existence and stability of periodic solutions for parabolic systems with time delays this paper is concerned with the existence and stability time periodic solutions for a class of coupled parabolic equations with time delay and time delays may appear in the nonlinear reaction functions the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement our approach to the problem is by the method of upper and lower solution and using schauder fixed point theorem some methods for proving the stability of the periodic solution are also given the results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system finally a model arising from chemistry is used to illustrate the obtained results

sample size formulas for estimating intraclass correlation coefficients with precision and assurance the number of subjects required to estimate the intraclass correlation coefficient in a reliability study has usually been determined on the basis of the expected width of a confidence interval however this approach fails to explicitly consider the probability of achieving the desired interval width and may thus provide sample sizes that are too small to have adequate chance of achieving the desired precision in this paper we present a method that explicitly incorporates a prespecified probability of achieving the prespecified width or lower limit of a confidence interval the resultant closed form formulas are shown to be very accurate copyright 2012 john wiley sons ltd

the effect of random measurement error on receiver operating characteristic roc curves in this paper confidence intervals for the area under the roc curve are adjusted for the presence of measurement error a parametric normal model is assumed the ratio of intra individual to inter individual variance provides a relative measure of the amount of measurement error an exact adjusted confidence interval is developed for the equal variance case and an approximation is derived for the unequal variance case we illustrate using an example the effect of ignoring the measurement error on the confidence interval for the area and show that the effect can be substantial on the decision as to the diagnostic effectiveness of the marker we also examine by means of a simulation study the coverage probability of the unadjusted confidence interval and show that it can be far from its nominal value when measurement error is present

estimation of roc curves based on stably distributed biomarkers subject to measurement error and pooling mixtures additive measurement errors and pooling design are objectively two different issues which have been separately and extensively dealt with in the biostatistics literature however these topics usually correspond to problems of reconstructing a summand s distribution of the biomarker by the distribution of the convoluted observations thus we associate the two issues into one stated problem the integrated approach creates an opportunity to investigate new fields e g a subject of pooling errors issues regarding pooled data affected by measurement errors to be specific we consider the stated problem in the context of the receiver operating characteristic roc curves analysis which is the well accepted tool for evaluating the ability of a biomarker to discriminate between two populations the present paper considers a wide family of biospecimen distributions in addition applied assumptions which are related to distribution functions of biomarkers are mainly conditioned by the reconstructing problem we propose and examine maximum likelihood techniques based on the following data a biomarker with measurement error pooled samples and pooled samples with measurement error the obtained methods are illustrated by applications to real data studies

global existence and asymptotic stability of equilibria to reaction diffusion systems in this paper we study weakly coupled reaction diffusion systems in unbounded domains of or where the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions such systems are more complicated than those in many previous publications and little is known about them a comparison principle and global existence and boundedness theorems for solutions to these systems are established sufficient conditions on the nonlinearities ensuring the positively ljapunov stability of the zero solution with respect to h2 perturbations are also obtained as samples of applications these results are applied to an autocatalytic chemical model and a concrete problem whose nonlinearities are nonquasimonotone our results are novel in particular we present a solution to an open problem posed by escher and yin 2005 j nonlinear anal theory methods appl 60 1065 84

periodic solutions of quasilinear parabolic systems with nonlinear boundary conditions abstract this paper is concerned with the existence of maximal and minimal periodic solutions of a class of quasilinear parabolic systems with nonlinear boundary conditions our approach to the problem is based on the method of upper and lower solutions and its associated monotone iterations an application is also made to the reaction diffusion system of lotka volterra competition model

construction of confidence limits about effect measures a general approach it is widely accepted that confidence interval construction has important advantages over significance testing for the presentation of research results as now facilitated by readily available software however for a number of effect measures procedures are either not available or not satisfactory in samples of small to moderate size in this paper we describe a general approach for estimating a difference between effect measures which can also be used to obtain confidence limits for a risk ratio and a lognormal mean numerical evaluation shows that this closed form procedure outperforms existing methods including the bootstrap

