periodic solutions for a class of non autonomous second order systems abstract the purpose of this paper is to study the existence of periodic solutions of non autonomous second order systems u t f t u t a e t 0 t u 0 u t u 0 u t 0 some new existence theorems are obtained by the least action principle

error estimation and adaptation for functional outputs in time dependent flow problems the paper presents an adjoint based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations the algorithm is derived for the unsteady euler equations that are discretized for second order accuracy in both space and time and takes into account the effect of dynamic meshes in addition to error due to temporal resolution the formulation also takes into account algebraic error arising from partial convergence of the governing equations at each implicit time step the resulting error distributions are then used to drive adaptation of the temporal resolution and the convergence tolerances for the governing equations at each time step the method is demonstrated in the context of both time integrated and instantaneous functionals and the results are compared against traditional adaptation methods

existence and subharmonicity of solutions for nonlinear non smooth periodic systems with a p laplacian abstract in the present paper we consider the nonlinear periodic systems driven by a vectorial p laplacian with a locally lipschitz nonlinearity some existence multiplicity and subharmonic results are obtained by using non smooth critical point theory

infinitely many nontrivial periodic solutions for damped vibration problems with asymptotically linear terms in this paper we study a class of damped vibration problem with asymptotically quadratic terms at infinity we obtain infinitely many nontrivial periodic solutions by variational method to the best of our knowledge there is no published result focusing on this class of damped vibration problem with asymptotically quadratic terms at infinity

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

existence of periodic solutions for a class of second order p laplacian systems abstract in this paper the existence of periodic solutions are obtained for a class of non autonomous second order p laplacian systems by the least action principle

existence theorems of periodic solutions for a class of damped vibration problems abstract in the present paper we research the following damped vibration problem 1 1 u t g t u t f t u t a e t 0 t u 0 u t u 0 u t 0 where t 0 g l 0 t r g t 0 t g s ds g t 0 and f 0 t r n r the variational principle is given and three existence theorems for periodic solutions are obtained

optimum shape design for unsteady flows with time accurate continuous and discrete adjoint methods this paper presents an adjoint method for the optimal control of unsteady flows the goal is to develop the continuous and discrete unsteady adjoint equations and their corresponding boundary conditions for the time accurate method first this paper presents the complete formulation of the time dependent optimal design problem second we present the time accurate unsteady continuous and discrete adjoint equations third we present results that demonstrate the application of the theory to a two dimensional oscillating airfoil the results are compared with a multipoint approach to illustrate the added benefit of performing full unsteady optimization

the existence of periodic solutions of non autonomous second order hamiltonian systems abstract the purpose of this paper is to study the existence of periodic solutions for a class of non autonomous second order hamiltonian systems some new existence theorems are obtained by using the least action principle and the saddle point theorem

sensitivity analysis of limit cycle oscillations many unsteady problems equilibrate to periodic behavior for these problems the sensitivity of periodic outputs to system parameters are often desired and must be estimated from a finite time span or frequency domain calculation sensitivities computed in the time domain over a finite time span can take excessive time to converge or fail altogether to converge to the periodic value additionally finite span outputs can exhibit local extrema in parameter space which the periodic outputs they approximate do not hindering their use in optimization we derive a theoretical basis for this error and demonstrate it using two examples a van der pol oscillator and vortex shedding from a low reynolds number airfoil we show that output windowing enables the accurate computation of periodic output sensitivities and may allow for decreased simulation time to compute both time averaged outputs and sensitivities we classify two distinct window types long time over a large not necessarily integer number of periods and short time over a small integer number of periods finally from these two classes we investigate several examples of window shape and demonstrate their convergence with window size and error in the period approximation respectively

aeroelastic solutions using the nonlinear frequency domain method in this work both fully implicit time domain and nonlinear frequency domain methods are used to compute aeroelastic solutions in transonic flows specifically flutter boundaries for a two dimensional naca64a010 airfoil are calculated and compared with preexisting numerical results the second order backward difference time accurate scheme will serve as our numerical benchmark when determining the computational efficiency of the nonlinear frequency domain method comparable results between the time domain and nonlinear frequency domain approaches will further justify the nonlinear frequency domain method as an efficient alternative to the study of unsteady periodic problems a temporal resolution study will establish the required number of modes or time steps per period required for unsteady transonic flows

