time discretization of hamiltonian dynamical systems abstract difference equations for hamiltonian systems are derived from a discrete variational principle the difference equations completely determine piecewise linear continuous trajectories which exactly conserve the hamiltonian function at the midpoints of each linear segment a generating function exists for transformations between the vertices of the trajectories existence and uniqueness results are present as well as simulation results for a simple pendulum and an inverse square law system

generalized beta prior models on fraction defective in reliability test planning in many reliability analyses the probability of obtaining a defective unit in a production process should not be considered constant even though the process is stable and in control engineering experience or previous data of similar or related products may often be used in the proper selection of a prior model to describe the random fluctuations in the fraction defective a generalized beta family of priors several maximum entropy priors and other prior models are considered for this purpose in order to determine the acceptability of a product based on the lifelengths of some test units failure censored reliability sampling plans for location scale distributions using average producer and consumer risks are designed our procedure allows the practitioners to incorporate a restricted parameter space into the reliability analysis and it is reasonably insensitive to small disturbances in the prior information impartial priors are used to reflect prior neutrality between the producer and the consumer when a consensus on the elicited prior model is required nonetheless our approach also enables the producer and the consumer to assume their own prior distributions the use of substantial prior information can in many cases significantly reduce the amount of testing required however the main advantage of utilizing a prior model for the fraction defective is not necessarily reduced sample size but improved assessment of the true sampling risks an example involving shifted exponential lifetimes is considered to illustrate the results

on variations in discrete mechanics and field theory in this paper we propose the difference variational approach with variable step length for discrete mechanics and field theory based upon the hamilton s principle for the vertical variations and the horizontal variations we get the equation of motion and the relevant relations between the equation of motion and conservation law of the energy energy momentum tensor for continuous as well as for the discrete systems respectively for those discrete cases these relations determine the variable step length of the differences in addition by taking the double operation of vertical exterior differential on action we show that there should exist the euler lagrange cohomology for both continuous and variable step length difference cases in general this indicates that the necessary and sufficient condition for symplectic multisymplectic structure preserving properties is the relevant euler lagrange one form being closed in each case our approach can be applied to both the lagrangian formalism and the hamiltonian formalism via discrete legendre transformation for the difference discrete mechanics and field theory c 2003 american institute of physics

joint reliability and weighted importance measures of a k out of n system with random weights for components abstract in this paper the joint importance of two components in a k out of n system with random weights for components is studied rahmani et al 2016 introduced the weighted importance wi measure corresponding to component i and investigated its properties we generalize this measure for two components i and j and its relation with joint reliability importance is studied finally the stochastic behavior of this measure is discussed

symplectic energy momentum preserving variational integrators the purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving to do this a space time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy criteria for the solvability of the time steps and some numerical examples are given

k out of n systems reliability and availability analyses are recognized as essential for guiding decision makers in the implementation of actions addressed to improve the technical and economical performance of complex systems for industrial systems with reparable components the most interesting parameter used to drive maintenance is the stationary availability in this regard the present paper proposes an exact formula for computing the system stationary availability of a k out of n system such a formula is proved to be in agreement with the fundamental theorem of markov chains then a multi objective mathematical model is formulated for choosing the optimal system configuration design the pareto front is developed using the lexicographic goal programming lgp method and the topsis method is successively implemented to choose the k out of n configuration that represents the best compromise between the considered objective functions a numerical example is provided stationary availability formula proposed for k out of n systems validation of the proposed formula by markov chains design of a k out of n system selection of pareto solution by means of topsis multi criteria method

long term dissipativity of time stepping algorithms for an abstract evolution equation with applications to the incompressible mhd and navier stokes equations abstract this paper examines the long term dissipativity and unconditional non linear stability of time integration algorithms for the incompressible mhd equations the results apply as a particular case to the uncoupled incompressible navier stokes equations the analysis is performed in the setting defined by an abstract evolution equation possessing the same long term dissipative structure as the above physical systems a general class of time stepping schemes is analyzed in this context showing the non linear unconditional stability and long term dissipativity of particular members of this family of algorithms in particular algorithms showing these strong properties which additionally involve the solution of a linear problem at each time step are identified a particular linear algorithm is shown to exhibit optimal long term dissipative properties and to possess an algorithmic global attractor these abstract results apply rigorously to galerkin mixed finite element discretizations of the problem to this end it is shown that such galerkin type projection inherits the dissipative properties of the continuum problem computational aspects involved in the numerical implementation of these methods are addressed and illustrated in representative numerical simulations