stability and attractivity of periodic solutions of parabolic systems with time delays abstract this paper is concerned with the existence stability and global attractivity of time periodic solutions for a class of coupled parabolic equations in a bounded domain the problem under consideration includes coupled system of parabolic and ordinary differential equations and time delays may appear in the nonlinear reaction functions our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement using schauder fixed point theorem while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme the results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system applications are also given to three lotka volterra reaction diffusion model problems and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions

existence and monotone scheme for time periodic nonquasimonotone reaction diffusion systems application to autocatalytic chemistry abstract the article considers time periodic reaction diffusion systems the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions dirichlet and robin boundary conditions are included the existence of periodic solutions is shown under appropriate conditions monotone approximating sequences closing in on the solutions from above and below are constructed application to autocatalysis in chemistry is given

periodic solutions of parabolic systems with time delays existence of maximal and minimal periodic solutions of a coupled system of parabolic equations with time delays and with nonlinear boundary conditions is discussed the proof of the existence theorem is based on the method of upper and lower solutions and its associated monotone iterations this method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic parabolic system an application is given to a competitor competitor mutualist model which consists of a coupled system of three reaction diffusion equations with time delays

convergence of poroelastic finite elements based on biot displacement formulation the convergence of linear poroelastic elements based on biot displacement formulation is investigated the aim is to determine a mesh criterion that provides reliable results under a given frequency limit the first part deals with 1d applications for which resonance frequencies can be related to biot wavelengths their relative contributions to the motion are given in order to determine if the mesh criteria for monophasic media are suitable for poroelastic media the imposition of six linear elements per wavelength is found for each biot wave as a primary condition for convergence for 3d applications convergence rules are derived from a generic configuration i e a clamped porous layer because of the complex deformation the previous criterion is shown to be insufficient influence of the coupling between the two phases is demonstrated

estimation of the area under the roc curve the area under the receiver operating characteristic curve is frequently used as a measure for the effectiveness of diagnostic markers in this paper we discuss and compare estimation procedures for this area these are based on i the mann whitney statistic ii kernel smoothing iii normal assumptions iv empirical transformations to normality these are compared in terms of bias and root mean square error in a large variety of situations by means of an extensive simulation study overall we find that transforming to normality usually is to be preferred except for bimodal cases where kernel methods can be effective

an efficient finite element scheme for solving the three dimensional poroelasticity problem in acoustics in this paper the finite element method fem is used to solve the three dimensional poroelasticity problem in acoustics based on the isotropic biot allard theory a displacement finite element model is derived using the lagrangian approach together with an analogy with solid elements from this model it is seen that the damping and stiffness matrices of the poroelastic media are complex and frequency dependent this leads to cumbersome calculations for large finite element models and spectral analyses to overcome this difficulty an efficient algorithm is proposed it is based on low frequency approximations of the frequency dependent dissipation mechanisms in poroelastic media this efficient algorithm allows the poroelastic materials to be modeled with classical fem codes also the acoustic poroelastic and the poroelastic poroelastic coupling conditions are presented the proposed model is compared to existing literature for both two dimensional and three dimensional problems excellent compari

efficient modeling of flat and homogeneous acoustic treatments for vibroacoustic finite element analysis direct field formulations abstract this paper is concerned with the development of a simplified model for noise control treatments to speed up finite element analysis in vibroacoustic applications the methodology relies on the assumption that the acoustic treatment is flat and homogeneous moreover its finite lateral extent is neglected this hypothesis is justified by short wavelength and large dissipation which suggest that the reflected field emanating from the acoustic treatment lateral boundaries does not substantially affect its dynamic response under these circumstances the response of the noise control treatment can be formally obtained by means of convolution integrals involving simple analytical kernels i e green functions such fundamental solutions can be computed efficiently by the transfer matrix method however some arbitrariness arises in the formulation of the mathematical model resulting in different baffling conditions at the two ends of the treatment to be considered thus the paper investigates the possibility of different formulations i e baffling conditions within the same hybrid finite element transfer matrix framework seeking for the best strategy in terms of tradeoff between efficiency and accuracy numerical examples are provided to show strengths and limitations of the proposed methodology

measuring the effectiveness of diagnostic markers in the presence of measurement error through the use of roc curves the area under the receiver operating characteristic curve is frequently used to assess the effectiveness of diagnostic markers in distinguishing between diseased and healthy individuals these markers are generally subject to measurement error in this paper confidence intervals for the area under the curve are developed which take measurement error into account these intervals depend on the availability of replicated observations for the subject both equal and unequal numbers of replicates per subject are considered the practice of averaging over replicates and then ignoring measurement error is examined and found wanting