periodic second order superlinear hamiltonian systems abstract we consider periodic solutions for superlinear second order non autonomous dynamical systems including both kinetic and potential terms we study the existence of nontrivial and ground state solutions

a predictive approach to the analysis of designed experiments abstract viewing the analysis of designed experiments as a model selection problem we introduce the use of a predictive bayesian criterion in this context based on the predictive density of a replicate experiment pdre a calibration of the criterion is provided to assist in the model choice the relationships of the proposed criterion to other prevalent criteria such as aic bic and mallows s c p are given an information theoretic criterion based on the pdre s of two competing models is also introduced and compared with the usual f statistic for two nested models examples are given to illustrate the proposed methodology

periodic solutions of second order nonlinear difference systems with φ laplacian a variational approach t periodic solutions of systems of difference equations of the form u n 1 u f n u n h n n z where strictly convex is a homeomorphism of rn onto the ball ba rn or of ba onto rn are considered under various conditions upon f and h the approach is variational 2011 elsevier ltd all rights reserved

sensitivity analysis of unsteady inviscid flow through turbomachinery cascades we present a novel sensitivity analysis for predicting the effect of airfoil shape on the unsteady aerodynamic and aeroacoustic response of turbomachinery blading the nominal steady and unsteady e ow in a cascade of turbomachinery blades is modeled using the steady euler equations and the time linearized euler equations respectively boththesteadyandunsteadyeulerequationsaresolvedusing atwo stepe nite volumelax wendroff discretizationwithmultigrid acceleration wecomputetheunsteady aerodynamicloadsduetoboth incominggusts and plunging motion of the cascade airfoils once the nominal steady and unsteady e ows have been computed a sensitivity analysis is performed using the discrete adjoint equations of the computational e uid dynamics scheme used to discretizetheeulerequations for each objectivefunction e g the amplitude peak of theaeroelastic blade motion theresultingadjointequationsaresolvedusingtheadjointlax wendroffscheme whichisalsoaccelerated using a multigrid technique once the adjoint equations have been solved the computed adjoint variables may be used to compute rapidly the sensitivities of the aeroelastic and aeroacoustic objective functions due to arbitrary changes in geometry the method is computationally efe cient with similar convergence rate histories for both the nominal and the adjoint solutions to demonstrate the utility of the present method we use the sensitivity analysis to redesign the shape of the airfoils of a cascade for increased aeroelastic stability we also redesign the shape of the airfoils of an exit guide vane for reduced downstream radiated noise

a variational finite element method for stationary nonlinear fluid solid interaction we consider the problem of the interaction of a stationary viscous fluid with an elastic solid that undergoes large displacement the fluid is modeled by the stationary incompressible navier stokes equations in an eulerian frame of reference while a lagrangian reference frame and large displacement small strain theory is used for the solid a variational formulation of the problem is developed that ensures satisfaction of continuity of interface tractions and velocities the variational formulation is approximated by a galerkin finite element method yielding a system of nonlinear algebraic equations in unknown fluid velocities and pressures and solid displacements a newton like method is introduced for solution of the discrete system the method employs a modified jacobian that enables decomposition into separate fluid and solid subdomains this domain decomposition avoids possible ill conditioning of the jacobian as well as the need to compute and store geometric coupling terms between fluid and interface shape the capability of the methodology is illustrated by solution of a problem of the flow induced large displacements of an elastic infinite cylinder

assessing differential gene expression with small sample sizes in oligonucleotide arrays using a mean variance model the identification of the genes that are differentially expressed in two sample microarray experiments remains a difficult problem when the number of arrays is very small we discuss the implications of using ordinary t statistics and examine other commonly used variants for oligonucleotide arrays with multiple probes per gene we introduce a simple model relating the mean and variance of expression possibly with gene specific random effects parameter estimates from the model have natural shrinkage properties that guard against inappropriately small variance estimates and the model is used to obtain a differential expression statistic a limiting value to the positive false discovery rate pfdr for ordinary t tests provides motivation for our use of the data structure to improve variance estimates our approach performs well compared to other proposed approaches in terms of the false discovery rate

bayesian variable selection in structured high dimensional covariate spaces with applications in genomics we consider the problem of variable selection in regression modeling in high dimensional spaces where there is known structure among the covariates this is an unconventional variable selection problem for two reasons 1 the dimension of the covariate space is comparable and often much larger than the number of subjects in the study and 2 the covariate space is highly structured and in some cases it is desirable to incorporate this structural information in to the model building process we approach this problem through the bayesian variable selection framework where we assume that the covariates lie on an undirected graph and formulate an ising prior on the model space for incorporating structural information certain computational and statistical problems arise that are unique to such high dimensional structured settings the most interesting being the phenomenon of phase transitions we propose theoretical and computational schemes to mitigate these problems we illustrate our methods on two

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

a bayesian determination of threshold for identifying differentially expressed genes in microarray experiments the original definitions of false discovery rate fdr and false non discovery rate fnr can be understood as the frequentist risks of false rejections and false non rejections respectively conditional on the unknown parameter while the bayesian posterior fdr and posterior fnr are conditioned on the data from a bayesian point of view it seems natural to take into account the uncertainties in both the parameter and the data in this spirit we propose averaging out the frequentist risks of false rejections and false non rejections with respect to some prior distribution of the parameters to obtain the average fdr afdr and average fnr afnr respectively a linear combination of the afdr and afnr called the average bayes error rate aber is considered as an overall risk some useful formulas for the afdr afnr and aber are developed for normal samples with hierarchical mixture priors the idea of finding threshold values by minimizing the aber or controlling the afdr is illustrated using a gene expression data set simulation studies show that the proposed approaches are more powerful and robust than the widely used fdr method

watch your adjoints lack of mesh convergence in inviscid adjoint solutions it has been long known that 2d and 3d inviscid adjoint solutions are generically singular at sharp trailing edges in this paper a concurrent effect is described by which wall boundary values of 2

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

detecting differentially expressed genes in microarrays using bayesian model selection dna microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease the high throughput nature of these arrays where differential expression for thousands of genes can be measured simultaneously creates an enormous wealth of information but also poses a challenge for data analysis because of the large multiple testing problem involved the solution has generally been to focus on optimizing false discovery rates while sacrificing power the drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold we introduce a new method for detecting differentially expressed genes based on a high dimensional model selection technique bayesian anova for microarrays bam which strikes a balance between false rejections and false nonrejections the basis of the new approach involves a weighted average of generalized ridge

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

spectral element method in time for rapidly actuated systems in this paper the spectral element se method is applied in time to find the entire time periodic or transient solution of time dependent differential equations the time periodic solution is computed by enforcing periodicity of the element set of particular interest are periodic forcing functions possessing high frequency content to maintain the spectral accuracy for such forcing functions an h refinement scheme is employed near the semi discontinuity without increasing the number of degrees of freedom time discretization by spectral elements is applied initially to a standard form of a set of linear first order differential equations subject to harmonic excitation and an excitation admitting rapid variation other case studies include the application of the se approach to parabolic and hyperbolic partial differential equations the first order form of these equations is obtained through semi discretization using conventional finite element spectral element and finite difference schemes element clustering h refinement is applied to maintain the high accuracy and efficiency in the region of the forcing function admitting rapid variation the convergence in time of the method is demonstrated in some cases machine precision is obtained with 25 degrees of freedom per cycle finally the method is applied to a weakly nonlinear problem with time periodic solution to demonstrate its future applicability to the analysis of limit cycle oscillations in aeroelastic systems

algorithm developments for discrete adjoint methods this paper presents a number of algorithm developments for adjoint methods using the discrete approach in which the discretisation of the non linear equations is linearised and the resulting matrix is then transposed with a new iterative procedure for solving the adjoint equations exact numerical equivalence is maintained between the linear and adjoint discretisations the incorporation of strong boundary conditions within the discrete approach is discussed as well as a new application of adjoint methods to linear unsteady flow in turbomachinery

multipoint and multi objective aerodynamic shape optimization a newton krylov algorithm is presented for the aerodynamic optimization of singleand multi element airfoil configurations the flow is governed by the compressible navier stokes equations in conjunction with a one equation turbulence model the preconditioned generalized minimum residual method is applied to solve the discreteadjoint equation leading to a fast computation of accurate objective function gradients optimization constraints are enforced through a penalty formulation and the resulting unconstrained problem is solved via a quasi newton method design examples include lift enhancement and multi point lift constrained drag minimization problems furthermore the new algorithm is used to compute a pareto front for a multi objective problem and the results are validated using a genetic algorithm overall the new algorithm provides an ecient and robust approach for addressing the issues of complex aerodynamic

time dependent adjoint based optimization for coupled fluid structure problems a formulation for sensitivity analysis of fully coupled time dependent aeroelastic problems is given in this paper both forward sensitivity and adjoint sensitivity formulations are derived that correspond to analogues of the fully coupled non linear aeroelastic analysis problem both sensitivity analysis formulations make use of the same iterative disciplinary solution techniques used for analysis and make use of an analogous coupling strategy the information passed between fluid and structural solvers is dimensionally equivalent in all cases enabling the use of the same data structures for analysis forward and adjoint problems the fully coupled adjoint formulation is then used to perform rotor blade design optimization for a four bladed hart2 rotor in hover conditions started impulsively from rest the effect of time step size and mesh resolution on optimization results is investigated a fully coupled unsteady aeroelastic sensitivity analysis formulation is given forward and adjoint sensitivity formulations are analogues of analysis formulation fluid structure interface information is dimensionally equivalent in all solvers a four bladed hart2 rotor shape is optimized in hover using the adjoint platform the effect of time step size and mesh resolution on optimization results is investigated

unsteady aerodynamic and aeroelastic calculations for wings using euler equations a procedure to solve simultaneously the euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings the euler flow equations are solved by a finite difference scheme with dynamic grids the coupled aeroelastic equations of motion are solved using the linear acceleration method the aeroelastic configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing the unsteady flow calculations are validated with the experiment both for a semi infinite wing and a wall mounted cantilever rectangular wing aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite element method the robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using potential equations are demonstrated

simultaneous single step one shot optimization with unsteady pdes the single step one shot method has proven to be very efficient for pde constrained optimization where the partial differential equation pde is solved by an iterative fixed point solver in this approach the simulation and optimization tasks are performed simultaneously in a single iteration if the pde is unsteady finding an appropriate fixed point iteration is non trivial in this paper we provide a framework that makes the single step one shot method applicable for unsteady pdes that are solved by classical time marching schemes the one shot method is applied to an optimal control problem with unsteady incompressible navier stokes equations that are solved by an industry standard simulation code with the van der pol oscillator as a generic model problem the modified simulation scheme is further improved using adaptive time scales finally numerical results for the advection diffusion equation are presented

singular and discontinuous solutions of the adjoint euler equations this study analyzes the behavior of solutions to the quasi one dimensional and two dimensional adjoint euler equations at singularities including shocks sonic points lines and sharp trailing edg

bayesian selection and clustering of polymorphisms in functionally related genes in epidemiologic studies there is often interest in assessing the relationship between polymorphisms in functionally related genes and a health outcome for each candidate gene single nucleotide polymorphism snp data are collected at a number of locations resulting in a large number of possible genotypes because instabilities can result in analyses that include all the snps dimensionality is typically reduced by conducting single snp analyses or attempting to identify haplotypes this article proposes an alternative bayesian approach for reducing dimensionality a multilevel dirichlet process prior is used for the distribution of the snp specific regression coefficients within genes incorporating a variable selection type mixture structure to allow snps with no effect this structure allows simultaneous selection of important snps and soft clustering of snps having similar impact on the health outcome the methods are illustrated using data from a study of pro and anti inflammatory cytokine polym

periodic non autonomous second order dynamical systems we study the existence of periodic solutions for a second order non autonomous dynamical system we give three sets of hypotheses which guarantee the existence of non constant solutions we were able to weaken the hypotheses considerably from those used previously for such systems we employ a saddle point theorem using linking methods

some existence results on periodic solutions of euler lagrange equations in an orlicz sobolev space setting abstract in this paper we consider the problem of finding periodic solutions of certain euler lagrange equations we employ the direct method of the calculus of variations i e we obtain solutions minimizing certain functional i we give conditions which ensure that i is finitely defined and differentiable on certain subsets of orlicz sobolev spaces w 1 l associated to an n function we show that in some sense it is necessary for the coercivity that the complementary function of satisfy the 2 condition we conclude by discussing conditions for the existence of minima of i

periodic solutions of non autonomous second order systems we obtain an existence theorem of periodic solutions of non autonomous second order systems with classical theorems of variational calculus

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

an adjoint method for shape optimization in unsteady viscous flows a new method for shape optimization for unsteady viscous flows is presented it is based on the continuous adjoint approach using a time accurate method and is capable of handling both inverse and direct objective functions the objective function is minimized or maximized subject to the satisfaction of flow equations the shape of the body is parametrized via a non uniform rational b splines nurbs curve and is updated by using the gradients obtained from solving the flow and adjoint equations a finite element method based on streamline upwind petrov galerkin supg and pressure stabilized petrov galerkin pspg stabilization techniques is used to solve both the flow and adjoint equations the method has been implemented and tested for the design of airfoils based on enhancing its time averaged aerodynamic coefficients interesting shapes are obtained especially when the objective is to produce high performance airfoils the effect of the extent of the window of time integration of flow and adjoint equations on the design process is studied it is found that when the window of time integration is insufficient the gradients are most likely to be erroneous

notes on periodic solutions of subquadratic second order systems some existence theorems are obtained for periodic solutions of the subquadratic second order systems by the minimax methods in critical point theory

method for optimally controlling unsteady shock strength in one dimension this paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation the adjoint system of equations for the unsteady euler system in one dimension is derived and used in an adjoint based solution procedure for the optimal control a novel algorithm is used to satisfy all necessary first order optimality conditions while locally minimizing an appropriate cost functional distributed control solutions with certain physical constraints are calculated for attenuating blast waves similar to those generated by ignition overpressure from the shuttle s solid rocket booster during launch results are presented for attenuating shocks traveling at mach 1 5 and 3 5 down to 85 80 and 75 of the uncontrolled wave s driving pressure the control solutions give insight into the magnitude and location of energy dissipation necessary to decrease a given blast wave s overpressure to a set target level over a given spatial domain while using only as m

bayesian models for gene expression with dna microarray data two of the critical issues that arise when examining dna microarray data are 1 determination of which genes best discriminate among the different types of tissue and 2 characterization of expression patterns in tumor tissues for 1 there are many genes that characterize dna expression and it is of critical importance to try and identify a small set of genes that best discriminate between normal and tumor tissues for 2 it is critical to be able to characterize the dna expression of the normal and tumor tissue samples and develop suitable models that explain patterns of dna expression for these types of tissues toward this goal we propose a novel bayesian model for analyzing dna microarray data and propose a model selection methodology for identifying subsets of genes that show different expression levels between normal and cancer tissues in addition we propose a novel class of hierarchical priors for the parameters that allow us to borrow strength across genes for making inference the pro

periodic solutions for some nonautonomous second order systems some existence theorems are obtained for periodic solutions of nonautonomous second order systems by using the least action principle and the minimax methods

periodic solutions of a class of non autonomous second order systems some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second order systems with a potential which is the sum of a subconvex function and a subquadratic function

on variational methods for a class of damped vibration problems abstract in the present paper the following damped vibration problems 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 and 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 are studied where t 0 0 q l 1 0 t r q t 0 t q s d s a t a i j t is a symmetric n n matrix valued function defined in 0 t with a i j l 0 t for all i j 1 2 n and there exists a positive constant such that a t 2 for all r n and a e t 0 t the variational principles are given and an existence theorem and three multiplicity theorems of periodic solutions are obtained

periodic solutions of nonautonomous second order hamiltonian systems with even typed potentials abstract some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second order hamiltonian systems with even typed potentials by the least action principle and the minimax methods in critical point theory

some existence results on periodic solutions of ordinary p laplacian systems some existence theorems are obtained for periodic solutions of ordinary p laplacian systems by the minimax methods in critical point theory