discrete time lagrangian mechanics on lie groups with an application to the lagrange top we develop the theory of discrete time lagrangian mechanics on lie groups originated in the work of veselov and moser and the theory of lagrangian reduction in the discrete time setting the results thus obtained are applied to the investigation of an integrable time discretization of a famous integrable system of classical mechanics the lagrange top we recall the derivation of the euler poinsot equations of motion both in the frame moving with the body and in the rest frame the latter ones being less widely known we find a discrete time lagrange function turning into the known continuous time lagrangian in the continuous limit and elaborate both descriptions of the resulting discrete time system namely in the body frame and in the rest frame this system naturally inherits poisson properties of the continuous time system the integrals of motion being deformed the discrete time lax representations are also found kirchhoff s kinetic analogy between elastic curves and motions of the lagrange top is also generalised to the discrete context

assessing the lifetime performance index of rayleigh products based on the bayesian estimation under progressive type ii right censored samples abstract lifetime performance assessment is important in service or manufacturing industries hence lifetime performance index c l is used to measure the potential and performance of a process where l is the lower specification limit in this paper assuming the conjugate prior distribution and squared error loss function this study constructs a bayes estimator under the rayleigh distribution with the progressive type ii right censored sample the bayes estimator of c l is then utilized to develop a credible interval in the condition of known l moreover we also propose a bayesian test to assess the lifetime performance of products finally we give two examples and the monte carlo simulation to assess the behavior of the lifetime performance index c l moreover the purchasers can then employ the credible interval and the bayesian test to determine whether the product performance adheres to the required level

bayesian analysis of binary sequences this manuscript details bayesian methodology for learning by example with binary n sequences encoding the objects under consideration priors prove influential conformable priors are described laplace approximation of bayes integrals yields posterior likelihoods for all n sequences this involves the optimization of a definite function over a convex domain efficiently effectuated by the sequential application of the quadratic program

bdf like methods for nonlinear dynamic analysis we present several time integration algorithms of second order accuracy that are numerically simple and effective for nonlinear elastodynamic problems these algorithms are based on a general four step scheme that has a resemblance to the backward differentiation formulas we also present an extension to the composite strategy of the bathe method appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity and less dissipative members of each algorithm have been identified we demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions and test these algorithms with several three dimensional nonlinear elastodynamic problems involving large deformations and rotations employing st venant kirchhoff and compressible neo hookean hyperelastic material models these tests show that stable computations are obtained with the proposed algorithms in nonlinear situations where the trapezoidal rule encounters a well known instability

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

bayesian prediction for flowgraph models with covariates an application to bladder carcinoma statistical flowgraph models are an efficient tool to model multi state stochastic processes they support both frequentist and bayesian approaches inclusion of covariates is also available in this paper we propose an easy way to perform a bayesian approach with covariates results are presented with an application to bladder carcinoma data

boundary regularity criteria for the 6d steady navier stokes and mhd equations abstract it is shown in this paper that suitable weak solutions to the 6d steady incompressible navier stokes and mhd equations are holder continuous near boundary provided that either r 3 b r u x 3 d x or r 2 b r u x 2 d x is sufficiently small which implies that the 2d hausdorff measure of the set of singular points near the boundary is zero this generalizes recent interior regularity results by dong strain 5

discrete versions of some classical integrable systems and factorization of matrix polynomials discrete versions of several classical integrable systems are investigated such as a discrete analogue of the higher dimensional force free spinning top euler arnold equations the heisenberg chain with classical spins and a new discrete system on the stiefel manifold the integrability is shown with the help of a lax pair representation which is found via a factorization of certain matrix polynomials the complete description of the dynamics is given in terms of abelian functions the flow becomes linear on a prym variety corresponding to a spectral curve the approach is also applied to the billiard problem in the interior of ann dimensional ellipsoid