wave properties in poroelastic media using a wave finite element method abstract the application of the bidirectional wave finite element method wfe to biot allard s theory of poroelasticity is investigated this method has been successfully used in previous elastodynamics studies in the case of porous media the rigidity of the layer is very low leading to very small wavelengths and a high dissipation rate occurs within the pores these differences with the elastic case justify a study of their consequences on numerical results in this paper it is shown that despite these difficulties the wfe provides an efficient tool to compute the waves propagating through poroelastic media the influence of boundary conditions on wave propagation is discussed as well as the convergence of the numerical results depending on the spatial discretization the order of shape functions and the choice of the formulation finally the wavenumbers predicted with this method are compared with some simplified models such as equivalent fluid models or equivalent plate models it is shown that the wfe can be used to validate the assumptions made by the simplified models

3d hierarchical hp fem applied to elasto acoustic modelling of layered porous media this paper presents a 3 d hierarchical p version finite element description of the solid displacement fluid displacement form of biot s equation for elasto acoustic modelling of multiple layered isotropic porous media the convergence related to mesh refinement extensions for different orders of polynomial approximation is briefly discussed for a homogeneous foam the highest computational efficiency for reasonable levels of the error in the low frequency region was obtained for fourth order polynomial finite element interpolations the main focus is on coupling conditions and on the convergence of solutions to biot s equations in cases with multiple layers having different material properties simulations of a two layered porous material with low flow resistivity suggest slow convergence rate of the fluid displacement field close to the interface between the layers

the partition of unity finite element method for the simulation of waves in air and poroelastic media recently chazot et al j sound vib 332 1918 1929 2013 applied the partition of unity finite element method for the analysis of interior sound fields with absorbing materials the method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard finite element method the work is however restricted to a certain class of absorbing materials that react like an equivalent fluid this paper presents an extension of the method to the numerical simulation of biot s waves in poroelastic materials the technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations to show the interest of the method for tackling problems of practical interests poroelastic acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested it is shown that the technique is a good candidate for solving noise control problems at medium and high frequency

on positive solutions of the lotka volterra cooperating models with diffusion abstract in this paper using the existence and comparison conclusion for the time periodic quasimonotone nondecreasing systems given by pao c v and iterative method we investigate the time periodic lotka volterra cooperating model and present some existence uniqueness and nonexistence results we also use similar methods to treat the corresponding stationary system to give parallel results

periodic solutions of parabolic systems with nonlinear boundary conditions this paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions the approach to the problem is by the method of upper and lower solutions and its associated monotone iterations this method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial boundary value problems a sufficient condition for the stability of a periodic solution is also given these results are applied to three model problems arising from chemical kinetics ecology and population biology

interval estimation for the area under the receiver operating characteristic curve when data are subject to error the area a under the receiver operating characteristic curve is commonly used to quantify the ability of a biomarker to correctly classify individuals into two populations however many markers are subject to measurement error which must be accounted for to prevent understating their effectiveness in this paper we develop a new confidence interval procedure for a which is adjusted for measurement error using either external or internal replicated measurements based on the observation that a is a function of normal means and variances we develop the procedure by recovering variance estimates needed from confidence limits for normal means and variances simulation results show that the procedure performs better than the previous ones based on the delta method in terms of coverage percentage balance of tail errors and interval width two examples are presented

statistical inference for pr y x the normal case this article examines statistical inference for pr y x where x and y are independent normal variates with unknown means and variances the case of unequal variances is stressed x can be interpreted as the strength of a component subjected to a stress y and pr y x is the component s reliability two approximate methods for obtaining confidence intervals and an approximate bayesian probability interval are obtained the actual coverage probabilities of these intervals are examined by simulation

quasisolutions and dynamics of time periodic nonquasimonotone reaction diffusion systems abstract in this paper using the upper lower solution method we investigate the properties of periodic quasisolutions for time periodic nonquasimonotone reaction diffusion systems and present some existence asymptotic behavior results for two ecological models