factorization properties of finite spaces in 1960 schwinger j schwinger 1960 proc natl acad sci 46 570 9 proposed the algorithm for factorization of unitary operators in the finite m dimensional hilbert space according to a coprime decomposition of m using a special permutation operator a we generalize the schwinger factorization to every decomposition of m we obtain the factorized pairs of unitary operators and show that they obey the same commutation relations as schwinger s we apply the new factorization to two problems first we show how to generate two kq like mutually unbiased bases for any composite dimension then using a harper like hamiltonian model in the finite dimension m m1m2 we show how to design a physical system with m1 energy levels each having degeneracy m2

a three scale offlineonline numerical method for fluid flow in porous media a new multiscale method combined with model order reduction is proposed for flow problems in a three scale porous material we derive an effective three scale model that couples a macroscopic darcy equation a mesoscopic stokesbrinkman equation and a microscopic stokes equation a corresponding three scale numerical method is then derived using the finite element discretization with numerical quadrature where the macroscopic and mesoscopic permeability is upscaled at quadrature points from mesoscopic and microscopic problems respectively the computational cost of solving numerous mesoscopic and microscopic flow problems is further reduced by applying a petrovgalerkin reduced basis method at the mesoscopic and microscopic scales as there is no natural way to obtain an affine decomposition of the mesoscopic problems which is instrumental for the efficiency of the model order reduction we derive a mesoscopic solver that makes use of empirical interpolation techniques a priori and a posteriori error estimates are derived for the new method that is also tested numerically to corroborate the theoretical convergence rates and illustrate its efficiency

estimating coefficient distributions in random coefficient regressions random coefficient regression models are important in representing linear models with heteroscedastic errors and in unifying the study of classical fixed effects and random effects linear models for prediction intervals and for bootstrapping in random coefficient regressions it is necessary to estimate the distributions of the random coefficients consistently we show that this is often possible and provide practical representative estimators of these distributions

multivariate regression models for panel data abstract the paper examines the relationship between heterogeneity bias and strict exogeneity in a distributed lag regression of y on x the relationship is very strong when x is continuous weaker when x is discrete and non existent as the order of the distributed lag becomes infinite the individual specific random variables introduce nonlinearity and heteroskedasticity so the paper provides an appropriate framework for the estimation of multivariate linear predictors restrictions are imposed using a minimum distance estimator it is generally more efficient than the conventional estimators such as quasi maximum likelihood there are computationally simple generalizations of two and three stage least squares that achieve this efficiency gain some of these ideas are illustrated using the sample of young men in the national longitudinal survey the paper reports regressions on the leads and lags of variables measuring union coverage smsa and region the results indicate that the leads and lags could have been generated just by a random intercept this gives some support for analysis of covariance type estimates these estimates indicate a substantial heterogeneity bias in the union smsa and region coefficients

a cbs type stabilizing algorithm for the consolidation of saturated porous media the presented method stems from the works by zienkiewicz and co workers for coupled fluid thermal problems starting from the early 1990s they propose algorithms to overcome the difficulties connected to the application of the fem to the area of fluid mechanics which include the problems of singular behaviour in incompressibility and the problems connected to convective terms the major step forward was to introduce the concept of characteristic lines the particle paths in a simple convection situation for a class of problems with a single scalar variable the equations in the characteristic co ordinates regain self adjointness the procedure is called characteristic based split algorithm cbs we use here a cbs type procedure for a saturated deformable elastic porous medium in which the fluid velocity is governed by darcy s equation which comes directly from navier stokes ones the physical mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains the power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual u p problem into a u v p one where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid respectively attention is focused on the expression of darcy s velocity which is considered as the starting point of the algorithm the accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u p solutions a good fitting among different results has been obtained it is further shown that the procedure eliminates the oscillations at the onset of consolidation typical for many schemes the fem code ed multifield has been used for implementing and testing the procedure copyright 2005 john wiley sons ltd

a hierarchical finite element monte carlo method for stochastic two scale elliptic equations we consider two scale elliptic equations whose coefficients are random in particular we study two cases in the first case the coefficients are obtained from an ergodic dynamical system acting on a probability space and in the second the case the coefficients are periodic in the microscale but are random we suppose that the coefficients also depend on the macroscopic slow variables while the effective coefficient of the ergodic homogenization problem is deterministic to approximate it it is necessary to solve cell equations in a large but finite size truncated cube and compute an approximated effective coefficient from the solution of this equation this approximated effective coefficient is however realization dependent and the deterministic effective coefficient of the homogenization problem can be approximated by taking its expectation in the periodic random setting the effective coefficient for each realization is obtained from the solutions of cell equations which are posed in the unit cube but to compute its average by the monte carlo method we need to consider many uncorrelated realizations to accurately approximate the average straightforward employment of finite element approximation and the monte carlo method to compute this expectation with the same level of finite element resolution and the same number of monte carlo samples at every macroscopic point is prohibitively expensive we develop a hierarchical finite element monte carlo algorithm to approximate the effective coefficients at a dense hierarchical network of macroscopic points the method requires an optimal level of complexity that is essentially equal to that for computing the effective coefficient at one macroscopic point and achieves essentially the same accuracy the levels of accuracy for solving cell problems and for the monte carlo sampling are chosen according to the level in the hierarchy that the macroscopic points belong to solutions and the effective coefficients at the points where the cell problems are solved with higher accuracy and the effective coefficients are approximated with a larger number of monte carlo samples are employed as correctors for the effective coefficient at those points at which the cell problems are solved with lower accuracy and fewer monte carlo samples the method combines the hierarchical finite element method for solving cell problems at a dense network of macroscopic points with the optimal complexity developed in brown etal 2013 with a hierarchical monte carlo sampling algorithm that uses different number of samples at different macroscopic points depending on the level in the hierarchy that the macroscopic points belong to proof of concept numerical examples confirm the theoretical results

conjugate variables in finite phase plane we construct two pairs of quasicoordinates and quasimomenta in a finite phase plane which form sets of conjugate variables in such a plane the coordinate x is quantized with a step c and the momentum p with a step where mc is the size of the phase plane in the x direction the construction depends crucially on the possibility of writing m m1m2 with m1 and m2 relatively prime the conjugate variables are applied to harper like hamiltonians it is shown how to design physical systems with energy spectra containing any desired number of discrete energy levels say m1 each of them having a prescribed degeneracy m2

on the chemical distance for supercritical bernoulli percolation we prove large deviation estimates at the correct order for the graph distance of two sites lying in the same cluster of an independent percolation process we improve earlier results of gartner and molchanov and grimmett and marstrand and answer affirmatively a conjecture of kozlov

darcy equation for random porous media many attempts have been made recently to deduce darcy equations for flows through porous media much has been done for models having a periodic microstructure this paper presents a mathematical analysis based on the more general and more realistic assumption that the microstructure of porous media is random and stochastically homogeneous for this type of random domain we consider homogenization of the poisson and stokes equations supplemented by homogeneous dirichlet boundary conditions on the random boundary with this approach we get the darcy equation in general as well as present details for the particular case of a checkerboard model of porous media 1996 john wiley sons inc

a two scale finite element formulation of stokes flow in porous media seepage through saturated porous material with an open pore system is modeled as a non linear stokes flow through a rigid matrix based on variationally consistent homogenization the resulting macroscale problem becomes a darcy type flow the prolongation of the darcy flow fulfills a macrohomogeneity condition which in a galerkin context implies a symmetric macroscale problem the homogenization is of 1st order and periodic boundary conditions are adopted on a representative volume element a nonlinear nested multiscale technique in which the subscale problem is used as a constitutive model is devised in the presented numerical investigation the effects of varying physical parameters as well as of the discretization are considered in particular it is shown that the two scale results agree well with those of the fully resolved fine scale problem

the triangular model with random coefficients abstract the triangular model is a very popular way to allow for causal inference in the presence of endogeneity in this model an outcome is determined by an endogenous regressor which in turn is first caused by an instrument we study the triangular model with random coefficients and additional exogenous regressors in both equations and establish non identification of the joint distribution of random coefficients this implies that counterfactual outcomes are not identified either non identification continues to hold if we confine ourselves to the joint distribution of coefficients in the outcome equation or indeed any marginal except the one on the endogenous regressor nonidentification prevails as well if we focus on means of random coefficients implying that iv is asymptotically biased based on these insights we derive bounds on the joint distribution of economically relevant functionals e g counterfactual outcomes and suggest an additional restriction that allows to point identify the distribution of random coefficients in the outcome equation we extend the model to cover the case where the regressors and instruments have limited support and analyze semi and nonparametric sample counterpart estimators in finite and large samples and we provide an application to consumer demand

von neumann lattices and magnetic orbitals in finite phase space it is proven that in the finite phase space of dimensionality m the number of independent von neumann states is m r where r is the number of distinct zeros of the kq function when applied to magnetic orbitals this leads to a linear dependence between them for each zero of the corresponding kq function different interesting identities follow from the linear dependence of von neumann states