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

vortical flow computations on swept flexible wings using navier stokes equations a procedure to couple the navier stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of swept flexible wings the navier stokes flow equations are solved by a finite difference scheme with dynamic grids the coupled aeroelastic equations of motion are solved using the linear acceleration method the configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing the calculations are compared with the experiment when available effects of flexibility sweep angle and pitch rate are demonstrated for flows with vortices

periodic solutions of non autonomous second order hamiltonian systems the purpose of this paper is to study the existence of periodic solutions for a class of non autonomous second order hamiltonian system some new existence theorems are obtained by the least action principle

computing stability derivatives and their gradients for aerodynamic shape optimization aerodynamic shape optimization of aircraft configurations often ignores stability considerations to address this a method for the computation of static dynamic and transient aircraft stability derivatives and their sensitivities for use in gradient based optimization is introduced and evaluated computational fluid dynamics in the form of a three dimensional structured grid multiblock flow solver with both euler and reynolds averaged navier stokes equations is used to compute the stability derivatives a time spectral formulation is used to compute an oscillating solution for the configuration of interest from this oscillating solution a series of linear regressions is performed to calculate the various stability derivatives because the solution is time dependent it contains the information required to compute the transient or dot derivatives for the configuration an adjoint method is used to compute the gradients of the stability derivatives of interest enabling gradient based stability co

periodic solutions of second order differential inclusions systems with p laplacian some existence results are obtained for periodic solutions of nonautonomous second order differential inclusions systems with p laplacian

saddle point characterization and multiplicity of periodic solutions of non autonomous second order systems abstract in the present paper the non autonomous second order systems 1 1 u t f t u t a e t 0 t u 0 u t u 0 u t 0 and 1 2 u t t u t f t u t a e t 0 t u 0 u t u 0 u t 0 are studied and a existence result of periodic solutions with saddle point character and two new multiplicity results are obtained

inverse eigenvalue problem of jacobi matrix with mixed data in this paper the inverse eigenvalue problem of reconstructing a jacobi matrix from its eigenvalues its leading principal submatrix and part of the eigenvalues of its submatrix is considered the necessary and sufficient conditions for the existence and uniqueness of the solution are derived furthermore a numerical algorithm and some numerical examples are given

bayesian robust inference for differential gene expression in microarrays with multiple samples summary we consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays because of the many steps involved in the experimental process from hybridization to image analysis cdna microarray data often contain outliers for example an outlying data value could occur because of scratches or dust on the surface imperfections in the glass or imperfections in the array production we develop a robust bayesian hierarchical model for testing for differential expression errors are modeled explicitly using a t distribution which accounts for outliers the model includes an exchangeable prior for the variances which allows different variances for the genes but still shrinks extreme empirical variances our model can be used for testing for differentially expressed genes among multiple samples and it can distinguish between the different possible patterns of differential expression when there are three or more samples parameter estimation is carried out using a novel version of markov chain monte carlo that is appropriate when the model puts mass on subspaces of the full parameter space the method is illustrated using two publicly available gene expression data sets we compare our method to six other baseline and commonly used techniques namely the t test the bonferroni adjusted t test significance analysis of microarrays sam efron s empirical bayes and ebarrays in both its lognormal normal and gamma gamma forms in an experiment with hiv data our method performed better than these alternatives on the basis of between replicate agreement and disagreement

derivatives for time spectral computational fluid dynamics using an automatic differentiation adjoint sensitivities for an oscillating onera m6 wing the sensitivities are shown to be accurate to 8 12 digits and the computational cost of the adjoint computations is shown to scale well up to problems of more than 41 million state variables

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus

multigrid solution of the discrete adjoint for optimization problems on unstructured meshes techniques for the efficient formulation and solution of the discrete adjoint problem for the reynolds averaged navier stokes equations and for the mesh deformation equations are developed for use on unstructured grids in two dimensions an explicit two pass approach is used to construct the second order accurate flow adjoint equations and a defect correction scheme is used to solve the flow adjoint equations employing a line implicit agglomeration multigrid strategy to drive the defect correction scheme a similar line implicit multigrid approach is used to solve the mesh deformation equations as well as the adjoint system of these equations for the flow sensitivity and mesh motion equations the multigrid solver is constructed to be duality preserving delivering similar convergence rates for the primal and dual adjoint problems in both cases these techniques are demonstrated for a viscous turbulent airfoil shape optimization problem

periodic solutions of some non autonomous second order hamiltonian systems abstract in this paper we study the existence of periodic solutions of some non autonomous second order hamiltonian systems u t f t u t a e t 0 t u 0 u t u 0 u t 0 we obtain some new existence theorems by the least action principle