assessing the lifetime performance index of products with the exponential distribution under progressively type ii right censored samples in practice lifetime performance index c l is used to measure the potential and performance of a process where l is the lower specification limit progressive censoring scheme is quite useful in many practical situations where budget constraints are in place or there is a demand for rapid testing in this paper under the assumption of exponential distribution this study constructs a maximum likelihood estimator mle of c l based on the progressively type ii right censored sample the mle of c l is then utilized to develop the hypothesis testing procedure in the condition of known l the new testing procedure can be employed by product managers to assess whether the lifetime of products or items adheres to the required level in the condition of known l finally we give one example to illustrate the use of the testing algorithmic procedure under given significance level

variational integrators and the newmark algorithm for conservative and dissipative mechanical systems the purpose of this work is twofold first we demonstrate analytically that the classical newmark family as well as related integration algorithms are variational in the sense of the veselov formulation of discrete mechanics such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior this analytical result is veried through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well second we develop algorithms for mechanical systems with forcing and in particular for dissipative systems in this case we develop integrators that are based on a discretization of the lagrange d alembert principle as well as on a variational formulation of dissipation it is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run

geometric integrators and nonholonomic mechanics a geometric derivation of nonholonomic integrators is developed it is based in the classical technique of generating functions adapted to the special features of nonholonomic systems the theoretical methodology and the integrators obtained are different from those obtained in cortes and martinez nonholonomic integrators nonlinearity 14 1365 1392 2001 in the case of mechanical systems with linear constraints a family of geometric integrators preserving the nonholonomic constraints is given

sparse bayesian learning for the laplace transform inversion in dynamic light scattering a new method is described using the sparse bayesian learning sbl algorithm of tipping to obtain an optimal and reliable solution to the laplace transform inversion in dynamic light scattering dls the linear inverse problem in dls has numerical solutions that depend on their domains and dimensions for a given domain and dimension a sparse solution in an sbl framework is the most probable solution and can be used for classifying a system of objects by a few relevant values recently we have shown that the sbl algorithm of tipping is suitable for studying cataract in ocular lenses by describing the opacity of a lens with a few dominant sizes of crystallin proteins in the lens however since the sparseness of sbl solutions cannot reflect a true system we need to develop a method by using the sbl algorithm to give a true description and at the same time a useful classification of the opacity of lenses we generate a set of sparse solutions of different domains but of the same dimension and then superimpose them to give a general solution with its dimension treated as a regularization parameter an optimal solution which provides a reliable description of a particle system is determined by the l curve criterion for selecting the suitable value of the regularization parameter the performance of our method is evaluated by analyzing simulated data generated from unimodal and bimodal distributions from the reconstructed distributions we see that our method gives high resolution comparable to the sophisticated bryan s maximum entropy algorithm which gives better resolution than contin our method is then applied to experimental dls data of the ocular lenses of a fetal calf and a rhesus monkey to obtain optimal particle size distributions of crystallins and the crystallin aggregates in the lenses we conclude by discussing possible improvements on our method for analyzing dls data and for solving any linear inverse problem by an sbl algorithm

reliability stochastic optimization for a series system with interval component reliability via genetic algorithm this paper deals with chance constraints based reliability stochastic optimization problem in the series system this problem can be formulated as a nonlinear integer programming problem of maximizing the overall system reliability under chance constraints due to resources the assumption of traditional reliability optimization problem is that the reliability of a component is known as a fixed quantity which lies in the open interval 0 1 however in real life situations the reliability of an individual component may vary due to some realistic factors and it is sensible to treat this as a positive imprecise number and this imprecise number is represented by an interval valued number in this work we have formulated the reliability optimization problem as a chance constraints based reliability stochastic optimization problem with interval valued reliabilities of components then the chance constraints of the problem are converted into the equivalent deterministic form the transformed problem has been formulated as an unconstrained integer programming problem with interval coefficients by big m penalty technique then to solve this problem we have developed a real coded genetic algorithm ga for integer variables with tournament selection uniform crossover and one neighborhood mutation to illustrate the model two numerical examples have been solved by our developed ga finally to study the stability of our developed ga with respect to the different ga parameters sensitivity analyses have been done graphically

numerical integration of lie poisson systems while preserving coadjoint orbits and energy in this paper we apply geometric integrators of the rkmk type to the problem of integrating lie poisson systems numerically by using the coadjoint action of the lie group g on the dual lie algebra mbox normalsize mathfrak g to advance the numerical flow we devise methods of arbitrary order that automatically stay on the coadjoint orbits first integrals known as casimirs are retained to machine accuracy by the numerical algorithm within the proposed class of methods we find integrators that also conserve the energy these schemes are implicit and of second order nonlinear iteration in the lie algebra and linear error growth of the global error are discussed numerical experiments with the rigid body and a finite dimensional truncation of the euler equations for a two dimensional 2d incompressible fluid are used to illustrate the properties of the algorithm

inequalities for the median of the gamma distribution we provide several new inequalities involving l n the median of the gamma distribution of order n 1 with parameter 1 among others we present sharp upper and lower bounds for the arithmetic mean of l 1 l 2 l n for all integers n 1 we have an 76 n2 8405h nn email protected email protected k bn 76 n2 8405h nn with the best possible constants email protected k 1 l k k 23 8405k email protected email protected 1 683405 0 0080 here h n denotes the nth harmonic number

a ga based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components in this paper we have considered the problem of constrained redundancy allocation of series system with interval valued reliability of components for maximizing the overall system reliability under limited resource constraints the problem is formulated as an unconstrained integer programming problem with interval coefficients by penalty function technique and solved by an advanced ga for integer variables with interval fitness function tournament selection uniform crossover uniform mutation and elitism as a special case considering the lower and upper bounds of the interval valued reliabilities of the components to be the same the corresponding problem has been solved the model has been illustrated with some numerical examples and the results of the series redundancy allocation problem with fixed value of reliability of the components have been compared with the existing results available in the literature finally sensitivity analyses have been shown graphically to study the stability of our developed ga with respect to the different ga parameters

on estimating the scale parameter of the selected gamma population under the scale invariant squared error loss function let x1 and x2 be two independent random variables representing the populations 1 and 2 respectively and suppose that the random variable xi has a gamma distribution with shape parameter p same for both the populations and unknown scale parameter i i 1 2 define m 1 if x1 x2 m 2 if x2 x1 and j 3 m we consider the component wise estimation of random parameters m and j under the scale invariant squared error loss functions l1 1 1 m 1 2 and l2 2 2 j 1 2 respectively sufficient conditions for the inadmissibility of equivariant estimators of m and j are derived as a consequence various natural estimators are shown to be inadmissible and better estimators are obtained

optimum attributes component test plans for k out of n f weibull systems using prior information abstract assuming that the proportion defective in a production process p is variable and the component lifetimes are weibull distributed integer nonlinear programming problems are formulated and solved in order to determine the optimum component inspection scheme by attributes for k out of n f system reliability demonstration using available prior knowledge a limited beta prior model is adopted to reflect the random fluctuations on p the required quantity of components to test and the permissible number of component failures up to a specified censoring time are found by solving a minimisation problem with nonlinear constraints which are related to the tolerable average producer and consumer risks first order taylor polynomials of the operating characteristic function are used to derive a quite accurate approximate solution lower and upper bounds are also deduced optimal solutions are usually robust to small variations in the weibull parameters and prior information existing technical knowledge and experience are shown to be of great practical value in designing optimal sampling plans for lot acceptance purposes the proposed approach generalises the classical viewpoint to those cases in which appreciable prior information on the fraction of defective systems exists and also allows the analyst to determine the acceptability of a k out of n f system before assembly and to limit the range of p moreover the practitioners may attain substantial savings in sample size and improved assessments of the true producer and consumer risks a 4 out of 5 f system of independent water pumps for cooling a reactor is considered to illustrate the suggested component test plans

improved time censored reliability test plans for k out of n gamma systems abstract relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes the classical viewpoint to the determination of acceptance sampling plans for k out of n gamma systems is generalized to those situations in which the available previous information is appreciable a beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems an integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds first lower and upper bounds as well as an approximate solution are derived then an efficient step by step procedure which finds the best acceptance sampling plan in a finite number of iterations is provided the inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability and also more accurate assessments of the actual producer and consumer risks a system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes

reliability computing method for generalized k out of n system the generalized k out of n f system g k n f consists of n modules ordered in a line or circle the ith module is composed of ni components in parallel ni1 i 1 2 n the g k n f fails if and only if there exist at least f failed components or if there exist at least k consecutive failed modules to evaluate the reliability of g k n f we introduce the concept of a generalized sequence of multivariate bernoulli trials gmvbt and define the bivariate run statistic based on this sequence we bring out the relation between the probability distribution of the bivariate run statistic and the reliability of g k n f we demonstrate the evaluation of reliability of g k n f and some other related systems through a numerical example

finite element analysis of nonsmooth contact this work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis following clarke f h clarke optimization and nonsmooth analysis john wiley and sons new york 1983 we specifically address contact geometries for which both the use of normals and gap functions have difficulties and therefore precludes the application of most contact algorithms proposed to date such situations arise in applications such as fragmentation where angular fragments undergo complex collision sequences before they scatter we demonstrate the robustness and versatility of the nonsmooth contact algorithms developed in this paper with the aid of selected two and three dimensional applications

explicit newmark verlet algorithm for time integration of the rotational dynamics of rigid bodies we reformulate the traditional velocity based vector space newmark algorithm for the rotational dynamics of rigid bodies that is for the setting of the so 3 lie group we show that the most naive re write of the vector space algorithm possesses the properties of symplecticity and almost momentum conservation thus we obtain an explicit algorithm for rigid body dynamics that matches or exceeds performance of existing algorithms but which curiously does not seem to have been considered in the open literature so far copyright 2005 john wiley sons ltd

optimal transportation meshfree approximation schemes for fluid and plastic flows we develop an optimal transportation meshfree otm method for simulating general solid and fluid flows including fluid structure interaction the method combines concepts from optimal transportation theory with material point sampling and max ent meshfree interpolation the proposed otm method generalizes the benamou brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior the otm method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities the otm method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems we illustrate the range and scope of the method by means of two examples of application the bouncing of a gas filled balloon off a rigid wall and the classical taylor anvil benchmark test extended to the hypervelocity range

a bayesian inference approach to identify a robin coefficient in one dimensional parabolic problems this paper investigates a nonlinear inverse problem associated with the heat conduction problem of identifying a robin coefficient from boundary temperature measurement a bayesian inference approach is presented for the solution of this problem the prior modeling is achieved via the markov random field mrf the use of a hierarchical bayesian method for automatic selection of the regularization parameter in the function estimation inverse problem is discussed the markov chain monte carlo mcmc algorithm is used to explore the posterior state space numerical results indicate that mrf provides an effective prior regularization and the bayesian inference approach can provide accurate estimates as well as uncertainty quantification to the solution of the inverse problem

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

a pathway from bayesian statistical analysis to superstatistics abstract superstatistics and tsallis statistics in statistical mechanics are given an interpretation in terms of bayesian statistical analysis subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by mathai s pathway model and further both components are replaced by mathai s pathway models this produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics it is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier those integrals are also connected to kratzel integrals in applied analysis inverse gaussian densities in stochastic processes reaction rate integrals in the theory of nuclear astrophysics and tsallis statistics in nonextensive statistical mechanics the final results are obtained in terms of fox s h function matrix variate analogue of one significant specific case is also pointed out

mechanical integrators derived from a discrete variational principle many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion in this paper we present a procedure to construct time stepping algorithms that approximate the flow of continuous odes for mechanical systems by discretizing hamilton s principle rather than the equations of motion the discrete equations share similarities to the continuous equations by preserving invariants including the symplectic form and the momentum map we first present a formulation of discrete mechanics along with a discrete variational principle we then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of noether s theorem we then use the discrete mechanics formulation to develop a procedure for constructing symplectic momentum mechanical integrators for lagrangian systems with holonomic constraints we apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators