections these bear a close relationship to certain height three ideals of

integrally closed and componentwise linear ideals in a two dimensional regular local ring integrally closed ideals have a unique factorization property and their associated graded ring is cohen macaulay in higher dimension these properties do not hold and the goal of the paper is to identify a subclass of integrally closed ideals for which they do we restrict our attention to 0 dimensional homogeneous ideals in polynomial rings r of arbitrary dimension we identify a class of integrally closed ideals the goto class mathcal g which is closed under product and it has a suitable unique factorization property ideals in mathcal g have a cohen macaulay associated graded ring if either they are monomial or dim r 3 our approach is based on the study of the relationship between the notions of integrally closed contracted full and componentwise linear ideals

free vibrations of a certain geometrically nonlinear system with initial imperfection the equations of motion of a beam are assumed within the framework of the moderately large bending theory the effects of an initial imperfection and amplitude on the nonlinear vibration frequency and value of axial internal force in a beam are presented for solving the problem the lindstedt poincare method is used

objective bayesian analysis of spatially correlated data spatially varying phenomena are often modeled using gaussian random fields specified by their mean function and covariance function the spatial correlation structure of these models is commonly specified to be of a certain form e g spherical power exponential rational quadratic or matern with a small number of unknown parameters we consider objective bayesian analysis of such spatial models when the mean function of the gaussian random field is specified as in a linear model it is thus necessary to determine an objective or default prior distribution for the unknown mean and covariance parameters of the random field we first show that common choices of default prior distributions such as the constant prior and the independent jeffreys prior typically result in improper posterior distributions for this model next the reference prior for the model is developed and is shown to yield a proper posterior distribution a further attractive property of the reference prior is that it can be used

asymptotic lech s inequality abstract we explore the classical lech s inequality relating the hilbert samuel multiplicity and colength of an m primary ideal in a noetherian local ring r m we prove optimal versions of lech s inequality for sufficiently deep ideals in characteristic p 0 and we conjecture that they hold in all characteristics our main technical result shows that if r m has characteristic p 0 and r is reduced equidimensional and has an isolated singularity then for any sufficiently deep m primary ideal i the colength and hilbert kunz multiplicity of i are sufficiently close to each other more precisely for all e 0 there exists n 0 such that for any i r with l r i n we have 1 e l r i e hk i 1 e l r i

the goto numbers of parameter ideals abstract let q be a parameter ideal of a noetherian local ring r m the goto number g q of q is the largest integer g such that q m g is integral over q we examine the values of g q as q varies over the parameter ideals of r we concentrate mainly on the case where dim r 1 and many of our results concern parameter ideals of a numerical semigroup ring

dynamic bit allocation for object tracking in wireless sensor networks in this paper we study the target tracking problem in wireless sensor networks wsns using quantized sensor measurements where the total number of bits that can be transmitted from sensors to the fusion center is limited at each time step of tracking a total of r available bits need to be distributed among the n sensors in the wsn for the next time step the optimal solution for the bit allocation problem can be obtained by using a combinatorial search which may become computationally prohibitive for large n and r therefore we develop two new suboptimal bit allocation algorithms which are based on convex optimization and approximate dynamic programming a dp we compare the mean squared error mse and computational complexity performances of convex optimization and a dp with other existing suboptimal bit allocation schemes based on generalized breiman friedman olshen and stone gbfos algorithm and greedy search simulation results show that a dp convex optimization and gbfos yield similar mse performance which is very close to that based on the optimal exhaustive search approach and they outperform greedy search and nearest neighbor based bit allocation approaches significantly computationally a dp is more efficient than the bit allocation schemes based on convex optimization and gbfos especially for a large sensor network

a variant of wangʼs theorem in this paper we give a new formula of j j for any parameter ideal j in a gorenstein local ring r of positive characteristic in terms of test ideals j j j jd 1 where jd 1 denotes the jd 1 test ideal of r as an application we give a variant of wang s theorem namely we prove that if j is a parameter ideal in a cohen macaulay local ring r m of dimension d 2 with j ms then j m d 1 s 1 resp j m d 1 s 1 1 is integral over j resp if r is not regular moreover we prove that after reduction to characteristic p 0 a similar assertion holds true for cohen macaulay q gorenstein normal local domain essentially of finite type over a field of characteristic zero under some extra assumption

projectively full ideals in noetherian rings ii abstract let r be a noetherian commutative ring with unit 1 0 and let i be a regular proper ideal of r the set p i of integrally closed ideals projectively equivalent to i is linearly ordered by inclusion and discrete there is naturally associated to p i a numerical semigroup s i we have s i n if and only if every element of p i is the integral closure of a power of the largest element j of p i if this holds the ideal j and the set p i are said to be projectively full if i is invertible and r is integrally closed we prove that p i is projectively full we investigate the behavior of projectively full ideals in various types of ring extensions we prove that a normal ideal i of a local ring r m is projectively full if i m 2 and both the associated graded ring g m and the fiber cone ring f i are reduced we present examples of normal local domains r m of altitude two for which the maximal ideal m is not projectively full

a semi analytical approach to the non linear dynamic response problem of beams at large vibration amplitudes part ii multimode approach to the steady state forced periodic response abstract the semi analytical approach to the non linear dynamic response of beams based on multimode analysis has been presented in part i of this series of papers azrar et al 1999 journal of sound and vibration 224 183 207 1 the mathematical formulation of the problem and single mode analysis have been studied the objective of this paper is to take advantage of applying this semi analytical approach to the large amplitude forced vibrations of beams various types of excitation forces such as harmonic distributed and concentrated loads are considered the governing equation of motion is obtained and can be considered as a multi dimensional form of the duffing equation using the harmonic balance method the equation of motion is converted into non linear algebraic form techniques of solution based on iterative incremental procedures are presented the non linear frequency and the non linear modes are determined at large amplitudes of vibration the basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated the percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution also the percentage contributions of the higher modes to the bending moment near to the clamps are given in order to determine accurately the error introduced in the non linear bending stress estimated by different approximations solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency the non linear deflection shapes in various regions of the solution the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes the numerical results obtained here for the non linear forced response are compared with those from the linear theory with available non linear results based on various approaches and with the single mode analysis

the almost gorenstein rees algebras of parameters abstract there is given a characterization for the rees algebras of parameters in a gorenstein local ring to be almost gorenstein graded rings a characterization is also given for the rees algebras of socle ideals of parameters the latter one shows almost gorenstein rees algebras rather rarely exist for socle ideals if the dimension of the base local ring is greater than two

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

monoidal extensions of a cohen macaulay unique factorization domain let a be a noetherian cohen macaulay domain b c 1 c g an a sequence j b c 1 c g a and b a j b then b is cohen macaulay there is a natural one to one correspondence between the sets ass b b bb and ass a a j and each q ass a a j has height g 1 if b does not have unique factorization then some height one prime ideals p of b are not principal these primes are identified in terms of j and p a and we consider the question of how far from principal they can be if a is integrally closed necessary and sufficient conditions are given for b to be integrally closed and sufficient conditions are given for b to be a ufd or a krull domain whose class group is torsion finite or finite cyclic it is shown that if p is a height one prime ideal of b then p a also has height one if and only if b p and thus p a has height one for all but finitely many of the height one primes p of b if a has unique factorization a description is given of whether or not such a prime p is a principal prime ideal or has a principal primary ideal in terms of properties of p n a a similar description is also given for the height one prime ideals p of b with p a of height greater than one if the prime factors of b satisfy a mild condition if a is a ufd and b is a power of a prime element then b is a krull domain with torsion class group if and only if j is primary and integrally closed and if this holds then b has finite cyclic class group also if j j is not primary then for each height one prime ideal p contained in at least one but not all prime divisors of j it holds that the height one prime pa 1 b b has no principal primary ideals this applies in particular to the rees ring r a 1 t tj as an application of these results it is shown how to construct for any finitely generated abelian group g a monoidal transform b a j b such that a is a ufd b is cohen macaulay and integrally closed and g cl b the divisor class group of b

direct and inverse dynamics of a very flexible beam abstract the problem of direct and inverse dynamics of a very flexible plane beam was discussed and analyzed direct dynamics is referred to as an ordinary dynamics problem where initial conditions are known and where three conditions either forces or motion are prescribed at each end of the beam as boundary conditions partially or fully inverse dynamics are defined to be the case when some or all of the conditions are moved from one end to the other so that one end is overprescribed including both forces and motion and the constraints at the other end of the beam are partially or fully unspecified a new model for direct and inverse dynamics of a straight or curved planar beam at small strains and large deflections has been derived lagrange equations in a local frame of reference and a finite element method were utilized for the formulation the direct dynamics problems were solved by a fast and relatively simple linear iteration method and verified by results of existing programs for specific cases this formulation is particularly useful for more complicated constitutive relations on the other hand inverse dynamics solutions were stable for only short periods of time this result demonstrates the need for further research in the area of inverse dynamics practical application of the study may be considered in the field of robotics where very flexible beams may be used in order to reduce the number of arms and actuators in a robotics system

hierarchical finite element analyses of geometrically non linear vibration of beams and plane frames geometrically non linear vibrations of beams and plane frameworks are analyzed by the hierarchical finite element method hfem two main points are of interest the first is to compare polynomials trigonometric functions and beam eigenfunctions as displacement shape functions for beam hierarchical finite elements the second is to examine the suitability of the hfem for time domain non linear analyses

calculation of eigenvalue and eigenvector derivatives for nonlinear beam vibrations a beam with immovable ends under large amplitude oscillations is axially subjected to an amplitudedependent stretching force which is induced by the geometrical nonlinearity the design sensitivity analysis for such a beam is investigated in this study two variational formulations pertaining to nonlinear beam vibration based on two different approximations of nonlinear stretching force are presented the analytical equations of design sensitivity analysis for these nonlinear equations are then derived finally a computational scheme using the finite element method is developed to calculate the design sensitivity derivatives of the eigenvalue and eigenvector numerically the numerical results show that the proposed algorithm for calculating design derivatives of nonlinear eigenvalues and eigenvectors is valid and compared with the direct finite difference method the proprosed algorithm is efficient

the buchsbaum rim polynomial of a module abstract for a noetherian local ring r m the hilbert functions of m primary ideals provide considerable information about constructions and singularities coded by the ideal for a module e which is the analogue of such ideals e is a proper submodule of a free module so that the quotient has finite length buchsbaum and rim defined a similar function and introduced the notion of buchsbaum rim multiplicity br e of the module unlike in the ideal case the information about these functions is still scant when r is cohen macaulay of dimension d 1 and e has rank r we develop some of their properties sufficiently enough to establish the following bound for the reduction number of the module e r e d r 1 br e 2 1 the same techniques lead to bounds on the number of generators of the integral closure of the powers of certain ideals and modules

global optimization algorithms for linearly constrained indefinite quadratic problems abstract in this paper we consider the problem of finding the constrained global optimum of an indefinite quadratic function since such a function may have many local optima finding the global optimum is a computationally difficult problem we give an overview of the most important methods used which include benders decomposition concave programming approaches enumerative techniques and bilinear programming

bounds related to projective equivalence classes of ideals let z be a regular ideal in noetherian ring r and let i denote the integral closure of i a situation which is often of interest is when there is an integer b z 2 0 such that i b a e i for all n 2 1 for instance in an analytically unramified local ring such a b z exists for all i now recall that the ideal h is projectively equivalent to i if there are positive integers r and s with h i in section 1 we make the easy observation that the existence of b z as above is an invariant of the projective equivalence class of i that is if such a b z exists and if the ideal h is projectively equivalent to z then there is a b h with h bch n c h for all n 2 1 of course it may happen that b h b z the main purpose of section 1 is to study the stronger condition that there exist a fixed integer b 3 0 such that for all ideals h projectively equivalent to z h c h for all n 1 we make use of a key result namely that given z there exists an integer d such that for any ideal h projectively equivalent to z one can write hd p for some s let s 2 1 be an integer and let the ideal k be a reduction of i this means there is an integer e 20 depending on s and k with k z z in section 2 we discuss a situation in which e can in fact

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

effective normality criteria for algebras of linear type abstract the algebras studied here are subalgebras of rings of polynomials generated by 1 forms so called rees algebras with coefficients in a noetherian ring given a normal domain r and a torsionfree module e with a free resolution f 2 f 1 f 0 e 0 we study the role of the matrices of syzygies in the normality of the rees algebra of e when the rees algebra r e and the symmetric algebra s e coincide the main results characterize normality in terms of the ideal ic s e and of the completeness of the first s symmetric powers of e where c rank and s rankf0 ranke it requires that r be a regular domain special results under broader conditions on r are still more effective

sensor selection based on generalized information gain for target tracking in large sensor networks in this paper sensor selection problems for target tracking in large sensor networks with linear equality or inequality constraints are considered first we derive an equivalent kalman filter for sensor selection i e generalized information filter then under a regularity condition we prove that the multistage look ahead policy that minimizes either the final or the average estimation error covariances of next multiple time steps is equivalent to a myopic sensor selection policy that maximizes the trace of the generalized information gain at each time step moreover when the measurement noises are uncorrelated between sensors the optimal solution can be obtained analytically for sensor selection when constraints are temporally separable when constraints are temporally inseparable sensor selections can be obtained by approximately solving a linear programming problem so that the sensor selection problem for a large sensor network can be dealt with quickly although there is no guarantee that the gap between the performance of the chosen subset and the performance bound is always small numerical examples suggest that the algorithm is near optimal in many cases finally when the measurement noises are correlated between sensors the sensor selection problem with temporally inseparable constraints can be relaxed to a boolean quadratic programming problem which can be efficiently solved by a gaussian randomization procedure along with solving a semi definite programming problem numerical examples show that the proposed method is much better than the method that ignores dependence of noises

a discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions abstract the purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams which may replace if sufficient degrees of freedom are used the previously developed continuous nonlinear beam constrained vibration models the discrete model proposed is an n degrees of freedom n dof system made of n masses placed at the ends of solid bars connected by torsional springs presenting the beam flexural rigidity the large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs the calculations made allowed application of the semi analytical model developed previously for nonlinear structural vibration involving three tensors namely the mass tensor m ij the linear rigidity tensor k ij and the nonlinearity tensor b ijkl by application of hamilton s principle and spectral analysis the nonlinear vibration problem is reduced to a nonlinear algebraic system examined for increasing numbers of dof the results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model for various fixed boundary conditions for both the linear frequencies and the nonlinear backbone curves and also for the corresponding mode shapes the model validated here for the simply supported and clamped ends may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions

optimal periodic sensor scheduling in networks of dynamical systems we consider the problem of finding optimal time periodic sensor schedules for estimating the state of discrete time dynamical systems we assume that multiple sensors have been deployed and that the sensors are subject to resource constraints which limits the number of times each can be activated over one period of the periodic schedule we seek an algorithm that strikes a balance between estimation accuracy and total sensor activations over one period we make a correspondence between active sensors and the nonzero columns of the estimator gain we formulate an optimization problem in which we minimize the trace of the error covariance with respect to the estimator gain while simultaneously penalizing the number of nonzero columns of the estimator gain this optimization problem is combinatorial in nature and we employ the alternating direction method of multipliers admm to find its locally optimal solutions numerical results and comparisons with other sensor scheduling algorithms in the literature are provided to illustrate the effectiveness of our proposed method

normal sally modules of rank one in this paper we explore the structure of the normal sally modules of rank one with respect to an m m primary ideal in a nagata reduced local ring r which is not necessary cohen macaulay as an application of this result when the base ring is cohen macaulay analytically unramified the extremal bound on the first normal hilbert coefficient leads to the depth of the associated graded rings g with respect to a normal filtration is at least dim r 1 dim r 1 and g turns in to cohen macaulay when the third normal hilbert coefficient is vanished

free vibration of structures with cubic non linearity remarks on amplitude equation and rayleigh quotient in the paper several aspects concerning the formulation of and solution to amplitude equations for free vibration of systems with cubic non linearity are discussed in detail the use of several possible constraint equations to achieve the non trivial solution to the amplitude equation is also presented the well known concept of the rayleigh quotient is extended to the non linear case of interest some general remarks on the formulation of the non linear amplitude equation and the non linear rayleigh quotient are also presented moreover the introduced rayleigh quotient is used to develop a new and suitably efficient method to solve amplitude equations the accuracy of solutions obtained by means of some widely used methods of analysis of free vibration problems is also presented it is found that the galerkin method gives the most accurate results

integrally closed almost complete intersection ideals abstract let a m be a local ring we study the existence and structure of the m primary integrally closed ideals generated by dim a 1 elements

rees algebras of f regular type abstract we study the f regularity of rees algebras r i a it in terms of the global f regularity of the blowing up x proj r i of spec a as it reads global f regularity is a global analog of strong f regularity defined via splitting of frobenius maps in prime characteristic and these notions are extended to characteristic zero by reduction modulo p 0 we study in detail the case where a m is a two dimensional local ring and i is an m primary ideal in characteristic zero the condition for r i to have f regular type is described in terms of the dual graph of a resolution x on which i o x is invertible we also prove some miscellaneous results concerning singularities of rees algebras and extended rees algebras of higher dimension

the equality i2 qi in sequentially cohen macaulay rings let r be a sequentially cohen macaulay local ring and assume that dimr 2 or that dimr 1 and e r 1 then the equality i2 qi holds true for every good parameter ideal q of r contained in a sufficiently high power of the maximal ideal m where i q rm the structure of the graded rings gr i n 0in in 1 r i n 0in and r i n zin associated to i is explored in connection to their sequential cohen macaulayness

algorithms for leader selection in stochastically forced consensus networks we are interested in assigning a pre specified number of nodes as leaders in order to minimize the mean square deviation from consensus in stochastically forced networks this problem arises in several applications including control of vehicular formations and localization in sensor networks for networks with leaders subject to noise we show that the boolean constraints which indicate whether a node is a leader are the only source of nonconvexity by relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value we also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound for networks with leaders that perfectly follow their desired trajectories we identify an additional source of nonconvexity in the form of a rank constraint removal of the rank constraint and relaxation of the boolean constraints yields a semidefinite program for which we develop a customized algorithm well suited for large networks several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms

target location estimation in sensor networks with quantized data a signal intensity based maximum likelihood ml target location estimator that uses quantized data is proposed for wireless sensor networks wsns the signal intensity received at local sensors is assumed to be inversely proportional to the square of the distance from the target the ml estimator and its corresponding crameacuter rao lower bound crlb are derived simulation results show that this estimator is much more accurate than the heuristic weighted average methods and it can reach the crlb even with a relatively small amount of data in addition the optimal design method for quantization thresholds as well as two heuristic design methods are presented the heuristic design methods which require minimum prior information about the system prove to be very robust under various situations

symmetric powers of complete modules over a two dimensional regular local ring this is the published version also available here http dx doi org 10 1090 s0002 9947 97 01819 9 first published in trans amer math soc in 1997 published by the american mathematical society

decentralized estimation with dependent gaussian observations this paper considers decentralized estimation with correlated noises under the bayesian framework for a tandem network with correlated additive gaussian noises we establish that threshold quantizers on local observations are optimal in the sense of maximizing fisher information at the fusion center this is true despite the fact that subsequent estimators may differ at the fusion center depending on the statistical distribution of the parameter to be estimated in addition it is always beneficial to have the better sensor i e the one with higher signal to noise ratio serve as the fusion center in a tandem network finally we identify different correlation regimes in terms of their impact on the estimation performance these include the well known case where negatively correlated noise benefits estimation performance as it facilitates noise cancellation as well as two distinct regimes with positively correlated noises

sensor selection in distributed multiple radar architectures for localization a knapsack problem formulation widely distributed multiple radar architectures offer parameter estimation improvement for target localization for a large number of radars with full resource allocation the achievable localization minimum estimation mean square error mse may extend beyond the system predetermined performance goals in this paper performance driven resource allocation schemes for multiple radar systems are proposed two operational policies are considered in the first the number of transmit and receive antennas employed in the estimation process is minimized by effectively selecting a subset of active antennas such that the required mse performance threshold is attained in the second an optimal subset of active antennas of predetermined size is selected such that the localization mse is minimized these problems are formulated in a combinatorial optimization framework as a knapsack problem kp where the goal is to obtain a performance level with the lowest cost in terms of active system elements the cramer rao bound crb is used as a performance metric cost parameters representing operational cost or any other utilization constraints on the antennas are associated with each of the radars these are incorporated in the kp formulation integrating decision making factors in the selection process antenna subset selection is implemented through a heuristic algorithm by successively selecting antennas so as to minimize the performance gap between the temporal crb and a given mse goal or a given subset size the proposed approximate algorithms offer considerable reduction in computational complexity when compared with an exhaustive search by minimizing the number of operational antennas needed to complete the task this concept introduces savings in both communication link needs and central processing load in addition to the operational ones

integral closure and generic elements abstract let r m be a formally equidimensional local ring with depth r 2 and i a 1 a n an m primary ideal in r the main result of this paper shows that if i is integrally closed then so is its image modulo a generic element that is if t r x 1 x n a 1 x 1 a n x n then i t i t