a reduced basis finite element heterogeneous multiscale method for stokes flow in porous media a reduced basis darcy stokes finite element heterogeneous multiscale method rb ds fe hmm is proposed for the stokes problem in porous media the multiscale method is based on the darcy stokes finite element heterogeneous multiscale method ds fe hmm introduced in abdulle and budac 2015 that couples a darcy equation solved on a macroscopic mesh with missing permeability data extracted from the solutions of stokes micro problems at each macroscopic quadrature point to overcome the increasingly growing cost of repeatedly solving the stokes micro problems as the macroscopic mesh is refined we parametrize the microscopic solid geometry and approximate the infinite dimensional manifold of parameter dependent solutions of stokes problems by a low dimensional space this low dimensional reduced basis space is obtained in an offline stage by a greedy algorithm and used in an online stage to compute the effective darcy permeability at a cost independent of the microscopic mesh the discretization of the parametrized stokes problems relies on a petrov galerkin formulation that allows for a stable and fast online evaluation of the required permeabilities a priori and a posteriori estimates of the rb ds fe hmm are derived and a residual based adaptive algorithm is proposed two and three dimensional numerical experiments confirm the accuracy of the rb ds fe hmm and illustrate the speedup compared to the ds fe hmm c 2016 elsevier b v all rights reserved

identification and estimation of average partial effects in irregular correlated random coefficient panel data models in this paper we study identification and estimation of a correlated random coefficients crc panel data model the outcome of interest varies linearly with a vector of endogenous regressors the coefficients on these regressors are heterogenous across units and may covary with them we consider the average partial effect ape of a small change in the regressor vector on the outcome cf chamberlain 1984 wooldridge 2005a chamberlain 1992 calculated the semiparametric efficiency bound for the ape in our model and proposed a n consistent estimator nonsingularity of the ape s information bound and hence the appropriateness of chamberlain s 1992 estimator requires i the time dimension of the panel t to strictly exceed the number of random coefficients p and ii strong conditions on the time series properties of the regressor vector we demonstrate irregular identification of the ape when t p and for more persistent regressor processes our approach exploits the different identifying content of the subpopulations of stayers or units whose regressor values change little across periods and movers or units whose regressor values change substantially across periods we propose a feasible estimator based on our identification result and characterize its large sample properties while irregularity precludes our estimator from attaining parametric rates of convergence its limiting distribution is normal and inference is straightforward to conduct standard software may be used to compute point estimates and standard errors we use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor nicaraguan households

on nonparametric estimation of intercept and slope distributions in random coefficient regression an experiment records stimulus and response for a random sample of cases the relationship between response and stimulus is thought to be linear the values of the slope and intercept varying by case from such data we construct a consistent asymptotically normal nonparametric estimator for the joint density of the slope and intercept our methodology incorporates the radial projection slice theorem for the radon transform a technique for locally linear nonparametric regression and a tapered fourier inversion computationally the new density estimator is more feasible than competing nonparametric estimators one of which is based on moments and the other on minimum distance considerations

random homogenization and singular perturbations in perforated domains the paper considers the singularly perturbed dirichlet problem u u f in a randomly perforated domain which is obtained from a bounded open set in r n after removing many holes of size q the perforated domain is described in terms of an ergodic dynamical system acting on a probability space imposing certain conditions on the domain the behaviour of u when 0 in lebesgue spaces l n is studied test functions together with the birkhoff ergodic theorem are the main tools of analysis the poisson distribution of holes of size p with the intensity r is then considered the above results apply in some cases other cases are treated by the wiener sausage approach

an entropy satisfying two speed relaxation system for the barotropic euler equations application to the numerical approximation of low mach number flows in the first part of this work we introduce a new relaxation system in order to approximate the solutions to the barotropic euler equations we show that the solutions to this two speed relaxation model can be understood as viscous approximations of the solutions to the barotropic euler equations under appropriate sub characteristic conditions our relaxation system is a generalization of the well known suliciu relaxation system and it is entropy satisfying a godunov type finite volume scheme based on the exact resolution of the riemann problem associated with the relaxation system is deduced as well as its stability properties in the second part of this work we show how the new relaxation approach can be successfully applied to the numerical approximation of low mach number flows we prove that the underlying scheme satisfies the well known asymptotic preserving property in the sense that it is uniformly first order accurate with respect to the mach number and at the same time it satisfies a fully discrete entropy inequality this discrete entropy inequality allows us to prove strong stability properties in the low mach regime at last numerical experiments are given to illustrate the behaviour of our scheme

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

wall laws for fluid flows at a boundary with random roughness the general concern of this paper is the effect of rough boundaries on fluids we consider a stationary flow governed by incompressible navier stokes equations in an infinite domain bounded by two horizontal rough plates the roughness is modeled by a spatially homogeneous random field with characteristic size e a mathematical analysis of the flow for small e is performed the navier s wall law is rigorously deduced from this analysis this substantially extends former results obtained in the case of periodic roughness notably in 16 17 2007 wiley periodicals inc

some asymptotics for multimodality tests based on kernel density estimates a test due to b w silverman for modality of a probability density is based on counting modes of a kernel density estimator and the idea of critical smoothing an asymptotic formula is given for the expected number of modes this together with other methods establishes the rate of convergence of the critically smoothed bandwidth these ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables